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class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Doppler effect</span> </div> </a> <ul id="toc-Doppler_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cosmic_expansion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cosmic_expansion"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Cosmic expansion</span> </div> </a> <ul id="toc-Cosmic_expansion-sublist" class="vector-toc-list"> <li id="toc-Distinguishing_between_cosmological_and_local_effects" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Distinguishing_between_cosmological_and_local_effects"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Distinguishing between cosmological and local effects</span> </div> </a> <ul id="toc-Distinguishing_between_cosmological_and_local_effects-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Gravitational_redshift" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gravitational_redshift"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Gravitational redshift</span> </div> </a> <ul id="toc-Gravitational_redshift-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Observations_in_astronomy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Observations_in_astronomy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Observations in astronomy</span> </div> </a> <button aria-controls="toc-Observations_in_astronomy-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Observations in astronomy subsection</span> </button> <ul id="toc-Observations_in_astronomy-sublist" class="vector-toc-list"> <li id="toc-Local_observations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Local_observations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Local observations</span> </div> </a> <ul id="toc-Local_observations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Extragalactic_observations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Extragalactic_observations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Extragalactic observations</span> </div> </a> <ul id="toc-Extragalactic_observations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Highest_redshifts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Highest_redshifts"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Highest redshifts</span> </div> </a> <ul id="toc-Highest_redshifts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Redshift_surveys" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Redshift_surveys"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Redshift surveys</span> </div> </a> <ul id="toc-Redshift_surveys-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Effects_from_physical_optics_or_radiative_transfer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Effects_from_physical_optics_or_radiative_transfer"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Effects from physical optics or radiative transfer</span> </div> </a> <ul id="toc-Effects_from_physical_optics_or_radiative_transfer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Blueshift" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Blueshift"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Blueshift</span> </div> </a> <button aria-controls="toc-Blueshift-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Blueshift subsection</span> </button> <ul id="toc-Blueshift-sublist" class="vector-toc-list"> <li id="toc-Doppler_blueshift" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Doppler_blueshift"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Doppler blueshift</span> </div> </a> <ul id="toc-Doppler_blueshift-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gravitational_blueshift" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gravitational_blueshift"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Gravitational blueshift</span> </div> </a> <ul id="toc-Gravitational_blueshift-sublist" class="vector-toc-list"> <li id="toc-Blue_outliers" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Blue_outliers"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2.1</span> <span>Blue outliers</span> </div> </a> <ul id="toc-Blue_outliers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Cosmological_blueshift" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cosmological_blueshift"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Cosmological blueshift</span> </div> </a> <ul id="toc-Cosmological_blueshift-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Sources</span> </div> </a> <button aria-controls="toc-Sources-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Sources subsection</span> </button> <ul id="toc-Sources-sublist" class="vector-toc-list"> <li id="toc-Articles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Articles</span> </div> </a> <ul id="toc-Articles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Books" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Books"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Books</span> </div> </a> <ul id="toc-Books-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Redshift</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 84 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-84" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">84 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Rooiverskuiwing" title="Rooiverskuiwing – Afrikaans" lang="af" hreflang="af" data-title="Rooiverskuiwing" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%86%D8%B2%D9%8A%D8%A7%D8%AD_%D9%86%D8%AD%D9%88_%D8%A7%D9%84%D8%A3%D8%AD%D9%85%D8%B1" title="انزياح نحو الأحمر – Arabic" lang="ar" hreflang="ar" data-title="انزياح نحو الأحمر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Desplazamientu_al_bermeyu" title="Desplazamientu al bermeyu – Asturian" lang="ast" hreflang="ast" data-title="Desplazamientu al bermeyu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Q%C4%B1rm%C4%B1z%C4%B1ya_s%C3%BCr%C3%BC%C5%9Fm%C9%99" title="Qırmızıya sürüşmə – Azerbaijani" lang="az" hreflang="az" data-title="Qırmızıya sürüşmə" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A7%8B%E0%A6%B9%E0%A6%BF%E0%A6%A4_%E0%A6%B8%E0%A6%B0%E0%A6%A3" title="লোহিত সরণ – Bangla" lang="bn" hreflang="bn" data-title="লোহিত সরণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A7%D1%8B%D1%80%D0%B2%D0%BE%D0%BD%D0%B0%D0%B5_%D0%B7%D1%80%D1%83%D1%88%D1%8D%D0%BD%D0%BD%D0%B5" title="Чырвонае зрушэнне – Belarusian" lang="be" hreflang="be" data-title="Чырвонае зрушэнне" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B2%D0%B5%D0%BD%D0%BE_%D0%BE%D1%82%D0%BC%D0%B5%D1%81%D1%82%D0%B2%D0%B0%D0%BD%D0%B5" title="Червено отместване – Bulgarian" lang="bg" hreflang="bg" data-title="Червено отместване" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%91%E0%BD%98%E0%BD%A2%E0%BC%8B%E0%BD%A6%E0%BE%A4%E0%BD%BC%E0%BC%8D" title="དམར་སྤོ། – Tibetan" lang="bo" hreflang="bo" data-title="དམར་སྤོ།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Crveni_pomak" title="Crveni pomak – Bosnian" lang="bs" hreflang="bs" data-title="Crveni pomak" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Despla%C3%A7ament_cap_al_roig" title="Desplaçament cap al roig – Catalan" lang="ca" hreflang="ca" data-title="Desplaçament cap al roig" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%C4%95%D1%80%D0%BB%C4%95_%D1%88%C4%83%D0%B2%C4%83%D0%BD%D1%83" title="Хĕрлĕ шăвăну – Chuvash" lang="cv" hreflang="cv" data-title="Хĕрлĕ шăвăну" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rud%C3%BD_posuv" title="Rudý posuv – Czech" lang="cs" hreflang="cs" data-title="Rudý posuv" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhuddiad" title="Rhuddiad – Welsh" lang="cy" hreflang="cy" data-title="Rhuddiad" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/R%C3%B8dforskydning" title="Rødforskydning – Danish" lang="da" hreflang="da" data-title="Rødforskydning" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Rotverschiebung" title="Rotverschiebung – German" lang="de" hreflang="de" data-title="Rotverschiebung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Punanihe" title="Punanihe – Estonian" lang="et" hreflang="et" data-title="Punanihe" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B5%CF%84%CE%B1%CF%84%CF%8C%CF%80%CE%B9%CF%83%CE%B7_%CF%80%CF%81%CE%BF%CF%82_%CF%84%CE%BF_%CE%B5%CF%81%CF%85%CE%B8%CF%81%CF%8C" title="Μετατόπιση προς το ερυθρό – Greek" lang="el" hreflang="el" data-title="Μετατόπιση προς το ερυθρό" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Corrimiento_al_rojo" title="Corrimiento al rojo – Spanish" lang="es" hreflang="es" data-title="Corrimiento al rojo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ru%C4%9Den%C5%9Dovi%C4%9Do" title="Ruĝenŝoviĝo – Esperanto" lang="eo" hreflang="eo" data-title="Ruĝenŝoviĝo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Gorriranzko_lerrakuntza" title="Gorriranzko lerrakuntza – Basque" lang="eu" hreflang="eu" data-title="Gorriranzko lerrakuntza" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%AA%D9%82%D8%A7%D9%84_%D8%A8%D9%87_%D8%B3%D8%B1%D8%AE" title="انتقال به سرخ – Persian" lang="fa" hreflang="fa" data-title="انتقال به سرخ" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/D%C3%A9calage_vers_le_rouge" title="Décalage vers le rouge – French" lang="fr" hreflang="fr" data-title="Décalage vers le rouge" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Readferskowing" title="Readferskowing – Western Frisian" lang="fy" hreflang="fy" data-title="Readferskowing" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Deargaistri%C3%BA" title="Deargaistriú – Irish" lang="ga" hreflang="ga" data-title="Deargaistriú" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Desprazamento_ao_vermello" title="Desprazamento ao vermello – Galician" lang="gl" hreflang="gl" data-title="Desprazamento ao vermello" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%81%EC%83%89%ED%8E%B8%EC%9D%B4" title="적색편이 – Korean" lang="ko" hreflang="ko" data-title="적색편이" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%A1%D6%80%D5%B4%D5%AB%D6%80_%D5%B7%D5%A5%D5%B2%D5%B8%D6%82%D5%B4" title="Կարմիր շեղում – Armenian" lang="hy" hreflang="hy" data-title="Կարմիր շեղում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%AD%E0%A4%BF%E0%A4%B0%E0%A4%95%E0%A5%8D%E0%A4%A4_%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%AA%E0%A4%A8" title="अभिरक्त विस्थापन – Hindi" lang="hi" hreflang="hi" data-title="अभिरक्त विस्थापन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Crveni_pomak" title="Crveni pomak – Croatian" lang="hr" hreflang="hr" data-title="Crveni pomak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Redesko" title="Redesko – Ido" lang="io" hreflang="io" data-title="Redesko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/Mgbanwe_uhie" title="Mgbanwe uhie – Igbo" lang="ig" hreflang="ig" data-title="Mgbanwe uhie" data-language-autonym="Igbo" data-language-local-name="Igbo" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pergeseran_merah" title="Pergeseran merah – Indonesian" lang="id" hreflang="id" data-title="Pergeseran merah" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Rau%C3%B0vik" title="Rauðvik – Icelandic" lang="is" hreflang="is" data-title="Rauðvik" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spostamento_verso_il_rosso" title="Spostamento verso il rosso – Italian" lang="it" hreflang="it" data-title="Spostamento verso il rosso" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A1%D7%97%D7%94_%D7%9C%D7%90%D7%93%D7%95%D7%9D" title="הסחה לאדום – Hebrew" lang="he" hreflang="he" data-title="הסחה לאדום" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%9A%D1%8A%D1%8B%D0%B7%D1%8B%D0%BB_%D1%82%D0%B5%D0%B1%D0%B8%D1%83%D0%BD%D1%8E_%D1%91%D0%BB%D1%87%D0%B5%D0%BC%D0%B8" title="Къызыл тебиуню ёлчеми – Karachay-Balkar" lang="krc" hreflang="krc" data-title="Къызыл тебиуню ёлчеми" data-language-autonym="Къарачай-малкъар" data-language-local-name="Karachay-Balkar" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AC%E1%83%98%E1%83%97%E1%83%94%E1%83%9A%E1%83%98_%E1%83%AC%E1%83%90%E1%83%9C%E1%83%90%E1%83%AA%E1%83%95%E1%83%9A%E1%83%94%E1%83%91%E1%83%90" title="წითელი წანაცვლება – Georgian" lang="ka" hreflang="ka" data-title="წითელი წანაცვლება" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D1%8B%D0%B7%D1%8B%D0%BB_%D1%8B%D2%93%D1%8B%D1%81%D1%83" title="Қызыл ығысу – Kazakh" lang="kk" hreflang="kk" data-title="Қызыл ығысу" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Msogeo_mwekundu" title="Msogeo mwekundu – Swahili" lang="sw" hreflang="sw" data-title="Msogeo mwekundu" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Motus_ad_rubrum" title="Motus ad rubrum – Latin" lang="la" hreflang="la" data-title="Motus ad rubrum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Sarkan%C4%81_nob%C4%ABde" title="Sarkanā nobīde – Latvian" lang="lv" hreflang="lv" data-title="Sarkanā nobīde" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Routverr%C3%A9cklung" title="Routverrécklung – Luxembourgish" lang="lb" hreflang="lb" data-title="Routverrécklung" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Raudonasis_poslinkis" title="Raudonasis poslinkis – Lithuanian" lang="lt" hreflang="lt" data-title="Raudonasis poslinkis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/V%C3%B6r%C3%B6seltol%C3%B3d%C3%A1s" title="Vöröseltolódás – Hungarian" lang="hu" hreflang="hu" data-title="Vöröseltolódás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A6%D1%80%D0%B2%D0%B5%D0%BD%D0%BE_%D0%BF%D0%BE%D0%BC%D0%B5%D1%81%D1%82%D1%83%D0%B2%D0%B0%D1%9A%D0%B5" title="Црвено поместување – Macedonian" lang="mk" hreflang="mk" data-title="Црвено поместување" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9A%E0%B5%81%E0%B4%B5%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B5%81%E0%B4%A8%E0%B5%80%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%82" title="ചുവപ്പുനീക്കം – Malayalam" lang="ml" hreflang="ml" data-title="ചുവപ്പുനീക്കം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A4%E0%A4%BE%E0%A4%AE%E0%A5%8D%E0%A4%B0%E0%A4%B8%E0%A5%83%E0%A4%A4%E0%A5%80" title="ताम्रसृती – Marathi" lang="mr" hreflang="mr" data-title="ताम्रसृती" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%86%D8%B2%D9%8A%D8%A7%D8%AD_%D8%A7%D8%AD%D9%85%D8%B1" title="انزياح احمر – Egyptian Arabic" lang="arz" hreflang="arz" data-title="انزياح احمر" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Anjakan_merah" title="Anjakan merah – Malay" lang="ms" hreflang="ms" data-title="Anjakan merah" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%94%E1%80%AE%E1%80%9B%E1%80%B1%E1%80%AC%E1%80%84%E1%80%BA%E1%80%A1%E1%80%9B%E1%80%BD%E1%80%B1%E1%80%B7" title="အနီရောင်အရွေ့ – Burmese" lang="my" hreflang="my" data-title="အနီရောင်အရွေ့" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Roodverschuiving" title="Roodverschuiving – Dutch" lang="nl" hreflang="nl" data-title="Roodverschuiving" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B0%E0%A5%87%E0%A4%A1%E0%A4%B8%E0%A4%BF%E0%A4%AB%E0%A5%8D%E0%A4%9F" title="रेडसिफ्ट – Nepali" lang="ne" hreflang="ne" data-title="रेडसिफ्ट" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%B5%A4%E6%96%B9%E5%81%8F%E7%A7%BB" title="赤方偏移 – Japanese" lang="ja" hreflang="ja" data-title="赤方偏移" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/R%C3%B8dforskyvning" title="Rødforskyvning – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Rødforskyvning" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Raudforskuving" title="Raudforskuving – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Raudforskuving" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Redesko" title="Redesko – Novial" lang="nov" hreflang="nov" data-title="Redesko" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Despla%C3%A7ament_cap_al_roge" title="Desplaçament cap al roge – Occitan" lang="oc" hreflang="oc" data-title="Desplaçament cap al roge" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B3%D9%88%D8%B1_%D8%B1%D9%86%DA%AB_%D8%AA%D9%87_%D9%84%DB%90%DA%96%D8%AF" title="سور رنګ ته لېږد – Pashto" lang="ps" hreflang="ps" data-title="سور رنګ ته لېږد" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przesuni%C4%99cie_ku_czerwieni" title="Przesunięcie ku czerwieni – Polish" lang="pl" hreflang="pl" data-title="Przesunięcie ku czerwieni" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Desvio_para_o_vermelho" title="Desvio para o vermelho – Portuguese" lang="pt" hreflang="pt" data-title="Desvio para o vermelho" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://ro.wikipedia.org/wiki/Deplasare_spre_ro%C8%99u" title="Deplasare spre roșu – Romanian" lang="ro" hreflang="ro" data-title="Deplasare spre roșu" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D1%80%D0%B0%D1%81%D0%BD%D0%BE%D0%B5_%D1%81%D0%BC%D0%B5%D1%89%D0%B5%D0%BD%D0%B8%D0%B5" title="Красное смещение – Russian" lang="ru" hreflang="ru" data-title="Красное смещение" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Redshift" title="Redshift – Albanian" lang="sq" hreflang="sq" data-title="Redshift" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Spustamentu_versu_lu_russu" title="Spustamentu versu lu russu – Sicilian" lang="scn" hreflang="scn" data-title="Spustamentu versu lu russu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Red_shift" title="Red shift – Simple English" lang="en-simple" hreflang="en-simple" data-title="Red shift" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C4%8Cerven%C3%BD_posun" title="Červený posun – Slovak" lang="sk" hreflang="sk" data-title="Červený posun" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Rde%C4%8Di_premik" title="Rdeči premik – Slovenian" lang="sl" hreflang="sl" data-title="Rdeči premik" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%D8%A7%D8%AF%D8%A7%D9%86%DB%8C_%D8%B3%D9%88%D9%88%D8%B1" title="لادانی سوور – Central Kurdish" lang="ckb" hreflang="ckb" data-title="لادانی سوور" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A6%D1%80%D0%B2%D0%B5%D0%BD%D0%B8_%D0%BF%D0%BE%D0%BC%D0%B0%D0%BA" title="Црвени помак – Serbian" lang="sr" hreflang="sr" data-title="Црвени помак" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Crveni_pomak" title="Crveni pomak – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Crveni pomak" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Punasiirtym%C3%A4" title="Punasiirtymä – Finnish" lang="fi" hreflang="fi" data-title="Punasiirtymä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/R%C3%B6df%C3%B6rskjutning" title="Rödförskjutning – Swedish" lang="sv" hreflang="sv" data-title="Rödförskjutning" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pulangpaglipat" title="Pulangpaglipat – Tagalog" lang="tl" hreflang="tl" data-title="Pulangpaglipat" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Q%C4%B1z%C4%B1l_tayp%C4%B1lma" title="Qızıl taypılma – Tatar" lang="tt" 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Click here for more information."><img alt="Featured article" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443" /></a></span></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Change of wavelength in photons during travel</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the astronomical phenomenon. For other uses, see <a href="/wiki/Redshift_(disambiguation)" class="mw-disambig" title="Redshift (disambiguation)">Redshift (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Redshift.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/170px-Redshift.svg.png" decoding="async" width="170" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/255px-Redshift.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/340px-Redshift.svg.png 2x" data-file-width="300" data-file-height="532" /></a><figcaption><a href="/wiki/Spectral_line" title="Spectral line">Absorption lines</a> in the <a href="/wiki/Visible_spectrum" title="Visible spectrum">visible spectrum</a> of a <a href="/wiki/Supercluster" title="Supercluster">supercluster</a> of distant galaxies (right), as compared to absorption lines in the visible spectrum of the <a href="/wiki/Sun" title="Sun">Sun</a> (left). Arrows indicate redshift. 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/General_relativity" title="General relativity">General relativity</a></th></tr><tr><td class="sidebar-image"><span class="notpageimage" typeof="mw:File"><a href="/wiki/File:Spacetime_lattice_analogy.svg" class="mw-file-description" title="Spacetime curvature schematic"><img alt="Spacetime curvature schematic" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/220px-Spacetime_lattice_analogy.svg.png" decoding="async" width="220" height="82" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/330px-Spacetime_lattice_analogy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Spacetime_lattice_analogy.svg/440px-Spacetime_lattice_analogy.svg.png 2x" data-file-width="1260" data-file-height="469" /></a></span><div class="sidebar-caption" style="padding:0.5em 0.2em 0.6em;border-bottom:1px solid #aaa; display:block;margin-bottom:0.1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Λ</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>κ</mi> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/124ab80fcb17e2733cc17ff6f93da5e52f355c77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.468ex; height:2.843ex;" alt="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}"></span></div></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.75em;"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><div class="hlist"><ul><li><a href="/wiki/History_of_general_relativity" title="History of general relativity">History</a></li><li><a href="/wiki/Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">Timeline</a></li><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Tests</a></li></ul></div></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Fundamental concepts</div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Pseudo-Riemannian_manifold" title="Pseudo-Riemannian manifold">Pseudo-Riemannian manifold</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Phenomena</div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Kepler problem</a></li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">Gravitational lensing</a></li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></li> <li><a href="/wiki/Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li> <li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">Frame-dragging</a></li> <li><a href="/wiki/Geodetic_effect" title="Geodetic effect">Geodetic effect</a></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Singularity</a></li> <li><a href="/wiki/Black_hole" title="Black hole">Black hole</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ececff; font-style:italic;font-weight:normal;"> <a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Spacetime_diagram" title="Spacetime diagram">Spacetime diagrams</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li> <li><a href="/wiki/Wormhole" title="Wormhole">Einstein–Rosen bridge</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>Equations</li><li>Formalisms</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;padding-bottom:0;margin-bottom:0;"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Equations</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mathisson%E2%80%93Papapetrou%E2%80%93Dixon_equations" title="Mathisson–Papapetrou–Dixon equations">Mathisson–Papapetrou–Dixon</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Formalisms</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;"> Advanced theory</th></tr><tr><td class="sidebar-content" style="padding-top:0;"> <ul><li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Interior_Schwarzschild_metric" title="Interior Schwarzschild metric">interior</a>)</li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li> <li><a href="/wiki/Einstein%E2%80%93Rosen_metric" title="Einstein–Rosen metric">Einstein–Rosen waves</a></li> <li><a href="/wiki/Wormhole" title="Wormhole">Wormhole</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a></li> <li><a href="/wiki/Kerr%E2%80%93Newman%E2%80%93de%E2%80%93Sitter_metric" title="Kerr–Newman–de–Sitter metric">Kerr–Newman–de Sitter</a></li> <li><a href="/wiki/Kasner_metric" title="Kasner metric">Kasner</a></li> <li><a href="/wiki/Lema%C3%AEtre%E2%80%93Tolman_metric" title="Lemaître–Tolman metric">Lemaître–Tolman</a></li> <li><a href="/wiki/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li> <li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Robertson–Walker</a></li> <li><a href="/wiki/Oppenheimer%E2%80%93Snyder_model" title="Oppenheimer–Snyder model">Oppenheimer–Snyder</a></li> <li><a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Weyl%E2%80%93Lewis%E2%80%93Papapetrou_coordinates" title="Weyl–Lewis–Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Hartle%E2%80%93Thorne_metric" title="Hartle–Thorne metric">Hartle–Thorne</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Scientists</div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Karl_Schwarzschild" title="Karl Schwarzschild">Schwarzschild</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Hans_Reissner" title="Hans Reissner">Reissner</a></li> <li><a href="/wiki/Gunnar_Nordstr%C3%B6m" title="Gunnar Nordström">Nordström</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/J._Robert_Oppenheimer" title="J. Robert Oppenheimer">Oppenheimer</a></li> <li><a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Gödel</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/James_M._Bardeen" title="James M. Bardeen">Bardeen</a></li> <li><a href="/wiki/Arthur_Geoffrey_Walker" title="Arthur Geoffrey Walker">Walker</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Amal_Kumar_Raychaudhuri" title="Amal Kumar Raychaudhuri">Raychaudhuri</a></li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Taylor</a></li> <li><a href="/wiki/Russell_Alan_Hulse" title="Russell Alan Hulse">Hulse</a></li> <li><a href="/wiki/Willem_Jacob_van_Stockum" title="Willem Jacob van Stockum">van Stockum</a></li> <li><a href="/wiki/Abraham_H._Taub" title="Abraham H. 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nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Physical_cosmology" title="Physical cosmology">Physical cosmology</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:WMAP_2012.png" class="mw-file-description"><img alt="Full-sky image derived from nine years' WMAP data" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/WMAP_2012.png/220px-WMAP_2012.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/WMAP_2012.png/330px-WMAP_2012.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/WMAP_2012.png/440px-WMAP_2012.png 2x" data-file-width="4096" data-file-height="2048" /></a></span></td></tr><tr><td class="sidebar-above" style="border:0;font-weight:normal; display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> <b>·</b> <a href="/wiki/Universe" title="Universe">Universe</a></li> <li><a href="/wiki/Age_of_the_universe" title="Age of the universe">Age of the universe</a></li> <li><a href="/wiki/Chronology_of_the_universe" title="Chronology of the universe">Chronology of the universe</a></li></ul></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Early universe</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Cosmic_inflation" title="Cosmic inflation">Inflation</a> <b>·</b> <a href="/wiki/Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Nucleosynthesis</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Backgrounds</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Gravitational_wave_background" title="Gravitational wave background">Gravitational wave (GWB)</a></li> <li><a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">Microwave (CMB)</a> <b>·</b> <a href="/wiki/Cosmic_neutrino_background" title="Cosmic neutrino background">Neutrino (CNB)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Expansion <b>·</b> Future</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a> <b>·</b> <a class="mw-selflink selflink">Redshift</a></li> <li><a href="/wiki/Expansion_of_the_universe" title="Expansion of the universe">Expansion of the universe</a></li> <li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW metric</a> <b>·</b> <a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a></li> <li><a href="/wiki/Inhomogeneous_cosmology" title="Inhomogeneous cosmology">Inhomogeneous cosmology</a></li> <li><a href="/wiki/Future_of_an_expanding_universe" title="Future of an expanding universe">Future of an expanding universe</a></li> <li><a href="/wiki/Ultimate_fate_of_the_universe" title="Ultimate fate of the universe">Ultimate fate of the universe</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Components <b>·</b> Structure</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Components</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a></li> <li><a href="/wiki/Dark_energy" title="Dark energy">Dark energy</a> <b>·</b> <a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-weight:normal;font-style:italic;"> Structure</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></li> <li><a href="/wiki/Galaxy_filament" title="Galaxy filament">Galaxy filament</a> <b>·</b> <a href="/wiki/Galaxy_formation_and_evolution" title="Galaxy formation and evolution">Galaxy formation</a></li> <li><a href="/wiki/Large_quasar_group" title="Large quasar group">Large quasar group</a></li> <li><a href="/wiki/Observable_universe#Large-scale_structure" title="Observable universe">Large-scale structure</a></li> <li><a href="/wiki/Reionization" title="Reionization">Reionization</a> <b>·</b> <a href="/wiki/Structure_formation" title="Structure formation">Structure formation</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)"><a href="/wiki/Observational_cosmology" title="Observational cosmology">Experiments</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Black_Hole_Initiative" title="Black Hole Initiative">Black Hole Initiative (BHI)</a></li> <li><a href="/wiki/BOOMERanG_experiment" title="BOOMERanG experiment">BOOMERanG</a></li> <li><a href="/wiki/Cosmic_Background_Explorer" title="Cosmic Background Explorer">Cosmic Background Explorer (COBE)</a></li> <li><a href="/wiki/Dark_Energy_Survey" title="Dark Energy Survey">Dark Energy Survey</a></li> <li><a href="/wiki/Planck_(spacecraft)" title="Planck (spacecraft)">Planck space observatory</a></li> <li><a href="/wiki/Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">Sloan Digital Sky Survey (SDSS)</a></li> <li><a href="/wiki/2dF_Galaxy_Redshift_Survey" title="2dF Galaxy Redshift Survey">2dF Galaxy Redshift Survey ("2dF")</a></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><a href="/wiki/Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">Wilkinson Microwave Anisotropy<br />Probe (WMAP)</a></div></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist" style="padding:0 0.9em;"> <ul><li><a href="/wiki/Marc_Aaronson" title="Marc Aaronson">Aaronson</a></li> <li><a href="/wiki/Hannes_Alfv%C3%A9n" title="Hannes Alfvén">Alfvén</a></li> <li><a href="/wiki/Ralph_Alpher" title="Ralph Alpher">Alpher</a></li> <li><a href="/wiki/Nicolaus_Copernicus" title="Nicolaus Copernicus">Copernicus</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Robert_H._Dicke" title="Robert H. Dicke">Dicke</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/George_F._R._Ellis" title="George F. R. Ellis">Ellis</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/George_Gamow" title="George Gamow">Gamow</a></li> <li><a href="/wiki/Alan_Guth" title="Alan Guth">Guth</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Hubble</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/John_C._Mather" title="John C. Mather">Mather</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Arno_Allan_Penzias" title="Arno Allan Penzias">Penzias</a></li> <li><a href="/wiki/Vera_Rubin" title="Vera Rubin">Rubin</a></li> <li><a href="/wiki/Brian_Schmidt" title="Brian Schmidt">Schmidt</a></li> <li><a href="/wiki/George_Smoot" title="George Smoot">Smoot</a></li> <li><a href="/wiki/Nicholas_B._Suntzeff" title="Nicholas B. Suntzeff">Suntzeff</a></li> <li><a href="/wiki/Rashid_Sunyaev" title="Rashid Sunyaev">Sunyaev</a></li> <li><a href="/wiki/Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li> <li><a href="/wiki/Robert_Woodrow_Wilson" title="Robert Woodrow Wilson">Wilson</a></li> <li><a href="/wiki/Yakov_Zeldovich" title="Yakov Zeldovich">Zeldovich</a></li></ul> </div> <ul><li><a href="/wiki/List_of_cosmologists" title="List of cosmologists">List of cosmologists</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddd8e7;text-align:center;;color: var(--color-base)"><a href="/wiki/Physical_cosmology#Subject_history" title="Physical cosmology">Subject history</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Discovery of cosmic microwave<br />background radiation</a></div></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">History of the Big Bang theory</a></li> <li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">Timeline of cosmological theories</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="display:block;margin-top:0.4em; line-height:1.6em;padding-bottom:0.5em;"> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Physical_cosmology" title="Category:Physical cosmology">Category</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/16px-Crab_Nebula.jpg" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/24px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/32px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">Astronomy portal</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Physical_cosmology" title="Template:Physical 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href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></th></tr><tr><td class="sidebar-image"><span class="notpageimage" typeof="mw:File"><a href="/wiki/File:World_line.svg" class="mw-file-description" title="The world line: a diagrammatic representation of spacetime"><img alt="The world line: a diagrammatic representation of spacetime" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/200px-World_line.svg.png" decoding="async" width="200" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/400px-World_line.svg.png 2x" data-file-width="481" data-file-height="491" /></a></span></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.6em;"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a></li> <li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li> <li><a href="/wiki/Formulations_of_special_relativity" title="Formulations of special relativity">Formulations</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">Foundations</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Postulates_of_special_relativity" title="Postulates of special relativity">Einstein's postulates</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">Consequences</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence</a></li> <li><a href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">Relativistic disk</a></li> <li><a href="/wiki/Bell%27s_spaceship_paradox" title="Bell's spaceship paradox">Bell's spaceship paradox</a></li> <li><a href="/wiki/Ehrenfest_paradox" title="Ehrenfest paradox">Ehrenfest paradox</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Spacetime diagram</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%"><a href="/wiki/Dynamics_(mechanics)" class="mw-redirect" title="Dynamics (mechanics)">Dynamics</a></span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Invariant_mass" title="Invariant mass">Proper mass</a></li> <li><a href="/wiki/Four-momentum" title="Four-momentum">Four-momentum</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist" style="font-size:110%;"><ul><li><a href="/wiki/History_of_special_relativity" title="History of special relativity">History</a></li><li>Precursors</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a></li> <li><a href="/wiki/Aether_theories" title="Aether theories">Aether theories</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">People</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"><div class="hlist"> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/Albert_A._Michelson" title="Albert A. Michelson">Michelson</a></li> <li><a href="/wiki/Edward_W._Morley" title="Edward W. Morley">Morley</a></li> <li><a href="/wiki/George_Francis_FitzGerald" title="George Francis FitzGerald">FitzGerald</a></li> <li><a href="/wiki/Gustav_Herglotz" title="Gustav Herglotz">Herglotz</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Minkowski</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Max_Abraham" title="Max Abraham">Abraham</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">von Laue</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Special_relativity" title="Category:Special relativity">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Special_relativity_sidebar" title="Template:Special relativity sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Special_relativity_sidebar" title="Template talk:Special relativity sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Special_relativity_sidebar" title="Special:EditPage/Template:Special relativity sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Physics" title="Physics">physics</a>, a <b>redshift</b> is an increase in the <a href="/wiki/Wavelength" title="Wavelength">wavelength</a>, and corresponding decrease in the <a href="/wiki/Frequency" title="Frequency">frequency</a> and <a href="/wiki/Photon_energy" title="Photon energy">photon energy</a>, of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> (such as <a href="/wiki/Light" title="Light">light</a>). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a <a href="#Blueshift">blueshift</a>, or negative redshift. The terms derive from the colours <a href="/wiki/Red" title="Red">red</a> and <a href="/wiki/Blue" title="Blue">blue</a> which form the extremes of the <a href="/wiki/Visible_spectrum" title="Visible spectrum">visible light spectrum</a>. The main causes of electromagnetic redshift in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> and <a href="/wiki/Cosmology" title="Cosmology">cosmology</a> are the relative motions of radiation sources, which give rise to the <a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">relativistic Doppler effect</a>, and gravitational potentials, which <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">gravitationally redshift</a> escaping radiation. All sufficiently distant light sources show <a href="/wiki/Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">cosmological redshift</a> corresponding to recession speeds proportional to their distances from Earth, a fact known as <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a> that implies the <a href="/wiki/Expansion_of_the_universe" title="Expansion of the universe">universe is expanding</a>. </p><p>All redshifts can be understood under the umbrella of <a href="/wiki/Frame_of_reference" title="Frame of reference">frame transformation laws</a>. <a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a>, which also travel at <a href="/wiki/Speed_of_light" title="Speed of light">the speed of light</a>, are subject to the same redshift phenomena.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The value of a redshift is often denoted by the letter <span class="texhtml"><i>z</i></span>, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio <span class="texhtml">1 + <i>z</i></span> (which is greater than 1 for redshifts and less than 1 for blueshifts). </p><p>Examples of strong redshifting are a <a href="/wiki/Gamma_ray" title="Gamma ray">gamma ray</a> perceived as an <a href="/wiki/X-ray" title="X-ray">X-ray</a>, or initially visible light perceived as <a href="/wiki/Radio_wave" title="Radio wave">radio waves</a>. Subtler redshifts are seen in the <a href="/wiki/Astronomical_spectroscopy" title="Astronomical spectroscopy">spectroscopic</a> observations of <a href="/wiki/Astronomical" class="mw-redirect" title="Astronomical">astronomical</a> objects, and are used in terrestrial technologies such as <a href="/wiki/Doppler_radar" title="Doppler radar">Doppler radar</a> and <a href="/wiki/Radar_gun" class="mw-redirect" title="Radar gun">radar guns</a>. </p><p>Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including <a href="/wiki/Scattering" title="Scattering">scattering</a> and <a href="/wiki/Physical_optics" title="Physical optics">optical effects</a>; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section on <a href="#Effects_from_physical_optics_or_radiative_transfer">physical optics and radiative transfer</a>). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The history of the subject began in the 19th century, with the development of classical <a href="/wiki/Wave" title="Wave">wave</a> mechanics and the exploration of phenomena which are associated with the <a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a>. The effect is named after the <a href="/wiki/Austria" title="Austria">Austrian</a> mathematician, <a href="/wiki/Christian_Doppler" title="Christian Doppler">Christian Doppler</a>, who offered the first known physical explanation for the phenomenon in 1842.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In 1845, the hypothesis was tested and confirmed for <a href="/wiki/Sound_wave" class="mw-redirect" title="Sound wave">sound waves</a> by the <a href="/wiki/Netherlands" title="Netherlands">Dutch</a> scientist <a href="/wiki/C._H._D._Buys_Ballot" title="C. H. D. Buys Ballot">Christophorus Buys Ballot</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that the varying <a href="/wiki/Color" title="Color">colors</a> of <a href="/wiki/Star" title="Star">stars</a> could be attributed to their motion with respect to the Earth.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Before this was verified, it was found that stellar colors were primarily due to a star's <a href="/wiki/Color_temperature" title="Color temperature">temperature</a>, not motion. Only later was Doppler vindicated by verified redshift observations.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup> </p><p>The Doppler redshift was first described by French physicist <a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Hippolyte Fizeau</a> in 1848, who noted the shift in <a href="/wiki/Spectral_line" title="Spectral line">spectral lines</a> seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer <a href="/wiki/William_Huggins" title="William Huggins">William Huggins</a> was the first to determine the velocity of a star moving away from the Earth by the method.<sup id="cite_ref-Huggins_5-0" class="reference"><a href="#cite_note-Huggins-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In 1871, optical redshift was confirmed when the phenomenon was observed in <a href="/wiki/Fraunhofer_lines" title="Fraunhofer lines">Fraunhofer lines</a>, using solar rotation, about 0.1 Å in the red.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> In 1887, Vogel and Scheiner discovered the "annual Doppler effect", the yearly change in the Doppler shift of stars located near the ecliptic, due to the orbital velocity of the Earth.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In 1901, <a href="/wiki/Aristarkh_Belopolsky" title="Aristarkh Belopolsky">Aristarkh Belopolsky</a> verified optical redshift in the laboratory using a system of rotating mirrors.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Arthur Eddington</a> used the term "red-shift" as early as 1923,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> although the word does not appear unhyphenated until about 1934, when <a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">Willem de Sitter</a> used it.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Beginning with observations in 1912, <a href="/wiki/Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> discovered that most <a href="/wiki/Spiral_galaxy" title="Spiral galaxy">spiral galaxies</a>, then mostly thought to be <a href="/wiki/Spiral_galaxy#Spiral_nebula" title="Spiral galaxy">spiral nebulae</a>, had considerable redshifts. Slipher first reported on his measurement in the inaugural volume of the <i><a href="/wiki/Lowell_Observatory" title="Lowell Observatory">Lowell Observatory</a> Bulletin</i>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Three years later, he wrote a review in the journal <i><a href="/wiki/Popular_Astronomy_(US_magazine)" title="Popular Astronomy (US magazine)">Popular Astronomy</a></i>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In it he stated that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well."<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Slipher reported the velocities for 15 spiral nebulae spread across the entire <a href="/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a>, all but three having observable "positive" (that is recessional) velocities. Subsequently, <a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Edwin Hubble</a> discovered an approximate relationship between the redshifts of such "nebulae", and the <a href="/wiki/Distance" title="Distance">distances</a> to them, with the formulation of his eponymous <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Milton_Humason" class="mw-redirect" title="Milton Humason">Milton Humason</a> worked on those observations with Hubble.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> These observations corroborated <a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Alexander Friedmann</a>'s 1922 work, in which he derived the <a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann–Lemaître equations</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> They are now considered to be strong evidence for an <a href="/wiki/Expanding_universe" class="mw-redirect" title="Expanding universe">expanding universe</a> and the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> theory.<sup id="cite_ref-Eddington_18-0" class="reference"><a href="#cite_note-Eddington-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Measurement,_characterization,_and_interpretation"><span id="Measurement.2C_characterization.2C_and_interpretation"></span>Measurement, characterization, and interpretation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=2" title="Edit section: Measurement, characterization, and interpretation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg/220px-High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg" decoding="async" width="220" height="245" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg/330px-High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg/440px-High-redshift_galaxy_candidates_in_the_Hubble_Ultra_Deep_Field_2012.jpg 2x" data-file-width="2400" data-file-height="2670" /></a><figcaption>High-redshift galaxy candidates in the <a href="/wiki/Hubble_Ultra_Deep_Field" class="mw-redirect" title="Hubble Ultra Deep Field">Hubble Ultra Deep Field</a>, 2012<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </figcaption></figure> <p>The <a href="/wiki/Visible_spectrum" title="Visible spectrum">spectrum</a> of light that comes from a source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as <a href="/wiki/Spectral_line" title="Spectral line">absorption lines</a>, <a href="/wiki/Spectral_line" title="Spectral line">emission lines</a>, or other variations in light intensity. If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on Earth. A very common <a href="/wiki/Chemical_element" title="Chemical element">atomic element</a> in space is <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a>. </p><p>The spectrum of originally featureless light shone through hydrogen will show a <a href="/wiki/Hydrogen_spectrum" class="mw-redirect" title="Hydrogen spectrum">signature spectrum</a> specific to hydrogen that has features at regular intervals. If restricted to absorption lines it would look similar to the illustration (top right). If the same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra—but at different wavelengths—then the redshift can be calculated using the table below. </p><p>Determining the redshift of an object in this way requires a frequency or wavelength range. In order to calculate the redshift, one has to know the wavelength of the emitted light in the rest frame of the source: in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require traveling to the distant star of interest, the method using spectral lines described here is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or <a href="/wiki/White_noise" title="White noise">white noise</a> (random fluctuations in a spectrum).<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless quantity</a> called <span class="texhtml"><i>z</i></span>. If <span class="texhtml"><i>λ</i></span> represents wavelength and <span class="texhtml"><i>f</i></span> represents frequency (note, <span class="texhtml"><i>λf</i> = <i>c</i></span> where <span class="texhtml"><i>c</i></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>), then <span class="texhtml"><i>z</i></span> is defined by the equations:<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="margin:auto;"> <caption><b>Calculation of redshift, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span></b> </caption> <tbody><tr> <th><b>Based on wavelength</b></th> <th><b>Based on frequency</b> </th></tr> <tr align="center"> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z={\frac {\lambda _{\mathrm {obsv} }-\lambda _{\mathrm {emit} }}{\lambda _{\mathrm {emit} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mrow> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z={\frac {\lambda _{\mathrm {obsv} }-\lambda _{\mathrm {emit} }}{\lambda _{\mathrm {emit} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a999cd6480ab61dddeeb5372c8037c0d533f2c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.486ex; height:5.843ex;" alt="{\displaystyle z={\frac {\lambda _{\mathrm {obsv} }-\lambda _{\mathrm {emit} }}{\lambda _{\mathrm {emit} }}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z={\frac {f_{\mathrm {emit} }-f_{\mathrm {obsv} }}{f_{\mathrm {obsv} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z={\frac {f_{\mathrm {emit} }-f_{\mathrm {obsv} }}{f_{\mathrm {obsv} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cf28c6ce6fcc3087c62bf506432ce3381236738" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.054ex; height:5.843ex;" alt="{\displaystyle z={\frac {f_{\mathrm {emit} }-f_{\mathrm {obsv} }}{f_{\mathrm {obsv} }}}}"></span> </td></tr> <tr align="center"> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {\lambda _{\mathrm {obsv} }}{\lambda _{\mathrm {emit} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {\lambda _{\mathrm {obsv} }}{\lambda _{\mathrm {emit} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f1dfb8b86273fadf1bd7cbe8b864da69b0915ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.865ex; height:5.843ex;" alt="{\displaystyle 1+z={\frac {\lambda _{\mathrm {obsv} }}{\lambda _{\mathrm {emit} }}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {f_{\mathrm {emit} }}{f_{\mathrm {obsv} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">v</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {f_{\mathrm {emit} }}{f_{\mathrm {obsv} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8747551886d0568e0d61ac980fdc9646872f67a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.649ex; height:5.843ex;" alt="{\displaystyle 1+z={\frac {f_{\mathrm {emit} }}{f_{\mathrm {obsv} }}}}"></span> </td></tr></tbody></table> <p>After <span class="texhtml"><i>z</i></span> is measured, the distinction between redshift and blueshift is simply a matter of whether <span class="texhtml"><i>z</i></span> is positive or negative. For example, <a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a> blueshifts (<span class="texhtml"><i>z</i> < 0</span>) are associated with objects approaching (moving closer to) the observer with the light shifting to greater <a href="/wiki/Energy" title="Energy">energies</a>. Conversely, Doppler effect redshifts (<span class="texhtml"><i>z</i> > 0</span>) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a> as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions. </p> <div class="mw-heading mw-heading2"><h2 id="Redshift_formulae">Redshift formulae</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=3" title="Edit section: Redshift formulae"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of <span class="texhtml"><i>z</i></span>) is independent of the wavelength.<sup id="cite_ref-basicastronomy_22-0" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="max-width:1000px;"> <caption><b>Redshift summary</b> </caption> <tbody><tr> <th>Redshift type</th> <th>Geometry</th> <th>Formula<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <td><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler</a></td> <td><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a><br />(flat spacetime)</td> <td> <p>For motion completely in the radial or<br />line-of-sight direction: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mi>γ</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d13cfbc8e65189ef9324e78d38b21d02045b9e12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:33.137ex; height:9.176ex;" alt="{\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z\approx {\frac {v_{\parallel }}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {v_{\parallel }}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95e407722c57dda3dd2e8a44cd590ddd13599d57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.205ex; height:5.176ex;" alt="{\displaystyle z\approx {\frac {v_{\parallel }}{c}}}"></span>  for small <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\parallel }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\parallel }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fdc28634f42e2cab943bba07f1b6b325a758ee9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.182ex; height:2.509ex;" alt="{\displaystyle v_{\parallel }}"></span></dd></dl> <p><br /> For motion completely in the transverse direction: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2090b5e3bc3d3397e2333b906efdc7de7be8eb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:18.188ex; height:9.343ex;" alt="{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b575800fbc4e47bdab02803747483d261f78f26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.489ex; height:5.176ex;" alt="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}}"></span>  for small <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\perp }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\perp }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f80a8cf80254aa3ef2640555e94986487d5cba0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.638ex; height:2.009ex;" alt="{\displaystyle v_{\perp }}"></span></dd></dl> </td></tr> <tr> <td><a href="/wiki/Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">Cosmological redshift</a></td> <td><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker" class="mw-redirect" title="Friedmann–Lemaître–Robertson–Walker">FLRW spacetime</a><br />(expanding Big Bang universe)</td> <td> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8db63140bbbaa2b19965b212dd79898dde04acf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.685ex; height:5.009ex;" alt="{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}"></span></dd></dl> <p><a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z\approx {\frac {H_{0}D}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>D</mi> </mrow> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {H_{0}D}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b761c1207889db302fda9cd1bb5a9123792f368e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.932ex; height:5.343ex;" alt="{\displaystyle z\approx {\frac {H_{0}D}{c}}}"></span>  for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D\ll {\frac {c}{H_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>≪</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D\ll {\frac {c}{H_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcda9d0b68d5d27ade4d4c2c59643b4a084193a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.36ex; height:5.176ex;" alt="{\displaystyle D\ll {\frac {c}{H_{0}}}}"></span></dd></dl> </td></tr> <tr> <td><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></td> <td>any <a href="/wiki/Stationary_spacetime" title="Stationary spacetime">stationary spacetime</a></td> <td> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>receiver</mtext> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>source</mtext> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebaa9033ebdaf13a0fadfae88aeb8d7e35b59a29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.514ex; height:7.509ex;" alt="{\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}}"></span></dd></dl> <p>For the <a href="/wiki/Schwarzschild_geometry" class="mw-redirect" title="Schwarzschild geometry">Schwarzschild geometry</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>receiver</mtext> </mrow> </msub> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>source</mtext> </mrow> </msub> </mfrac> </mrow> </mrow> </mfrac> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>receiver</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>source</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961eb0e3a1c7c3c22eb1798bdc3d41b353cf34dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:39.887ex; height:10.009ex;" alt="{\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>source</mtext> </mrow> </msub> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>receiver</mtext> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/586969f3a4d4c16a054646159501b843c37544c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.091ex; height:6.176ex;" alt="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)}"></span>  for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\gg r_{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>≫</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\gg r_{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/188b346af97604ae2105ff5dd3871833a4b731f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.004ex; height:2.176ex;" alt="{\displaystyle r\gg r_{S}}"></span></dd></dl> <p>In terms of <a href="/wiki/Escape_velocity" title="Escape velocity">escape velocity</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msubsup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>source</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msubsup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>receiver</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5e3f2277e29aa283a5239ed57475b6d16efbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.915ex; height:5.343ex;" alt="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}}"></span></dd></dl> <p>for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{e}}\ll c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mo>≪</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{e}}\ll c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4435035a4c2319b96d9bb16eb29311886acb28c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.711ex; height:2.176ex;" alt="{\displaystyle v_{\text{e}}\ll c}"></span> </p> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Doppler_effect">Doppler effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=4" title="Edit section: Doppler effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a> and <a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Suzredshift.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Suzredshift.gif/220px-Suzredshift.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Suzredshift.gif/330px-Suzredshift.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Suzredshift.gif/440px-Suzredshift.gif 2x" data-file-width="800" data-file-height="600" /></a><figcaption><a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a>, yellow (~575 <a href="/wiki/Nanometre" title="Nanometre">nm</a> wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turns <a href="/wiki/Orange_(colour)" title="Orange (colour)">orange</a> (redshift to ~585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in color, the object would have to be traveling at approximately 5,200 <a href="/wiki/Metre_per_second" title="Metre per second">km/s</a>, or about 32 times faster than the speed record for the <a href="/wiki/Parker_Solar_Probe" title="Parker Solar Probe">fastest space probe</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Redshift_blueshift.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/220px-Redshift_blueshift.svg.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/330px-Redshift_blueshift.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/440px-Redshift_blueshift.svg.png 2x" data-file-width="800" data-file-height="500" /></a><figcaption>Redshift and blueshift</figcaption></figure> <p>If a source of the light is moving away from an observer, then redshift (<span class="texhtml"><i>z</i> > 0</span>) occurs; if the source moves towards the observer, then <a href="/wiki/Blueshift" class="mw-redirect" title="Blueshift">blueshift</a> (<span class="texhtml"><i>z</i> < 0</span>) occurs. This is true for all electromagnetic waves and is explained by the <a href="/wiki/Doppler_effect" title="Doppler effect">Doppler effect</a>. Consequently, this type of redshift is called the <i>Doppler redshift</i>. If the source moves away from the observer with <a href="/wiki/Velocity" title="Velocity">velocity</a> <span class="texhtml"><i>v</i></span>, which is much less than the speed of light (<span class="texhtml"><i>v</i> ≪ <i>c</i></span>), the redshift is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z\approx {\frac {v}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {v}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebb477fa2d573b6c2c0629fe2d63adf8d871488d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.15ex; height:4.676ex;" alt="{\displaystyle z\approx {\frac {v}{c}}}"></span>     (since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma \approx 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>≈</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma \approx 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fcbd0174b5d1b88845a6b75ee34893bda890f25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.523ex; height:2.676ex;" alt="{\displaystyle \gamma \approx 1}"></span>)</dd></dl> <p>where <span class="texhtml"><i>c</i></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency. </p><p>A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the <a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">relativistic Doppler effect</a>. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the <a href="/wiki/Time_dilation" title="Time dilation">time dilation</a> of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> which can be corrected for by introducing the <a href="/wiki/Lorentz_factor" title="Lorentz factor">Lorentz factor</a> <span class="texhtml"><i>γ</i></span> into the classical Doppler formula as follows (for motion solely in the line of sight): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi>γ</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79c2489cb67179db42f3f7dbc3f60d08ac91a0c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.228ex; height:4.843ex;" alt="{\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma .}"></span></dd></dl> <p>This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the <a href="/wiki/Ives%E2%80%93Stilwell_experiment" title="Ives–Stilwell experiment">Ives–Stilwell experiment</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Since the Lorentz factor is dependent only on the <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a> of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the <a href="/wiki/Scalar_resolute" class="mw-redirect" title="Scalar resolute">projection</a> of the movement of the source into the <a href="/wiki/Line-of-sight_propagation" title="Line-of-sight propagation">line-of-sight</a> which yields different results for different orientations. If <span class="texhtml"><i>θ</i></span> is the angle between the direction of relative motion and the direction of emission in the observer's frame<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>v</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ead26fb14d65657facfb3a6860ee4308a186a98a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.723ex; height:7.009ex;" alt="{\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}"></span></dd></dl> <p>and for motion solely in the line of sight (<span class="texhtml"><i>θ</i> = 0°</span>), this equation reduces to: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\sqrt {\frac {1+v/c}{1-v/c}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\sqrt {\frac {1+v/c}{1-v/c}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c30334b803cfb927650f90f3f866836c50514e53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.649ex; height:7.509ex;" alt="{\displaystyle 1+z={\sqrt {\frac {1+v/c}{1-v/c}}}}"></span></dd></dl> <p>For the special case that the light is moving at <a href="/wiki/Right_angle" title="Right angle">right angle</a> (<span class="texhtml"><i>θ</i> = 90°</span>) to the direction of relative motion in the observer's frame,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> the relativistic redshift is known as the <a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">transverse redshift</a>, and a redshift: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e4094514c80479a19c599ddaeff025509cb6daf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:20.758ex; height:6.509ex;" alt="{\displaystyle 1+z={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}"></span></dd></dl> <p>is measured, even though the object is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cosmic_expansion">Cosmic expansion</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=5" title="Edit section: Cosmic expansion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Expansion_of_the_universe" title="Expansion of the universe">Expansion of the universe</a></div> <p>In the earlier part of the twentieth century, Slipher, Wirtz and others made the first measurements of the redshifts and blueshifts of galaxies beyond the <a href="/wiki/Milky_Way" title="Milky Way">Milky Way</a>. They initially interpreted these redshifts and blueshifts as being due to random motions, but later Lemaître (1927) and Hubble (1929), using previous data, discovered a roughly linear correlation between the increasing redshifts of, and distances to, galaxies. Lemaître realized that these observations could be explained by a mechanism of producing redshifts seen in Friedmann's solutions to <a href="/wiki/Einstein%27s_equations" class="mw-redirect" title="Einstein's equations">Einstein's equations</a> of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. The correlation between redshifts and distances arises in all expanding models.<sup id="cite_ref-Eddington_18-1" class="reference"><a href="#cite_note-Eddington-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>This <a href="/wiki/Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">cosmological redshift</a> is commonly attributed to stretching of the wavelengths of photons propagating through the expanding space. This interpretation can be misleading, however; expanding space is only a choice of <a href="/wiki/Coordinate_conditions" title="Coordinate conditions">coordinates</a> and thus cannot have physical consequences. The cosmological redshift is more naturally interpreted as a Doppler shift arising due to the recession of distant objects.<sup id="cite_ref-Hogg_28-0" class="reference"><a href="#cite_note-Hogg-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>The observational consequences of this effect can be derived using <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">the equations</a> from <a href="/wiki/General_relativity" title="General relativity">general relativity</a> that describe a <a href="/wiki/Cosmological_principle" title="Cosmological principle">homogeneous and isotropic universe</a>. The cosmological redshift can thus be written as a function of <span class="texhtml"><i>a</i></span>, the time-dependent cosmic <a href="/wiki/Scale_factor_(cosmology)" title="Scale factor (cosmology)">scale factor</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8db63140bbbaa2b19965b212dd79898dde04acf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.685ex; height:5.009ex;" alt="{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}"></span></dd></dl> <p>In an expanding universe such as the one we inhabit, the scale factor is <a href="/wiki/Monotonic_function" title="Monotonic function">monotonically increasing</a> as time passes, thus, <span class="texhtml"><i>z</i></span> is positive and distant galaxies appear redshifted. </p><p>Using a model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called <i><a href="/wiki/Cosmic_time" title="Cosmic time">cosmic time</a>–redshift relation</i>. Denote a density ratio as <span class="texhtml">Ω<sub>0</sub></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega _{0}={\frac {\rho }{\rho _{\text{crit}}}}\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>crit</mtext> </mrow> </msub> </mfrac> </mrow> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega _{0}={\frac {\rho }{\rho _{\text{crit}}}}\ ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/365f968094b2ae86425425b1f4b8ce2b174f97ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.8ex; height:5.343ex;" alt="{\displaystyle \Omega _{0}={\frac {\rho }{\rho _{\text{crit}}}}\ ,}"></span></dd></dl> <p>with <span class="texhtml"><i>ρ</i><sub>crit</sub></span> the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space.<sup id="cite_ref-Weinberg_29-0" class="reference"><a href="#cite_note-Weinberg-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> At large redshifts, <span class="texhtml"> <i>1 + z</i> > Ω<sub>0</sub><sup>−1</sup></span>, one finds: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t(z)\approx {\frac {2}{3H_{0}{\Omega _{0}}^{1/2}}}z^{-3/2}\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mrow> <mn>3</mn> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t(z)\approx {\frac {2}{3H_{0}{\Omega _{0}}^{1/2}}}z^{-3/2}\ ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b35f0563369c2ee1555ff73db0fdff6d4f4670b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:23.545ex; height:6.343ex;" alt="{\displaystyle t(z)\approx {\frac {2}{3H_{0}{\Omega _{0}}^{1/2}}}z^{-3/2}\ ,}"></span></dd></dl> <p>where <span class="texhtml"><i>H</i><sub>0</sub></span> is the present-day <a href="/wiki/Hubble_constant" class="mw-redirect" title="Hubble constant">Hubble constant</a>, and <span class="texhtml"><i>z</i></span> is the redshift.<sup id="cite_ref-Bergström_30-0" class="reference"><a href="#cite_note-Bergström-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Longair_31-0" class="reference"><a href="#cite_note-Longair-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters.<sup id="cite_ref-UCLA-2015_32-0" class="reference"><a href="#cite_note-UCLA-2015-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-UCLA-2018_33-0" class="reference"><a href="#cite_note-UCLA-2018-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ICRAR-2022_34-0" class="reference"><a href="#cite_note-ICRAR-2022-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-KEMP-2022_35-0" class="reference"><a href="#cite_note-KEMP-2022-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Distinguishing_between_cosmological_and_local_effects">Distinguishing between cosmological and local effects</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=6" title="Edit section: Distinguishing between cosmological and local effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For cosmological redshifts of <span class="texhtml"><i>z</i> < 0.01</span> additional Doppler redshifts and blueshifts due to the <a href="/wiki/Peculiar_velocity" title="Peculiar velocity">peculiar motions</a> of the galaxies relative to one another cause a wide <a href="/wiki/Variance" title="Variance">scatter</a> from the standard <a href="/wiki/Hubble_Law" class="mw-redirect" title="Hubble Law">Hubble Law</a>.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> The resulting situation can be illustrated by the <a href="/wiki/Expansion_of_the_universe#Other_conceptual_models_of_expansion" title="Expansion of the universe">Expanding Rubber Sheet Universe</a>, a common cosmological analogy used to describe the expansion of the universe. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched.<sup id="cite_ref-Kuhn_37-0" class="reference"><a href="#cite_note-Kuhn-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lewis_38-0" class="reference"><a href="#cite_note-Lewis-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Chodorowski_39-0" class="reference"><a href="#cite_note-Chodorowski-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>The redshifts of galaxies include both a component related to <a href="/wiki/Recessional_velocity" title="Recessional velocity">recessional velocity</a> from expansion of the universe, and a component related to <a href="/wiki/Peculiar_motion" class="mw-redirect" title="Peculiar motion">peculiar motion</a> (Doppler shift).<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity.<sup id="cite_ref-Harrison2_41-0" class="reference"><a href="#cite_note-Harrison2-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Describing the cosmological expansion origin of redshift, cosmologist <a href="/wiki/Edward_Robert_Harrison" title="Edward Robert Harrison">Edward Robert Harrison</a> said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that..."<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a> clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of <span class="texhtml"><i>a</i>(<i>t</i>)</span> [the <a href="/wiki/Scale_factor_(cosmology)" title="Scale factor (cosmology)">scale factor</a>] at the times of emission or absorption, but on the increase of <span class="texhtml"><i>a</i>(<i>t</i>)</span> in the whole period from emission to absorption."<sup id="cite_ref-Weinberg_Cosmology_43-0" class="reference"><a href="#cite_note-Weinberg_Cosmology-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Gravitational_redshift">Gravitational redshift</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=7" title="Edit section: Gravitational redshift"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></div> <p>In the theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, there is time dilation within a gravitational well. This is known as the <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a> or <i>Einstein Shift</i>.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> The theoretical derivation of this effect follows from the <a href="/wiki/Schwarzschild_solution" class="mw-redirect" title="Schwarzschild solution">Schwarzschild solution</a> of the <a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein equations</a> which yields the following formula for redshift associated with a photon traveling in the <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a> of an <a href="/wiki/Electric_charge" title="Electric charge">uncharged</a>, <a href="/wiki/Rotation" title="Rotation">nonrotating</a>, <a href="/wiki/Spherical_symmetry" class="mw-redirect" title="Spherical symmetry">spherically symmetric</a> mass: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>G</mi> <mi>M</mi> </mrow> <mrow> <mi>r</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </msqrt> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32281ba5d64b16f8f2379257d6c1182af6c7481e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:20.676ex; height:8.009ex;" alt="{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}},}"></span></dd></dl> <p>where </p> <ul><li><span class="texhtml"><i>G</i></span> is the <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a>,</li> <li><span class="texhtml"><i>M</i></span> is the <a href="/wiki/Mass" title="Mass">mass</a> of the object creating the gravitational field,</li> <li><span class="texhtml"><i>r</i></span> is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a <a href="/wiki/Schwarzschild_coordinates" title="Schwarzschild coordinates">Schwarzschild coordinate</a>), and</li> <li><span class="texhtml"><i>c</i></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>.</li></ul> <p>This gravitational redshift result can be derived from the assumptions of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> and the <a href="/wiki/Equivalence_principle" title="Equivalence principle">equivalence principle</a>; the full theory of general relativity is not required.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>The effect is very small but measurable on Earth using the <a href="/wiki/M%C3%B6ssbauer_effect" title="Mössbauer effect">Mössbauer effect</a> and was first observed in the <a href="/wiki/Pound%E2%80%93Rebka_experiment" title="Pound–Rebka experiment">Pound–Rebka experiment</a>.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> However, it is significant near a <a href="/wiki/Black_hole" title="Black hole">black hole</a>, and as an object approaches the <a href="/wiki/Event_horizon" title="Event horizon">event horizon</a> the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> radiation (see <a href="/wiki/Sachs%E2%80%93Wolfe_effect" title="Sachs–Wolfe effect">Sachs–Wolfe effect</a>).<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Observations_in_astronomy">Observations in astronomy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=8" title="Edit section: Observations in astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Look-back_time_by_redshift.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Look-back_time_by_redshift.png/220px-Look-back_time_by_redshift.png" decoding="async" width="220" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Look-back_time_by_redshift.png/330px-Look-back_time_by_redshift.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Look-back_time_by_redshift.png/440px-Look-back_time_by_redshift.png 2x" data-file-width="576" data-file-height="455" /></a><figcaption>The <a href="/wiki/Lookback_time" class="mw-redirect" title="Lookback time">lookback time</a> of extragalactic observations by their redshift up to z=20.<sup id="cite_ref-Pilipenko_49-0" class="reference"><a href="#cite_note-Pilipenko-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> There are websites for calculating many such physical measures from redshift.<sup id="cite_ref-UCLA-2015_32-1" class="reference"><a href="#cite_note-UCLA-2015-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-UCLA-2018_33-1" class="reference"><a href="#cite_note-UCLA-2018-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ICRAR-2022_34-1" class="reference"><a href="#cite_note-ICRAR-2022-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-KEMP-2022_35-1" class="reference"><a href="#cite_note-KEMP-2022-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The redshift observed in astronomy can be measured because the <a href="/wiki/Emission_spectrum" title="Emission spectrum">emission</a> and <a href="/wiki/Absorption_spectroscopy" title="Absorption spectroscopy">absorption</a> spectra for <a href="/wiki/Atom" title="Atom">atoms</a> are distinctive and well known, calibrated from <a href="/wiki/Spectroscopic" class="mw-redirect" title="Spectroscopic">spectroscopic</a> experiments in <a href="/wiki/Laboratories" class="mw-redirect" title="Laboratories">laboratories</a> on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, <span class="texhtml"><i>z</i></span> is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by <a href="/wiki/Kinetic_theory_of_gases" title="Kinetic theory of gases">thermal</a> or mechanical <a href="/wiki/Motion" title="Motion">motion</a> of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as <a href="/wiki/Tired_light" title="Tired light">tired light</a> are not generally considered plausible.<sup id="cite_ref-reboul_50-0" class="reference"><a href="#cite_note-reboul-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p><p>Spectroscopy, as a measurement, is considerably more difficult than simple <a href="/wiki/Photometry_(astronomy)" title="Photometry (astronomy)">photometry</a>, which measures the <a href="/wiki/Brightness" title="Brightness">brightness</a> of astronomical objects through certain <a href="/wiki/Optical_filter" title="Optical filter">filters</a>.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> When photometric data is all that is available (for example, the <a href="/wiki/Hubble_Deep_Field" title="Hubble Deep Field">Hubble Deep Field</a> and the <a href="/wiki/Hubble_Ultra_Deep_Field" class="mw-redirect" title="Hubble Ultra Deep Field">Hubble Ultra Deep Field</a>), astronomers rely on a technique for measuring <a href="/wiki/Photometric_redshift" title="Photometric redshift">photometric redshifts</a>.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, <a href="/wiki/Observational_error" title="Observational error">errors</a> for these sorts of measurements can range up to <span class="texhtml">δ<i>z</i> = 0.5</span>, and are much less reliable than spectroscopic determinations.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>However, photometry does at least allow a qualitative characterization of a redshift. For example, if a Sun-like spectrum had a redshift of <span class="texhtml"><i>z</i> = 1</span>, it would be brightest in the <a href="/wiki/Infrared" title="Infrared">infrared</a>(1000nm) rather than at the blue-green(500nm) color associated with the peak of its <a href="/wiki/Black_body" title="Black body">blackbody</a> spectrum, and the light intensity will be reduced in the filter by a factor of four, <span class="texhtml">(1 + <i>z</i>)<sup>2</sup></span>. Both the photon count rate and the photon energy are redshifted. (See <a href="/wiki/K_correction" title="K correction">K correction</a> for more details on the photometric consequences of redshift.)<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Local_observations">Local observations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=9" title="Edit section: Local observations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In nearby objects (within our <a href="/wiki/Milky_Way" title="Milky Way">Milky Way</a> galaxy) observed redshifts are almost always related to the <a href="/wiki/Line-of-sight_propagation" title="Line-of-sight propagation">line-of-sight</a> velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure <a href="/wiki/Velocity" title="Velocity">velocities</a> and parametrize the <a href="/wiki/Mass" title="Mass">masses</a> of the <a href="/wiki/Orbit" title="Orbit">orbiting</a> <a href="/wiki/Star" title="Star">stars</a> in <a href="/wiki/Spectroscopic_binaries" class="mw-redirect" title="Spectroscopic binaries">spectroscopic binaries</a>, a method first employed in 1868 by British astronomer <a href="/wiki/William_Huggins" title="William Huggins">William Huggins</a>.<sup id="cite_ref-Huggins_5-1" class="reference"><a href="#cite_note-Huggins-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to <a href="/wiki/Methods_of_detecting_exoplanets#Radial_velocity" title="Methods of detecting exoplanets">diagnose and measure</a> the presence and characteristics of <a href="/wiki/Exoplanet" title="Exoplanet">planetary systems</a> around other stars and have even made very <a href="/wiki/Rossiter%E2%80%93McLaughlin_effect" title="Rossiter–McLaughlin effect">detailed differential measurements</a> of redshifts during <a href="/wiki/Methods_of_detecting_exoplanets" title="Methods of detecting exoplanets">planetary transits</a> to determine precise orbital parameters.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p>Finely detailed measurements of redshifts are used in <a href="/wiki/Helioseismology" title="Helioseismology">helioseismology</a> to determine the precise movements of the <a href="/wiki/Photosphere" title="Photosphere">photosphere</a> of the <a href="/wiki/Sun" title="Sun">Sun</a>.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> Redshifts have also been used to make the first measurements of the <a href="/wiki/Rotation" title="Rotation">rotation</a> rates of <a href="/wiki/Planet" title="Planet">planets</a>,<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> velocities of <a href="/wiki/Interstellar_cloud" title="Interstellar cloud">interstellar clouds</a>,<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> the <a href="/wiki/Galaxy_rotation_curve" title="Galaxy rotation curve">rotation of galaxies</a>,<sup id="cite_ref-basicastronomy_22-1" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Dynamics_(mechanics)" class="mw-redirect" title="Dynamics (mechanics)">dynamics</a> of <a href="/wiki/Accretion_disk" title="Accretion disk">accretion</a> onto <a href="/wiki/Neutron_star" title="Neutron star">neutron stars</a> and <a href="/wiki/Black_hole" title="Black hole">black holes</a> which exhibit both Doppler and gravitational redshifts.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Temperature" title="Temperature">temperatures</a> of various emitting and absorbing objects can be obtained by measuring <a href="/wiki/Doppler_broadening" title="Doppler broadening">Doppler broadening</a>—effectively redshifts and blueshifts over a single emission or absorption line.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> By measuring the broadening and shifts of the 21-centimeter <a href="/wiki/Hydrogen_line" title="Hydrogen line">hydrogen line</a> in different directions, astronomers have been able to measure the <a href="/wiki/Recessional_velocity" title="Recessional velocity">recessional velocities</a> of <a href="/wiki/Interstellar_gas" class="mw-redirect" title="Interstellar gas">interstellar gas</a>, which in turn reveals the <a href="/wiki/Rotation_curve" class="mw-redirect" title="Rotation curve">rotation curve</a> of our Milky Way.<sup id="cite_ref-basicastronomy_22-2" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Similar measurements have been performed on other galaxies, such as <a href="/wiki/Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda</a>.<sup id="cite_ref-basicastronomy_22-3" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> As a diagnostic tool, redshift measurements are one of the most important <a href="/wiki/Astronomical_spectroscopy" title="Astronomical spectroscopy">spectroscopic measurements</a> made in astronomy. </p> <div class="mw-heading mw-heading3"><h3 id="Extragalactic_observations">Extragalactic observations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=10" title="Edit section: Extragalactic observations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Age_by_redshift.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Age_by_redshift.png/220px-Age_by_redshift.png" decoding="async" width="220" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Age_by_redshift.png/330px-Age_by_redshift.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Age_by_redshift.png/440px-Age_by_redshift.png 2x" data-file-width="580" data-file-height="455" /></a><figcaption>The age of the universe versus redshift from z=5 to 20.<sup id="cite_ref-Pilipenko_49-1" class="reference"><a href="#cite_note-Pilipenko-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The most distant objects exhibit larger redshifts corresponding to the <a href="/wiki/Hubble_flow" class="mw-redirect" title="Hubble flow">Hubble flow</a> of the <a href="/wiki/Universe" title="Universe">universe</a>. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> radiation; the <a href="/wiki/Hubble%27s_law#Redshift_velocity" title="Hubble's law">numerical value of its redshift</a> is about <span class="texhtml"><i>z</i> = 1089</span> (<span class="texhtml"><i>z</i> = 0</span> corresponds to present time), and it shows the state of the universe about 13.8 billion years ago,<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> and 379,000 years after the initial moments of the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a>.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p><p>The luminous point-like cores of <a href="/wiki/Quasar" title="Quasar">quasars</a> were the first "high-redshift" (<span class="texhtml"><i>z</i> > 0.1</span>) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup> </p><p>For galaxies more distant than the <a href="/wiki/Local_Group" title="Local Group">Local Group</a> and the nearby <a href="/wiki/Virgo_Cluster" title="Virgo Cluster">Virgo Cluster</a>, but within a thousand mega<a href="/wiki/Parsec" title="Parsec">parsecs</a> or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by <a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Edwin Hubble</a> and has come to be known as <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a>. <a href="/wiki/Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> was the first to discover galactic redshifts, in about 1912, while Hubble correlated Slipher's measurements with distances he <a href="/wiki/Cosmic_distance_ladder" title="Cosmic distance ladder">measured by other means</a> to formulate his Law.<sup id="cite_ref-Peebles-1993_63-0" class="reference"><a href="#cite_note-Peebles-1993-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> Hubble's law follows in part from the <a href="/wiki/Copernican_principle" title="Copernican principle">Copernican principle</a>.<sup id="cite_ref-Peebles-1993_63-1" class="reference"><a href="#cite_note-Peebles-1993-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> Because it is usually not known how <a href="/wiki/Luminosity" title="Luminosity">luminous</a> objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup> </p><p><a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">Gravitational</a> interactions of galaxies with each other and clusters cause a significant <a href="/wiki/Variance" title="Variance">scatter</a> in the normal plot of the Hubble diagram. The <a href="/wiki/Peculiar_velocity" title="Peculiar velocity">peculiar velocities</a> associated with galaxies superimpose a rough trace of the <a href="/wiki/Mass" title="Mass">mass</a> of <a href="/wiki/Virial_theorem" title="Virial theorem">virialized objects</a> in the universe. This effect leads to such phenomena as nearby galaxies (such as the <a href="/wiki/Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a>) exhibiting blueshifts as we fall towards a common <a href="/wiki/Barycenter" class="mw-redirect" title="Barycenter">barycenter</a>, and redshift maps of clusters showing a <a href="/wiki/Fingers_of_god" class="mw-redirect" title="Fingers of god">fingers of god</a> effect due to the scatter of peculiar velocities in a roughly spherical distribution.<sup id="cite_ref-Peebles-1993_63-2" class="reference"><a href="#cite_note-Peebles-1993-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> This added component gives cosmologists a chance to measure the masses of objects independent of the <a href="/wiki/Mass-to-light_ratio" title="Mass-to-light ratio">mass-to-light ratio</a> (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a>.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (March 2023)">page needed</span></a></i>]</sup> </p><p>The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup> </p><p>While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, observations beginning in 1988 of the redshift-distance relationship using <a href="/wiki/Type_Ia_supernova" title="Type Ia supernova">Type Ia supernovae</a> have suggested that in comparatively recent times the expansion rate of the universe has <a href="/wiki/Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">begun to accelerate</a>.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Highest_redshifts">Highest redshifts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=11" title="Edit section: Highest redshifts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_the_most_distant_astronomical_objects#List_of_most_distant_objects_by_type" title="List of the most distant astronomical objects">List of most distant objects by type</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Comoving_distance_and_lookback_time_(Planck_2018).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Comoving_distance_and_lookback_time_%28Planck_2018%29.png/400px-Comoving_distance_and_lookback_time_%28Planck_2018%29.png" decoding="async" width="400" height="267" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Comoving_distance_and_lookback_time_%28Planck_2018%29.png/600px-Comoving_distance_and_lookback_time_%28Planck_2018%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Comoving_distance_and_lookback_time_%28Planck_2018%29.png/800px-Comoving_distance_and_lookback_time_%28Planck_2018%29.png 2x" data-file-width="1941" data-file-height="1294" /></a><figcaption><a href="/wiki/Comoving_and_proper_distances" title="Comoving and proper distances">Comoving distance</a> and <a href="/wiki/Lookback_time" class="mw-redirect" title="Lookback time">lookback time</a> for the Planck 2018 cosmology parameters, from redshift 0 to 15, with distance (blue solid line) on the left axis, and time (orange dashed line) on the right. Note that the time that has passed (in giga years) from a given redshift until now is not the same as the distance (in giga light years) light would have traveled from that redshift, due to the expansion of the universe over the intervening period.</figcaption></figure> <p>Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2024)">citation needed</span></a></i>]</sup> The most reliable redshifts are from <a href="/wiki/Spectroscopic" class="mw-redirect" title="Spectroscopic">spectroscopic</a> data,<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2024)">citation needed</span></a></i>]</sup> and the highest-confirmed spectroscopic redshift of a galaxy is that of <a href="/wiki/JADES-GS-z14-0" title="JADES-GS-z14-0">JADES-GS-z14-0</a> with a redshift of <span class="texhtml"><i>z</i> = 14.32</span>, corresponding to 290 million years after the Big Bang.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> The previous record was held by <a href="/wiki/GN-z11" title="GN-z11">GN-z11</a>,<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> with a redshift of <span class="texhtml"><i>z</i> = 11.1</span>, corresponding to 400 million years after the Big Bang, and by <a href="/wiki/UDFy-38135539" title="UDFy-38135539">UDFy-38135539</a><sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> at a redshift of <span class="texhtml"><i>z</i> = 8.6</span>, corresponding to 600 million years after the Big Bang. </p><p>Slightly less reliable are <a href="/wiki/Lyman-break_galaxy" title="Lyman-break galaxy">Lyman-break</a> redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift <span class="texhtml"><i>z</i> = 7.5</span><sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> and the next highest being <span class="texhtml"><i>z</i> = 7.0</span>.<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> The most distant-observed <a href="/wiki/Gamma-ray_burst" title="Gamma-ray burst">gamma-ray burst</a> with a spectroscopic redshift measurement was <a href="/wiki/GRB_090423" title="GRB 090423">GRB 090423</a>, which had a redshift of <span class="texhtml"><i>z</i> = 8.2</span>.<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> The most distant-known quasar, <a href="/wiki/ULAS_J1342%2B0928" title="ULAS J1342+0928">ULAS J1342+0928</a>, is at <span class="texhtml"><i>z</i> = 7.54</span>.<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Nature-2018-01_74-0" class="reference"><a href="#cite_note-Nature-2018-01-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> The highest-known redshift radio galaxy (TGSS1530) is at a redshift <span class="texhtml"><i>z</i> = 5.72</span><sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at <span class="texhtml"><i>z</i> = 6.42</span>.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> </p><p><i>Extremely red objects</i> (EROs) are <a href="/wiki/Radio_astronomy#Astronomical_sources" title="Radio astronomy">astronomical sources</a> of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> Objects that are even redder than EROs are termed <i>hyper extremely red objects</i> (HEROs).<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> has a redshift of <span class="texhtml">z = 1089</span>, corresponding to an age of approximately 379,000 years after the Big Bang and a <a href="/wiki/Comoving_and_proper_distances" title="Comoving and proper distances">proper distance</a> of more than 46 billion light-years.<sup id="cite_ref-ly93_79-0" class="reference"><a href="#cite_note-ly93-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> The yet-to-be-observed first light from the oldest <a href="/wiki/Population_III_stars" class="mw-redirect" title="Population III stars">Population III stars</a>, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of <span class="texhtml">20 < <i>z</i> < 100</span>.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> Other high-redshift events predicted by physics but not presently observable are the <a href="/wiki/Cosmic_neutrino_background" title="Cosmic neutrino background">cosmic neutrino background</a> from about two seconds after the Big Bang (and a redshift in excess of <span class="texhtml"><i>z</i> > 10<sup>10</sup></span>)<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> and the cosmic <a href="/wiki/Gravitational_wave_background" title="Gravitational wave background">gravitational wave background</a> emitted directly from <a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">inflation</a> at a redshift in excess of <span class="texhtml"><i>z</i> > 10<sup>25</sup></span>.<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> </p><p>In June 2015, astronomers reported evidence for <a href="/wiki/Stellar_population#Population_III_stars" title="Stellar population">Population III stars</a> in the <a href="/wiki/Cosmos_Redshift_7" title="Cosmos Redshift 7">Cosmos Redshift 7</a> <a href="/wiki/Galaxy" title="Galaxy">galaxy</a> at <span class="texhtml"><i>z</i> = 6.60</span>. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of <a href="/wiki/Chemical_element" title="Chemical element">chemical elements</a> heavier than <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> that are needed for the later formation of <a href="/wiki/Planet" title="Planet">planets</a> and <a href="/wiki/Life" title="Life">life</a> as we know it.<sup id="cite_ref-AJ-20150604_83-0" class="reference"><a href="#cite_note-AJ-20150604-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-NYT-20150617_84-0" class="reference"><a href="#cite_note-NYT-20150617-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Redshift_surveys">Redshift surveys</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=12" title="Edit section: Redshift surveys"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:2dfgrs.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/2dfgrs.png/220px-2dfgrs.png" decoding="async" width="220" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/2dfgrs.png/330px-2dfgrs.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/2dfgrs.png/440px-2dfgrs.png 2x" data-file-width="900" data-file-height="529" /></a><figcaption>Rendering of the 2dFGRS data</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Redshift_survey" title="Redshift survey">Redshift survey</a></div> <p>With advent of automated <a href="/wiki/Telescope" title="Telescope">telescopes</a> and improvements in <a href="/wiki/Astronomical_spectroscopy" title="Astronomical spectroscopy">spectroscopes</a>, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the <a href="/wiki/Observable_universe" title="Observable universe">large-scale structure</a> of the universe. The <a href="/wiki/CfA2_Great_Wall" title="CfA2 Great Wall">Great Wall</a>, a vast <a href="/wiki/Supercluster" title="Supercluster">supercluster</a> of galaxies over 500 million <a href="/wiki/Light-year" title="Light-year">light-years</a> wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup> </p><p>The first redshift survey was the <a href="/wiki/CfA_Redshift_Survey" title="CfA Redshift Survey">CfA Redshift Survey</a>, started in 1977 with the initial data collection completed in 1982.<sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> More recently, the <a href="/wiki/2dF_Galaxy_Redshift_Survey" title="2dF Galaxy Redshift Survey">2dF Galaxy Redshift Survey</a> determined the large-scale structure of one section of the universe, measuring redshifts for over 220,000 galaxies; data collection was completed in 2002, and the final <a href="/wiki/Data_set" title="Data set">data set</a> was released 30 June 2003.<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">Sloan Digital Sky Survey</a> (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects.<sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup> SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection of <a href="/wiki/Quasar" title="Quasar">quasars</a> beyond <span class="texhtml"><i>z</i> = 6</span>. The <a href="/wiki/DEEP2_Redshift_Survey" title="DEEP2 Redshift Survey">DEEP2 Redshift Survey</a> uses the <a href="/wiki/Keck_telescopes" class="mw-redirect" title="Keck telescopes">Keck telescopes</a> with the new "DEIMOS" <a href="/wiki/Spectrograph" class="mw-redirect" title="Spectrograph">spectrograph</a>; a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a high-redshift complement to SDSS and 2dF.<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Effects_from_physical_optics_or_radiative_transfer">Effects from physical optics or radiative transfer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=13" title="Edit section: Effects from physical optics or radiative transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The interactions and phenomena summarized in the subjects of <a href="/wiki/Radiative_transfer" title="Radiative transfer">radiative transfer</a> and <a href="/wiki/Physical_optics" title="Physical optics">physical optics</a> can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases, the shifts correspond to a physical energy transfer to matter or other photons rather than being by a transformation between reference frames. Such shifts can be from such physical phenomena as <a href="/wiki/Wolf_effect" title="Wolf effect">coherence effects</a> or the <a href="/wiki/Scattering" title="Scattering">scattering</a> of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> whether from <a href="/wiki/Electric_charge" title="Electric charge">charged</a> <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a>, from <a href="/wiki/Particulates" title="Particulates">particulates</a>, or from fluctuations of the <a href="/wiki/Index_of_refraction" class="mw-redirect" title="Index of refraction">index of refraction</a> in a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> medium as occurs in the radio phenomenon of <a href="/wiki/Whistler_(radio)" title="Whistler (radio)">radio whistlers</a>.<sup id="cite_ref-basicastronomy_22-4" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the <a href="#Redshift_formulae">effects discussed above</a>.<sup id="cite_ref-basicastronomy_22-5" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>In many circumstances scattering causes radiation to redden because <a href="/wiki/Entropy" title="Entropy">entropy</a> results in the predominance of many low-<a href="/wiki/Energy" title="Energy">energy</a> photons over few high-energy ones (while <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conserving total energy</a>).<sup id="cite_ref-basicastronomy_22-6" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated <span class="texhtml"><i>z</i></span> is generally a <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a> of wavelength. Furthermore, scattering from <a href="/wiki/Randomness" title="Randomness">random</a> <a href="/wiki/Matter" title="Matter">media</a> generally occurs at many <a href="/wiki/Angle" title="Angle">angles</a>, and <span class="texhtml"><i>z</i></span> is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of <a href="/wiki/Spectral_line" title="Spectral line">spectral lines</a> as well.<sup id="cite_ref-basicastronomy_22-7" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Interstellar_medium" title="Interstellar medium">interstellar astronomy</a>, <a href="/wiki/Visible_spectrum" title="Visible spectrum">visible spectra</a> can appear redder due to scattering processes in a phenomenon referred to as <a href="/wiki/Interstellar_reddening" class="mw-redirect" title="Interstellar reddening">interstellar reddening</a><sup id="cite_ref-basicastronomy_22-8" class="reference"><a href="#cite_note-basicastronomy-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>—similarly <a href="/wiki/Rayleigh_scattering" title="Rayleigh scattering">Rayleigh scattering</a> causes the <a href="/wiki/Atmosphere_of_Earth" title="Atmosphere of Earth">atmospheric</a> reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from red<i>shift</i>ing because the <a href="/wiki/Spectroscopic" class="mw-redirect" title="Spectroscopic">spectroscopic</a> lines are not shifted to other wavelengths in reddened objects and there is an additional <a href="/wiki/Extinction_(astronomy)" title="Extinction (astronomy)">dimming</a> and distortion associated with the phenomenon due to photons being scattered in and out of the <a href="/wiki/Line-of-sight_propagation" title="Line-of-sight propagation">line of sight</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Blueshift">Blueshift</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=14" title="Edit section: Blueshift"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Blueshift" redirects here. For the term as used in photochemistry, see <a href="/wiki/Hypsochromic_shift" title="Hypsochromic shift">hypsochromic shift</a>. For the political phenomenon, see <a href="/wiki/Blue_shift_(politics)" title="Blue shift (politics)">blue shift (politics)</a>. For other uses of "blueshift" or "blue shift", see <a href="/wiki/Blueshift_(disambiguation)" class="mw-disambig" title="Blueshift (disambiguation)">Blueshift (disambiguation)</a>.</div> <p>The opposite of a redshift is a <b>blueshift</b>. A blueshift is any decrease in <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> (increase in <a href="/wiki/Energy" title="Energy">energy</a>), with a corresponding increase in frequency, of an <a href="/wiki/Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic wave</a>. In <a href="/wiki/Light" title="Light">visible light</a>, this shifts a color towards the blue end of the spectrum. </p> <div class="mw-heading mw-heading3"><h3 id="Doppler_blueshift">Doppler blueshift</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=15" title="Edit section: Doppler blueshift"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Redshift_blueshift.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/220px-Redshift_blueshift.svg.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/330px-Redshift_blueshift.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Redshift_blueshift.svg/440px-Redshift_blueshift.svg.png 2x" data-file-width="800" data-file-height="500" /></a><figcaption>Doppler redshift and blueshift</figcaption></figure> <p><a href="/wiki/Doppler_effect" title="Doppler effect">Doppler</a> blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside the <a href="/wiki/Visible_spectrum" title="Visible spectrum">visible spectrum</a>. Only objects moving at near-<a href="/wiki/Relativistic_speed" title="Relativistic speed">relativistic speeds</a> toward the observer are noticeably bluer to the <a href="/wiki/Naked_eye" title="Naked eye">naked eye</a>, but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.<sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup> </p><p>Doppler blueshift is used in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> to determine relative motion: </p> <ul><li>The <a href="/wiki/Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a> is moving toward our own <a href="/wiki/Milky_Way" title="Milky Way">Milky Way</a> <a href="/wiki/Galaxy" title="Galaxy">galaxy</a> within the <a href="/wiki/Local_Group" title="Local Group">Local Group</a>; thus, when observed from Earth, its light is undergoing a blueshift.<sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup></li> <li>Components of a <a href="/wiki/Binary_star" title="Binary star">binary star</a> system will be blueshifted when moving towards Earth</li> <li>When observing spiral galaxies, the side spinning toward us will have a slight blueshift <i>relative to</i> the side spinning away from us (see <a href="/wiki/Tully%E2%80%93Fisher_relation" title="Tully–Fisher relation">Tully–Fisher relation</a>).</li> <li><a href="/wiki/Blazar" title="Blazar">Blazars</a> are known to propel <a href="/wiki/Relativistic_jet" class="mw-redirect" title="Relativistic jet">relativistic jets</a> toward us, emitting <a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">synchrotron radiation</a> and <a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">bremsstrahlung</a> that appears blueshifted.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup></li> <li>Nearby stars such as <a href="/wiki/Barnard%27s_Star" title="Barnard's Star">Barnard's Star</a> are moving toward us, resulting in a very small blueshift.</li> <li>Doppler blueshift of distant objects with a high <i>z</i> can be subtracted from the much larger <a href="/wiki/Hubble%27s_law" title="Hubble's law">cosmological redshift</a> to determine relative motion in the <a href="/wiki/Metric_expansion_of_space" class="mw-redirect" title="Metric expansion of space">expanding universe</a>.<sup id="cite_ref-Aoki2005_92-0" class="reference"><a href="#cite_note-Aoki2005-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Gravitational_blueshift">Gravitational blueshift</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=16" title="Edit section: Gravitational blueshift"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gravitional_well.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Gravitional_well.jpg/220px-Gravitional_well.jpg" decoding="async" width="220" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Gravitional_well.jpg/330px-Gravitional_well.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Gravitional_well.jpg/440px-Gravitional_well.jpg 2x" data-file-width="796" data-file-height="462" /></a><figcaption><a href="/wiki/Matter_waves" class="mw-redirect" title="Matter waves">Matter waves</a> (protons, electrons, photons, etc.) falling into a <a href="/wiki/Gravity_well" class="mw-redirect" title="Gravity well">gravity well</a> become more energetic and undergo observer-independent blueshifting.</figcaption></figure> <p>Unlike the <i>relative</i> Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift is <i>absolute</i> and does not depend on the received angle of the photon: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.<sup id="cite_ref-R.N_1_93-0" class="reference"><a href="#cite_note-R.N_1-93"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-R.N_2_94-0" class="reference"><a href="#cite_note-R.N_2-94"><span class="cite-bracket">[</span>94<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>It is a natural consequence of <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> and <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy equivalence</a>, and was confirmed experimentally in 1959 with the <a href="/wiki/Pound%E2%80%93Rebka_experiment" title="Pound–Rebka experiment">Pound–Rebka experiment</a>. Gravitational blueshift contributes to <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> (CMB) anisotropy via the <a href="/wiki/Sachs%E2%80%93Wolfe_effect" title="Sachs–Wolfe effect">Sachs–Wolfe effect</a>: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of <a href="/wiki/Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a> as it leaves the region.<sup id="cite_ref-Bonometto2002_95-0" class="reference"><a href="#cite_note-Bonometto2002-95"><span class="cite-bracket">[</span>95<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Blue_outliers">Blue outliers</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=17" title="Edit section: Blue outliers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are faraway <a href="/wiki/Active_galaxies" class="mw-redirect" title="Active galaxies">active galaxies</a> that show a blueshift in their <a href="/wiki/Doubly_ionized_oxygen" title="Doubly ionized oxygen">[O III]</a> emission <a href="/wiki/Emission_spectrum" title="Emission spectrum">lines</a>. One of the largest blueshifts is found in the narrow-line <a href="/wiki/Quasar" title="Quasar">quasar</a>, <a href="/wiki/PG_1543%2B489" title="PG 1543+489">PG 1543+489</a>, which has a relative velocity of -1150 km/s.<sup id="cite_ref-Aoki2005_92-1" class="reference"><a href="#cite_note-Aoki2005-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> These types of galaxies are called "blue outliers".<sup id="cite_ref-Aoki2005_92-2" class="reference"><a href="#cite_note-Aoki2005-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cosmological_blueshift">Cosmological blueshift</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=18" title="Edit section: Cosmological blueshift"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a hypothetical universe undergoing a runaway <a href="/wiki/Big_Crunch" title="Big Crunch">Big Crunch</a> contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observed <a href="/wiki/Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">cosmological redshift</a> in the present <a href="/wiki/Expanding_universe" class="mw-redirect" title="Expanding universe">expanding universe</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=19" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Gravitational_potential" title="Gravitational potential">Gravitational potential</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=20" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDing2021" class="citation journal cs1">Ding, Qianhang (August 2021). 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(1999). "On the Curvature of Space". <i><a href="/wiki/General_Relativity_and_Gravitation" title="General Relativity and Gravitation">General Relativity and Gravitation</a></i>. <b>31</b> (12): 1991–2000. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999GReGr..31.1991F">1999GReGr..31.1991F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FA%3A1026751225741">10.1023/A:1026751225741</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122950995">122950995</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=General+Relativity+and+Gravitation&rft.atitle=On+the+Curvature+of+Space&rft.volume=31&rft.issue=12&rft.pages=1991-2000&rft.date=1999&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122950995%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1023%2FA%3A1026751225741&rft_id=info%3Abibcode%2F1999GReGr..31.1991F&rft.aulast=Friedman&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span>)</span> </li> <li id="cite_note-Eddington-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eddington_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eddington_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">This was recognized early on by physicists and astronomers working in cosmology in the 1930s. The earliest layman publication describing the details of this correspondence is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEddington1933" class="citation book cs1"><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington, Arthur</a> (1933). <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.220736"><i>The Expanding Universe: Astronomy's 'Great Debate', 1900–1931</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Expanding+Universe%3A+Astronomy%27s+%27Great+Debate%27%2C+1900%E2%80%931931&rft.pub=Cambridge+University+Press&rft.date=1933&rft.aulast=Eddington&rft.aufirst=Arthur&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.220736&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> (Reprint: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-34976-5" title="Special:BookSources/978-0-521-34976-5">978-0-521-34976-5</a>)</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://esahubble.org/news/heic1219/">"Hubble census finds galaxies at redshifts 9 to 12"</a>. <i>ESA/Hubble Press Release</i><span class="reference-accessdate">. Retrieved <span class="nowrap">13 December</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ESA%2FHubble+Press+Release&rft.atitle=Hubble+census+finds+galaxies+at+redshifts+9+to+12&rft_id=https%3A%2F%2Fesahubble.org%2Fnews%2Fheic1219%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">See, for example, this 25 May 2004 <a rel="nofollow" class="external text" href="https://heasarc.gsfc.nasa.gov/docs/swift/about_swift/redshift.html">press release</a> from <a href="/wiki/NASA" title="NASA">NASA</a>'s <a href="/wiki/Swift_Gamma-Ray_Burst_Mission" class="mw-redirect" title="Swift Gamma-Ray Burst Mission">Swift</a> <a href="/wiki/Space_telescope" title="Space telescope">space telescope</a> that is researching <a href="/wiki/Gamma-ray_burst" title="Gamma-ray burst">gamma-ray bursts</a>: "Measurements of the gamma-ray spectra obtained during the main outburst of the GRB have found little value as redshift indicators, due to the lack of well-defined features. However, optical observations of GRB afterglows have produced spectra with identifiable lines, leading to precise redshift measurements."</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">For a tutorial on how to define and interpret large redshift measurements, see:<br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuchra" class="citation web cs1">Huchra, John. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131222052715/http://ned.ipac.caltech.edu/help/zdef.html">"Extragalactic Redshifts"</a>. <i>NASA/IPAC Extragalactic Database</i>. Harvard-Smithsonian Center for Astrophysics. Archived from <a rel="nofollow" class="external text" href="http://ned.ipac.caltech.edu/help/zdef.html">the original</a> on 2013-12-22<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-03-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NASA%2FIPAC+Extragalactic+Database&rft.atitle=Extragalactic+Redshifts&rft.aulast=Huchra&rft.aufirst=John&rft_id=http%3A%2F%2Fned.ipac.caltech.edu%2Fhelp%2Fzdef.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-basicastronomy-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-basicastronomy_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-basicastronomy_22-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text">See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Where z = redshift; v<sub>||</sub> = <a href="/wiki/Velocity" title="Velocity">velocity</a> parallel to line-of-sight (positive if moving away from receiver); c = <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>; <i>γ</i> = <a href="/wiki/Lorentz_factor" title="Lorentz factor">Lorentz factor</a>; <i>a</i> = <a href="/wiki/Scale_factor_(Universe)" class="mw-redirect" title="Scale factor (Universe)">scale factor</a>; G = <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a>; M = object <a href="/wiki/Mass" title="Mass">mass</a>; r = <a href="/wiki/Schwarzschild_coordinates" title="Schwarzschild coordinates">radial Schwarzschild coordinate</a>, g<sub>tt</sub> = t,t component of the <a href="/wiki/Metric_tensor" title="Metric tensor">metric tensor</a></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIvesStilwell1938" class="citation journal cs1">Ives, H.; Stilwell, G. (1938). "An Experimental study of the rate of a moving atomic clock". <i>Journal of the Optical Society of America</i>. <b>28</b> (7): 215–226. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1938JOSA...28..215I">1938JOSA...28..215I</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2Fjosa.28.000215">10.1364/josa.28.000215</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Optical+Society+of+America&rft.atitle=An+Experimental+study+of+the+rate+of+a+moving+atomic+clock&rft.volume=28&rft.issue=7&rft.pages=215-226&rft.date=1938&rft_id=info%3Adoi%2F10.1364%2Fjosa.28.000215&rft_id=info%3Abibcode%2F1938JOSA...28..215I&rft.aulast=Ives&rft.aufirst=H.&rft.au=Stilwell%2C+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFreund2008" class="citation book cs1">Freund, Jurgen (2008). <i>Special Relativity for Beginners</i>. World Scientific. p. 120. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-277-160-5" title="Special:BookSources/978-981-277-160-5"><bdi>978-981-277-160-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Special+Relativity+for+Beginners&rft.pages=120&rft.pub=World+Scientific&rft.date=2008&rft.isbn=978-981-277-160-5&rft.aulast=Freund&rft.aufirst=Jurgen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDitchburn1961" class="citation book cs1">Ditchburn, R. (1961). <i>Light</i>. Dover. p. 329. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-218101-6" title="Special:BookSources/978-0-12-218101-6"><bdi>978-0-12-218101-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Light&rft.pages=329&rft.pub=Dover&rft.date=1961&rft.isbn=978-0-12-218101-6&rft.aulast=Ditchburn&rft.aufirst=R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"> See "<a rel="nofollow" class="external text" href="http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm">Photons, Relativity, Doppler shift</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060827063802/http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm">Archived</a> 2006-08-27 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> " at the University of Queensland</span> </li> <li id="cite_note-Hogg-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hogg_28-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBunnHogg2009" class="citation journal cs1">Bunn, E. F.; Hogg, D. W. (2009). "The kinematic origin of the cosmological redshift". <i>American Journal of Physics</i>. <b>77</b> (8): 688–694. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0808.1081">0808.1081</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009AmJPh..77..688B">2009AmJPh..77..688B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.3129103">10.1119/1.3129103</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1365918">1365918</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=The+kinematic+origin+of+the+cosmological+redshift&rft.volume=77&rft.issue=8&rft.pages=688-694&rft.date=2009&rft_id=info%3Aarxiv%2F0808.1081&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1365918%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1119%2F1.3129103&rft_id=info%3Abibcode%2F2009AmJPh..77..688B&rft.aulast=Bunn&rft.aufirst=E.+F.&rft.au=Hogg%2C+D.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Weinberg-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Weinberg_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeinberg1993" class="citation book cs1">Weinberg, Steven (1993). <a href="/wiki/The_First_Three_Minutes:_A_Modern_View_of_the_Origin_of_the_Universe" class="mw-redirect" title="The First Three Minutes: A Modern View of the Origin of the Universe"><i>The First Three Minutes: A Modern View of the Origin of the Universe</i></a> (2nd ed.). Basic Books. p. 34. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780-465-02437-7" title="Special:BookSources/9780-465-02437-7"><bdi>9780-465-02437-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+First+Three+Minutes%3A+A+Modern+View+of+the+Origin+of+the+Universe&rft.pages=34&rft.edition=2nd&rft.pub=Basic+Books&rft.date=1993&rft.isbn=9780-465-02437-7&rft.aulast=Weinberg&rft.aufirst=Steven&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Bergström-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bergström_30-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBergströmGoobar2006" class="citation book cs1"><a href="/wiki/Lars_Bergstr%C3%B6m_(physicist)" title="Lars Bergström (physicist)">Bergström, Lars</a>; <a href="/w/index.php?title=Ariel_Goobar&action=edit&redlink=1" class="new" title="Ariel Goobar (page does not exist)">Goobar, Ariel</a> (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=CQYu_sutWAoC&pg=PA77"><i>Cosmology and Particle Astrophysics</i></a> (2nd ed.). Springer. p. 77, Eq.4.79. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-32924-4" title="Special:BookSources/978-3-540-32924-4"><bdi>978-3-540-32924-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cosmology+and+Particle+Astrophysics&rft.pages=77%2C+Eq.4.79&rft.edition=2nd&rft.pub=Springer&rft.date=2006&rft.isbn=978-3-540-32924-4&rft.aulast=Bergstr%C3%B6m&rft.aufirst=Lars&rft.au=Goobar%2C+Ariel&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCQYu_sutWAoC%26pg%3DPA77&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Longair-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-Longair_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLongair1998" class="citation book cs1">Longair, M. S. (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2ARuLT-tk5EC&pg=PA161"><i>Galaxy Formation</i></a>. Springer. p. 161. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-63785-1" title="Special:BookSources/978-3-540-63785-1"><bdi>978-3-540-63785-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Galaxy+Formation&rft.pages=161&rft.pub=Springer&rft.date=1998&rft.isbn=978-3-540-63785-1&rft.aulast=Longair&rft.aufirst=M.+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2ARuLT-tk5EC%26pg%3DPA161&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-UCLA-2015-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-UCLA-2015_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-UCLA-2015_32-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStaff2015" class="citation web cs1">Staff (2015). <a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/ACC.html">"UCLA Cosmological Calculator"</a>. <i><a href="/wiki/UCLA" class="mw-redirect" title="UCLA">UCLA</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 August</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=UCLA&rft.atitle=UCLA+Cosmological+Calculator&rft.date=2015&rft.au=Staff&rft_id=http%3A%2F%2Fwww.astro.ucla.edu%2F~wright%2FACC.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2015: H<sub>0</sub>=67.74 and Omega<sub>M</sub>=0.3089 (see Table/Planck2015 at "<a href="/wiki/Lambda-CDM_model#Parameters" title="Lambda-CDM model">Lambda-CDM model#Parameters</a>" )</span> </li> <li id="cite_note-UCLA-2018-33"><span class="mw-cite-backlink">^ <a href="#cite_ref-UCLA-2018_33-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-UCLA-2018_33-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStaff2018" class="citation web cs1">Staff (2018). <a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/ACC.html">"UCLA Cosmological Calculator"</a>. <i><a href="/wiki/UCLA" class="mw-redirect" title="UCLA">UCLA</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 August</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=UCLA&rft.atitle=UCLA+Cosmological+Calculator&rft.date=2018&rft.au=Staff&rft_id=http%3A%2F%2Fwww.astro.ucla.edu%2F~wright%2FACC.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2018: H<sub>0</sub>=67.4 and Omega<sub>M</sub>=0.315 (see Table/Planck2018 at "<a href="/wiki/Lambda-CDM_model#Parameters" title="Lambda-CDM model">Lambda-CDM model#Parameters</a>" )</span> </li> <li id="cite_note-ICRAR-2022-34"><span class="mw-cite-backlink">^ <a href="#cite_ref-ICRAR-2022_34-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ICRAR-2022_34-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStaff2022" class="citation web cs1">Staff (2022). <a rel="nofollow" class="external text" href="https://cosmocalc.icrar.org/">"ICRAR Cosmology Calculator"</a>. <i><a href="/wiki/International_Centre_for_Radio_Astronomy_Research" title="International Centre for Radio Astronomy Research">International Centre for Radio Astronomy Research</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 August</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=International+Centre+for+Radio+Astronomy+Research&rft.atitle=ICRAR+Cosmology+Calculator&rft.date=2022&rft.au=Staff&rft_id=https%3A%2F%2Fcosmocalc.icrar.org%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> ICRAR Cosmology Calculator - Set H<sub>0</sub>=67.4 and Omega<sub>M</sub>=0.315 (see Table/Planck2018 at "<a href="/wiki/Lambda-CDM_model#Parameters" title="Lambda-CDM model">Lambda-CDM model#Parameters</a>")</span> </li> <li id="cite_note-KEMP-2022-35"><span class="mw-cite-backlink">^ <a href="#cite_ref-KEMP-2022_35-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-KEMP-2022_35-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKempner2022" class="citation web cs1">Kempner, Joshua (2022). <a rel="nofollow" class="external text" href="https://www.kempner.net/cosmic.php">"KEMPNER Cosmology Calculator"</a>. <i>Kempner.net</i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 August</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Kempner.net&rft.atitle=KEMPNER+Cosmology+Calculator&rft.date=2022&rft.aulast=Kempner&rft.aufirst=Joshua&rft_id=https%3A%2F%2Fwww.kempner.net%2Fcosmic.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> KEMP Cosmology Calculator - Set H<sub>0</sub>=67.4, Omega<sub>M</sub>=0.315, and Omega<sub>Λ</sub>=0.6847 (see Table/Planck2018 at "<a href="/wiki/Lambda-CDM_model#Parameters" title="Lambda-CDM model">Lambda-CDM model#Parameters</a>")</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">Measurements of the peculiar velocities out to 5 <a href="/wiki/Parsec" title="Parsec">Mpc</a> using the <a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a> were reported in 2003 by <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKarachentsevMakarovSharinaDolphin2003" class="citation journal cs1">Karachentsev, I. D.; et al. (2003). "Local galaxy flows within 5 Mpc". <i><a href="/wiki/Astronomy_and_Astrophysics" class="mw-redirect" title="Astronomy and Astrophysics">Astronomy and Astrophysics</a></i>. <b>398</b> (2): 479–491. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0211011">astro-ph/0211011</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003A&A...398..479K">2003A&A...398..479K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%3A20021566">10.1051/0004-6361:20021566</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:26822121">26822121</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Local+galaxy+flows+within+5+Mpc&rft.volume=398&rft.issue=2&rft.pages=479-491&rft.date=2003&rft_id=info%3Aarxiv%2Fastro-ph%2F0211011&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A26822121%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1051%2F0004-6361%3A20021566&rft_id=info%3Abibcode%2F2003A%26A...398..479K&rft.aulast=Karachentsev&rft.aufirst=I.+D.&rft.au=Makarov%2C+D.+I.&rft.au=Sharina%2C+M.+E.&rft.au=Dolphin%2C+A.+E.&rft.au=Grebel%2C+E.+K.&rft.au=Geisler%2C+D.&rft.au=Guhathakurta%2C+P.&rft.au=Hodge%2C+P.+W.&rft.au=Karachentseva%2C+V.+E.&rft.au=Sarajedini%2C+A.&rft.au=Seitzer%2C+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Kuhn-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kuhn_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoupelisKuhn2007" class="citation book cs1">Koupelis, Theo; Kuhn, Karl F. (2007). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/inquestofunivers00koup"><i>In Quest of the Universe</i></a></span> (5th ed.). Jones & Bartlett Publishers. p. <a rel="nofollow" class="external text" href="https://archive.org/details/inquestofunivers00koup/page/557">557</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7637-4387-1" title="Special:BookSources/978-0-7637-4387-1"><bdi>978-0-7637-4387-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=In+Quest+of+the+Universe&rft.pages=557&rft.edition=5th&rft.pub=Jones+%26+Bartlett+Publishers&rft.date=2007&rft.isbn=978-0-7637-4387-1&rft.aulast=Koupelis&rft.aufirst=Theo&rft.au=Kuhn%2C+Karl+F.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Finquestofunivers00koup&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Lewis-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lewis_38-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewisFrancisBarnesKwan2008" class="citation journal cs1">Lewis, Geraint F.; Francis, Matthew J.; Barnes, Luke A.; Kwan, Juliana; et al. (2008). <a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2008.13477.x">"Cosmological Radar Ranging in an Expanding Universe"</a>. <i><a href="/wiki/Monthly_Notices_of_the_Royal_Astronomical_Society" title="Monthly Notices of the Royal Astronomical Society">Monthly Notices of the Royal Astronomical Society</a></i>. <b>388</b> (3): 960–964. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0805.2197">0805.2197</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008MNRAS.388..960L">2008MNRAS.388..960L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2008.13477.x">10.1111/j.1365-2966.2008.13477.x</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15147382">15147382</a>. <q>It is perfectly valid to interpret the equations of relativity in terms of an expanding space. The mistake is to push analogies too far and imbue space with physical properties that are not consistent with the equations of relativity.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=Cosmological+Radar+Ranging+in+an+Expanding+Universe&rft.volume=388&rft.issue=3&rft.pages=960-964&rft.date=2008&rft_id=info%3Aarxiv%2F0805.2197&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15147382%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2966.2008.13477.x&rft_id=info%3Abibcode%2F2008MNRAS.388..960L&rft.aulast=Lewis&rft.aufirst=Geraint+F.&rft.au=Francis%2C+Matthew+J.&rft.au=Barnes%2C+Luke+A.&rft.au=Kwan%2C+Juliana&rft.au=James%2C+J.+Berian&rft_id=https%3A%2F%2Fdoi.org%2F10.1111%252Fj.1365-2966.2008.13477.x&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Chodorowski-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chodorowski_39-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChodorowski2007" class="citation journal cs1">Chodorowski, Michal (2007). "Is space really expanding? A counterexample". <i>Concepts Phys</i>. <b>4</b> (1): 17–34. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0601171">astro-ph/0601171</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007ONCP....4...15C">2007ONCP....4...15C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2478%2Fv10005-007-0002-2">10.2478/v10005-007-0002-2</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15931627">15931627</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Concepts+Phys&rft.atitle=Is+space+really+expanding%3F+A+counterexample&rft.volume=4&rft.issue=1&rft.pages=17-34&rft.date=2007&rft_id=info%3Aarxiv%2Fastro-ph%2F0601171&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15931627%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.2478%2Fv10005-007-0002-2&rft_id=info%3Abibcode%2F2007ONCP....4...15C&rft.aulast=Chodorowski&rft.aufirst=Michal&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBedran2002" class="citation journal cs1">Bedran, M. L. (2002). <a rel="nofollow" class="external text" href="http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf">"A comparison between the Doppler and cosmological redshifts"</a> <span class="cs1-format">(PDF)</span>. <i>American Journal of Physics</i>. <b>70</b> (4): 406–408. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002AmJPh..70..406B">2002AmJPh..70..406B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1446856">10.1119/1.1446856</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-03-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=A+comparison+between+the+Doppler+and+cosmological+redshifts&rft.volume=70&rft.issue=4&rft.pages=406-408&rft.date=2002&rft_id=info%3Adoi%2F10.1119%2F1.1446856&rft_id=info%3Abibcode%2F2002AmJPh..70..406B&rft.aulast=Bedran&rft.aufirst=M.+L.&rft_id=http%3A%2F%2Fwww.df.uba.ar%2Fusers%2Fsgil%2Fphysics_paper_doc%2Fpapers_phys%2Fcosmo%2Fdoppler_redshift.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Harrison2-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-Harrison2_41-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarrison1992" class="citation journal cs1">Harrison, Edward (1992). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F172179">"The redshift-distance and velocity-distance laws"</a>. <i>Astrophysical Journal, Part 1</i>. <b>403</b>: 28–31. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993ApJ...403...28H">1993ApJ...403...28H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F172179">10.1086/172179</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysical+Journal%2C+Part+1&rft.atitle=The+redshift-distance+and+velocity-distance+laws&rft.volume=403&rft.pages=28-31&rft.date=1992&rft_id=info%3Adoi%2F10.1086%2F172179&rft_id=info%3Abibcode%2F1993ApJ...403...28H&rft.aulast=Harrison&rft.aufirst=Edward&rft_id=https%3A%2F%2Fdoi.org%2F10.1086%252F172179&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span>. A pdf file can be found here <a rel="nofollow" class="external autonumber" href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993ApJ...403...28H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf">[1]</a>.</span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><a href="#CITEREFHarrison2000">Harrison 2000</a>, p. 302.</span> </li> <li id="cite_note-Weinberg_Cosmology-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-Weinberg_Cosmology_43-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeinberg2008" class="citation book cs1">Weinberg, Steven (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=48C-ym2EmZkC&pg=PA11"><i>Cosmology</i></a>. Oxford University Press. p. 11. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-852682-7" title="Special:BookSources/978-0-19-852682-7"><bdi>978-0-19-852682-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cosmology&rft.pages=11&rft.pub=Oxford+University+Press&rft.date=2008&rft.isbn=978-0-19-852682-7&rft.aulast=Weinberg&rft.aufirst=Steven&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D48C-ym2EmZkC%26pg%3DPA11&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text">This is only true in a universe where there are no <a href="/wiki/Peculiar_velocity" title="Peculiar velocity">peculiar velocities</a>. Otherwise, redshifts combine as <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fe0c8de8ae09afbfdfc8822be962e2508baa28e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.267ex; height:3.009ex;" alt="{\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}"></span></dd></dl> which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavisLineweaverWebb2003" class="citation journal cs1">Davis, T. M.; Lineweaver, C. H.; Webb, J. K. (April 2003). "Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects". <i>American Journal of Physics</i>. <b>71</b> (4): 358–364. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0104349">astro-ph/0104349</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003AmJPh..71..358D">2003AmJPh..71..358D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1528916">10.1119/1.1528916</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3219383">3219383</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Solutions+to+the+tethered+galaxy+problem+in+an+expanding+universe+and+the+observation+of+receding+blueshifted+objects&rft.volume=71&rft.issue=4&rft.pages=358-364&rft.date=2003-04&rft_id=info%3Aarxiv%2Fastro-ph%2F0104349&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3219383%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1119%2F1.1528916&rft_id=info%3Abibcode%2F2003AmJPh..71..358D&rft.aulast=Davis&rft.aufirst=T.+M.&rft.au=Lineweaver%2C+C.+H.&rft.au=Webb%2C+J.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChant1930" class="citation journal cs1">Chant, C. A. (1930). "Notes and Queries (Telescopes and Observatory Equipment – The Einstein Shift of Solar Lines)". <i><a href="/wiki/Journal_of_the_Royal_Astronomical_Society_of_Canada" title="Journal of the Royal Astronomical Society of Canada">Journal of the Royal Astronomical Society of Canada</a></i>. <b>24</b>: 390. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1930JRASC..24..390C">1930JRASC..24..390C</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Royal+Astronomical+Society+of+Canada&rft.atitle=Notes+and+Queries+%28Telescopes+and+Observatory+Equipment+%E2%80%93+The+Einstein+Shift+of+Solar+Lines%29&rft.volume=24&rft.pages=390&rft.date=1930&rft_id=info%3Abibcode%2F1930JRASC..24..390C&rft.aulast=Chant&rft.aufirst=C.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein1907" class="citation journal cs1"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, A.</a> (1907). "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen". <i>Jahrbuch der Radioaktivität und Elektronik</i>. <b>4</b>: 411–462. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1908JRE.....4..411E">1908JRE.....4..411E</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Jahrbuch+der+Radioaktivit%C3%A4t+und+Elektronik&rft.atitle=%C3%9Cber+das+Relativit%C3%A4tsprinzip+und+die+aus+demselben+gezogenen+Folgerungen&rft.volume=4&rft.pages=411-462&rft.date=1907&rft_id=info%3Abibcode%2F1908JRE.....4..411E&rft.aulast=Einstein&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> See p. 458 <i>The influence of a gravitational field on clocks</i></span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoundRebka1960" class="citation journal cs1">Pound, R.; Rebka, G. (1960). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.4.337">"Apparent Weight of Photons"</a>. <i>Physical Review Letters</i>. <b>4</b> (7): 337–341. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960PhRvL...4..337P">1960PhRvL...4..337P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.4.337">10.1103/PhysRevLett.4.337</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Apparent+Weight+of+Photons&rft.volume=4&rft.issue=7&rft.pages=337-341&rft.date=1960&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.4.337&rft_id=info%3Abibcode%2F1960PhRvL...4..337P&rft.aulast=Pound&rft.aufirst=R.&rft.au=Rebka%2C+G.&rft_id=https%3A%2F%2Fdoi.org%2F10.1103%252FPhysRevLett.4.337&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span>. This paper was the first measurement.</span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSachsWolfe1967" class="citation journal cs1"><a href="/wiki/Rainer_K._Sachs" title="Rainer K. Sachs">Sachs, R. K.</a>; <a href="/wiki/Arthur_M._Wolfe" title="Arthur M. Wolfe">Wolfe, A. M.</a> (1967). "Perturbations of a cosmological model and angular variations of the cosmic microwave background". <i>Astrophysical Journal</i>. <b>147</b> (73): 73. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1967ApJ...147...73S">1967ApJ...147...73S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F148982">10.1086/148982</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysical+Journal&rft.atitle=Perturbations+of+a+cosmological+model+and+angular+variations+of+the+cosmic+microwave+background&rft.volume=147&rft.issue=73&rft.pages=73&rft.date=1967&rft_id=info%3Adoi%2F10.1086%2F148982&rft_id=info%3Abibcode%2F1967ApJ...147...73S&rft.aulast=Sachs&rft.aufirst=R.+K.&rft.au=Wolfe%2C+A.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Pilipenko-49"><span class="mw-cite-backlink">^ <a href="#cite_ref-Pilipenko_49-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Pilipenko_49-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">S.V. Pilipenko (2013-2021) <a rel="nofollow" class="external text" href="https://arxiv.org/abs/1303.5961">"Paper-and-pencil cosmological calculator"</a> arxiv:1303.5961, including <a rel="nofollow" class="external text" href="https://code.google.com/archive/p/cosmonom/downloads">Fortran-90 code</a> upon which the citing charts and formulae are based.</span> </li> <li id="cite_note-reboul-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-reboul_50-0">^</a></b></span> <span class="reference-text">When cosmological redshifts were first discovered, <a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Fritz Zwicky</a> proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with <a href="/wiki/Intrinsic_redshift" class="mw-redirect" title="Intrinsic redshift">intrinsic redshift</a> suggestions, utilized by <a href="/wiki/Nonstandard_cosmologies" class="mw-redirect" title="Nonstandard cosmologies">nonstandard cosmologies</a>. In 1981, H. J. Reboul summarised many <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1981A%26AS...45..129R&db_key=AST&data_type=HTML&format=&high=42ca922c9c23806">alternative redshift mechanisms</a> that had been discussed in the literature since the 1930s. In 2001, <a href="/wiki/Geoffrey_Burbidge" title="Geoffrey Burbidge">Geoffrey Burbidge</a> remarked in a <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001PASP..113..899B&db_key=AST&data_type=HTML">review</a> that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and <a href="/wiki/Halton_Arp" title="Halton Arp">Halton Arp</a>, while investigating the mystery of <a href="/wiki/Quasar#History_of_quasar_observation" title="Quasar">the nature of quasars</a>, tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work. Moreover, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldhaberGroomKimAldering2001" class="citation journal cs1">Goldhaber, G.; et al. (2001). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F322460">"Timescale Stretch Parameterization of Type Ia Supernova B-Band Lightcurves"</a>. <i>Astrophysical Journal</i>. <b>558</b> (1): 359–386. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0104382">astro-ph/0104382</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001ApJ...558..359G">2001ApJ...558..359G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F322460">10.1086/322460</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17237531">17237531</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysical+Journal&rft.atitle=Timescale+Stretch+Parameterization+of+Type+Ia+Supernova+B-Band+Lightcurves&rft.volume=558&rft.issue=1&rft.pages=359-386&rft.date=2001&rft_id=info%3Aarxiv%2Fastro-ph%2F0104382&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17237531%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1086%2F322460&rft_id=info%3Abibcode%2F2001ApJ...558..359G&rft.aulast=Goldhaber&rft.aufirst=G.&rft.au=Groom%2C+D.+E.&rft.au=Kim%2C+A.&rft.au=Aldering%2C+G.&rft.au=Astier%2C+P.&rft.au=Conley%2C+A.&rft.au=Deustua%2C+S.+E.&rft.au=Ellis%2C+R.&rft.au=Fabbro%2C+S.&rft.au=Fruchter%2C+A.+S.&rft.au=Goobar%2C+A.&rft.au=Hook%2C+I.&rft.au=Irwin%2C+M.&rft.au=Kim%2C+M.&rft.au=Knop%2C+R.+A.&rft.au=Lidman%2C+C.&rft.au=McMahon%2C+R.&rft.au=Nugent%2C+P.+E.&rft.au=Pain%2C+R.&rft.au=Panagia%2C+N.&rft.au=Pennypacker%2C+C.+R.&rft.au=Perlmutter%2C+S.&rft.au=Ruiz-Lapuente%2C+P.&rft.au=Schaefe%2C+B.&rft.au=Walton%2C+N.+A.&rft.au=York%2C+T.&rft_id=https%3A%2F%2Fdoi.org%2F10.1086%252F322460&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> pointed out that alternative theories are unable to account for timescale stretch observed in <a href="/wiki/Type_Ia_supernovae" class="mw-redirect" title="Type Ia supernovae">type Ia supernovae</a></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text">For a review of the subject of photometry, consider: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBudding1993" class="citation book cs1">Budding, E. (September 24, 1993). <i>Introduction to Astronomical Photometry</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-41867-4" title="Special:BookSources/0-521-41867-4"><bdi>0-521-41867-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Astronomical+Photometry&rft.pub=Cambridge+University+Press&rft.date=1993-09-24&rft.isbn=0-521-41867-4&rft.aulast=Budding&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text">The technique was first described by: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaum1962" class="citation conference cs1">Baum, W. A. (1962). McVittie, G. C. (ed.). <i>Problems of extra-galactic research</i>. IAU Symposium No. 15. p. 390.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Problems+of+extra-galactic+research&rft.pages=390&rft.date=1962&rft.aulast=Baum&rft.aufirst=W.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBolzonellaMirallesPelló2000" class="citation journal cs1">Bolzonella, M.; Miralles, J.-M.; Pelló, R. (2000). "Photometric redshifts based on standard SED fitting procedures". <i>Astronomy and Astrophysics</i>. <b>363</b>: 476–492. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0003380">astro-ph/0003380</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000A&A...363..476B">2000A&A...363..476B</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Photometric+redshifts+based+on+standard+SED+fitting+procedures&rft.volume=363&rft.pages=476-492&rft.date=2000&rft_id=info%3Aarxiv%2Fastro-ph%2F0003380&rft_id=info%3Abibcode%2F2000A%26A...363..476B&rft.aulast=Bolzonella&rft.aufirst=M.&rft.au=Miralles%2C+J.-M.&rft.au=Pell%C3%B3%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text">A pedagogical overview of the K-correction by David Hogg and other members of the <a href="/wiki/Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">SDSS</a> collaboration can be found at: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoggBaldryBlantonEisenstein2002" class="citation arxiv cs1">Hogg, David W.; et al. (October 2002). "The K correction". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0210394">astro-ph/0210394</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=The+K+correction&rft.date=2002-10&rft_id=info%3Aarxiv%2Fastro-ph%2F0210394&rft.aulast=Hogg&rft.aufirst=David+W.&rft.au=Baldry%2C+Ivan+K.&rft.au=Blanton%2C+Michael+R.&rft.au=Eisenstein%2C+Daniel+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text">The <a href="/w/index.php?title=Exoplanet_Tracker&action=edit&redlink=1" class="new" title="Exoplanet Tracker (page does not exist)">Exoplanet Tracker</a> is the newest observing project to use this technique, able to track the redshift variations in multiple objects at once, as reported in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeVan_EykenMahadevanDewitt2006" class="citation journal cs1">Ge, Jian; Van Eyken, Julian; <a href="/wiki/Suvrath_Mahadevan" title="Suvrath Mahadevan">Mahadevan, Suvrath</a>; Dewitt, Curtis; et al. (2006). "The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument". <i>The Astrophysical Journal</i>. <b>648</b> (1): 683–695. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0605247">astro-ph/0605247</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006ApJ...648..683G">2006ApJ...648..683G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F505699">10.1086/505699</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13879217">13879217</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Astrophysical+Journal&rft.atitle=The+First+Extrasolar+Planet+Discovered+with+a+New-Generation+High-Throughput+Doppler+Instrument&rft.volume=648&rft.issue=1&rft.pages=683-695&rft.date=2006&rft_id=info%3Aarxiv%2Fastro-ph%2F0605247&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A13879217%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1086%2F505699&rft_id=info%3Abibcode%2F2006ApJ...648..683G&rft.aulast=Ge&rft.aufirst=Jian&rft.au=Van+Eyken%2C+Julian&rft.au=Mahadevan%2C+Suvrath&rft.au=Dewitt%2C+Curtis&rft.au=Kane%2C+Stephen+R.&rft.au=Cohen%2C+Roger&rft.au=Vanden+Heuvel%2C+Andrew&rft.au=Fleming%2C+Scott+W.&rft.au=Guo%2C+Pengcheng&rft.au=Henry%2C+Gregory+W.&rft.au=Schneider%2C+Donald+P.&rft.au=Ramsey%2C+Lawrence+W.&rft.au=Wittenmyer%2C+Robert+A.&rft.au=Endl%2C+Michael&rft.au=Cochran%2C+William+D.&rft.au=Ford%2C+Eric+B.&rft.au=Martin%2C+Eduardo+L.&rft.au=Israelian%2C+Garik&rft.au=Valenti%2C+Jeff&rft.au=Montes%2C+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLibbrecht1988" class="citation journal cs1">Libbrecht, Keng (1988). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/104214/1/1988SSRv___47__275L.pdf">"Solar and stellar seismology"</a> <span class="cs1-format">(PDF)</span>. <i>Space Science Reviews</i>. <b>47</b> (3–4): 275–301. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988SSRv...47..275L">1988SSRv...47..275L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00243557">10.1007/BF00243557</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120897051">120897051</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Space+Science+Reviews&rft.atitle=Solar+and+stellar+seismology&rft.volume=47&rft.issue=3%E2%80%934&rft.pages=275-301&rft.date=1988&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120897051%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF00243557&rft_id=info%3Abibcode%2F1988SSRv...47..275L&rft.aulast=Libbrecht&rft.aufirst=Keng&rft_id=https%3A%2F%2Fauthors.library.caltech.edu%2F104214%2F1%2F1988SSRv___47__275L.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text">In 1871 <a href="/wiki/Hermann_Carl_Vogel" title="Hermann Carl Vogel">Hermann Carl Vogel</a> measured the rotation rate of <a href="/wiki/Venus" title="Venus">Venus</a>. <a href="/wiki/Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> was working on such measurements when he turned his attention to spiral nebulae.</span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text">An early review by <a href="/wiki/Jan_Hendrik_Oort" class="mw-redirect" title="Jan Hendrik Oort">Oort, J. H.</a> on the subject: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOort1970" class="citation journal cs1">Oort, J. H. (1970). "The formation of galaxies and the origin of the high-velocity hydrogen". <i><a href="/wiki/Astronomy_and_Astrophysics" class="mw-redirect" title="Astronomy and Astrophysics">Astronomy and Astrophysics</a></i>. <b>7</b>: 381. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1970A&A.....7..381O">1970A&A.....7..381O</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=The+formation+of+galaxies+and+the+origin+of+the+high-velocity+hydrogen&rft.volume=7&rft.pages=381&rft.date=1970&rft_id=info%3Abibcode%2F1970A%26A.....7..381O&rft.aulast=Oort&rft.aufirst=J.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAsaoka1989" class="citation journal cs1">Asaoka, Ikuko (1989). "X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole". <i>Publications of the Astronomical Society of Japan</i>. <b>41</b> (4): 763–778. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989PASJ...41..763A">1989PASJ...41..763A</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+of+the+Astronomical+Society+of+Japan&rft.atitle=X-ray+spectra+at+infinity+from+a+relativistic+accretion+disk+around+a+Kerr+black+hole&rft.volume=41&rft.issue=4&rft.pages=763-778&rft.date=1989&rft_id=info%3Abibcode%2F1989PASJ...41..763A&rft.aulast=Asaoka&rft.aufirst=Ikuko&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRybickiLightman1979" class="citation book cs1">Rybicki, G. B.; Lightman, A. R. (1979). <i>Radiative Processes in Astrophysics</i>. John Wiley & Sons. p. 288. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-82759-2" title="Special:BookSources/0-471-82759-2"><bdi>0-471-82759-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Radiative+Processes+in+Astrophysics&rft.pages=288&rft.pub=John+Wiley+%26+Sons&rft.date=1979&rft.isbn=0-471-82759-2&rft.aulast=Rybicki&rft.aufirst=G.+B.&rft.au=Lightman%2C+A.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives">"Cosmic Detectives"</a>. The European Space Agency (ESA). 2013-04-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-04-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Cosmic+Detectives&rft.pub=The+European+Space+Agency+%28ESA%29&rft.date=2013-04-02&rft_id=http%3A%2F%2Fwww.esa.int%2FOur_Activities%2FSpace_Science%2FCosmic_detectives&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text">An accurate measurement of the cosmic microwave background was achieved by the <a href="/wiki/Cosmic_Background_Explorer" title="Cosmic Background Explorer">COBE</a> experiment. The final published temperature of 2.73 K was reported in this paper: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFixsenChengCottinghamEplee1994" class="citation journal cs1">Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E. Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.; <a href="/wiki/Nancy_Boggess" title="Nancy Boggess">Boggess, N. W.</a>; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T. (January 1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument". <i>Astrophysical Journal</i>. <b>420</b>: 445. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994ApJ...420..445F">1994ApJ...420..445F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F173575">10.1086/173575</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysical+Journal&rft.atitle=Cosmic+microwave+background+dipole+spectrum+measured+by+the+COBE+FIRAS+instrument&rft.volume=420&rft.pages=445&rft.date=1994-01&rft_id=info%3Adoi%2F10.1086%2F173575&rft_id=info%3Abibcode%2F1994ApJ...420..445F&rft.aulast=Fixsen&rft.aufirst=D.+J.&rft.au=Cheng%2C+E.+S.&rft.au=Cottingham%2C+D.+A.&rft.au=Eplee%2C+R.+E.+Jr.&rft.au=Isaacman%2C+R.+B.&rft.au=Mather%2C+J.+C.&rft.au=Meyer%2C+S.+S.&rft.au=Noerdlinger%2C+P.+D.&rft.au=Shafer%2C+R.+A.&rft.au=Weiss%2C+R.&rft.au=Wright%2C+E.+L.&rft.au=Bennett%2C+C.+L.&rft.au=Boggess%2C+N.+W.&rft.au=Kelsall%2C+T.&rft.au=Moseley%2C+S.+H.&rft.au=Silverberg%2C+R.+F.&rft.au=Smoot%2C+G.+F.&rft.au=Wilkinson%2C+D.+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span>. The most accurate measurement as of 2006 was achieved by the <a href="/wiki/Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">WMAP</a> experiment.</span> </li> <li id="cite_note-Peebles-1993-63"><span class="mw-cite-backlink">^ <a href="#cite_ref-Peebles-1993_63-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Peebles-1993_63-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Peebles-1993_63-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Peebles (1993).</span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBinneyTreimane1994" class="citation book cs1">Binney, James; Treimane, Scott (1994). <i>Galactic dynamics</i>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-08445-9" title="Special:BookSources/978-0-691-08445-9"><bdi>978-0-691-08445-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Galactic+dynamics&rft.pub=Princeton+University+Press&rft.date=1994&rft.isbn=978-0-691-08445-9&rft.aulast=Binney&rft.aufirst=James&rft.au=Treimane%2C+Scott&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nobelprize.org/uploads/2019/05/popular-physicsprize2011.pdf">"The Nobel Prize in Physics 2011: Information for the Public"</a> <span class="cs1-format">(PDF)</span>. <i>nobelprize.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-06-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=nobelprize.org&rft.atitle=The+Nobel+Prize+in+Physics+2011%3A+Information+for+the+Public&rft_id=https%3A%2F%2Fwww.nobelprize.org%2Fuploads%2F2019%2F05%2Fpopular-physicsprize2011.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarnianiHainlineD’EugenioEisenstein2024" class="citation journal cs1">Carniani, Stefano; Hainline, Kevin; D’Eugenio, Francesco; Eisenstein, Daniel J.; Jakobsen, Peter; Witstok, Joris; Johnson, Benjamin D.; Chevallard, Jacopo; Maiolino, Roberto; Helton, Jakob M.; Willott, Chris; Robertson, Brant; Alberts, Stacey; Arribas, Santiago; Baker, William M. 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"Mapping the Universe". <i>Science</i>. <b>246</b> (4932): 897–903. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989Sci...246..897G">1989Sci...246..897G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.246.4932.897">10.1126/science.246.4932.897</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17812575">17812575</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:31328798">31328798</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Mapping+the+Universe&rft.volume=246&rft.issue=4932&rft.pages=897-903&rft.date=1989&rft_id=info%3Adoi%2F10.1126%2Fscience.246.4932.897&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A31328798%23id-name%3DS2CID&rft_id=info%3Apmid%2F17812575&rft_id=info%3Abibcode%2F1989Sci...246..897G&rft.aulast=Geller&rft.aufirst=M.+J.&rft.au=Huchra%2C+J.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-86"><span class="mw-cite-backlink"><b><a href="#cite_ref-86">^</a></b></span> <span class="reference-text">See the CfA website for more details: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuchra" class="citation web cs1"><a href="/wiki/John_Huchra" title="John Huchra">Huchra, John P.</a> <a rel="nofollow" class="external text" href="https://lweb.cfa.harvard.edu/~dfabricant/huchra/zcat/">"The CfA Redshift Survey"</a>. Harvard & Smithsonian Center for Astrophysics<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-03-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+CfA+Redshift+Survey&rft.pub=Harvard+%26+Smithsonian+Center+for+Astrophysics&rft.aulast=Huchra&rft.aufirst=John+P.&rft_id=https%3A%2F%2Flweb.cfa.harvard.edu%2F~dfabricant%2Fhuchra%2Fzcat%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-87"><span class="mw-cite-backlink"><b><a href="#cite_ref-87">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColePercivalPeacockNorberg2005" class="citation journal cs1"><a href="/wiki/Shaun_Cole" title="Shaun Cole">Cole, Shaun</a>; Percival, Will J.; Peacock, John A.; Norberg, Peder; et al. (2005). <a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2005.09318.x">"The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications"</a>. <i>Monthly Notices of the Royal Astronomical Society</i>. <b>362</b> (2): 505–34. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0501174">astro-ph/0501174</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005MNRAS.362..505C">2005MNRAS.362..505C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2005.09318.x">10.1111/j.1365-2966.2005.09318.x</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6906627">6906627</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=The+2dF+galaxy+redshift+survey%3A+Power-spectrum+analysis+of+the+final+dataset+and+cosmological+implications&rft.volume=362&rft.issue=2&rft.pages=505-34&rft.date=2005&rft_id=info%3Aarxiv%2Fastro-ph%2F0501174&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A6906627%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2966.2005.09318.x&rft_id=info%3Abibcode%2F2005MNRAS.362..505C&rft.aulast=Cole&rft.aufirst=Shaun&rft.au=Percival%2C+Will+J.&rft.au=Peacock%2C+John+A.&rft.au=Norberg%2C+Peder&rft.au=Baugh%2C+Carlton+M.&rft.au=Frenk%2C+Carlos+S.&rft.au=Baldry%2C+Ivan&rft.au=Bland-Hawthorn%2C+Joss&rft.au=Bridges%2C+Terry&rft.au=Cannon%2C+Russell&rft.au=Colless%2C+Matthew&rft.au=Collins%2C+Chris&rft.au=Couch%2C+Warrick&rft.au=Cross%2C+Nicholas+J.+G.&rft.au=Dalton%2C+Gavin&rft.au=Eke%2C+Vincent+R.&rft.au=De+Propris%2C+Roberto&rft.au=Driver%2C+Simon+P.&rft.au=Efstathiou%2C+George&rft.au=Ellis%2C+Richard+S.&rft.au=Glazebrook%2C+Karl&rft.au=Jackson%2C+Carole&rft.au=Jenkins%2C+Adrian&rft.au=Lahav%2C+Ofer&rft.au=Lewis%2C+Ian&rft.au=Lumsden%2C+Stuart&rft.au=Maddox%2C+Steve&rft.au=Madgwick%2C+Darren&rft.au=Peterson%2C+Bruce+A.&rft.au=Sutherland%2C+Will&rft.au=Taylor%2C+Keith&rft_id=https%3A%2F%2Fdoi.org%2F10.1111%252Fj.1365-2966.2005.09318.x&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://msowww.anu.edu.au/2dFGRS/">2dF Galaxy Redshift Survey homepage</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070205010241/http://msowww.anu.edu.au/2dFGRS/">Archived</a> 2007-02-05 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-88"><span class="mw-cite-backlink"><b><a href="#cite_ref-88">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sdss3.org/">"SDSS-III"</a>. <i>www.sdss3.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-03-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.sdss3.org&rft.atitle=SDSS-III&rft_id=https%3A%2F%2Fwww.sdss3.org%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-89"><span class="mw-cite-backlink"><b><a href="#cite_ref-89">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavisDEEP2_collaboration2002" class="citation conference cs1">Davis, Marc; DEEP2 collaboration (2002). <i>Science objectives and early results of the DEEP2 redshift survey</i>. Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22–28 Aug 2002. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0209419">astro-ph/0209419</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003SPIE.4834..161D">2003SPIE.4834..161D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1117%2F12.457897">10.1117/12.457897</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Science+objectives+and+early+results+of+the+DEEP2+redshift+survey&rft.date=2002&rft_id=info%3Aarxiv%2Fastro-ph%2F0209419&rft_id=info%3Adoi%2F10.1117%2F12.457897&rft_id=info%3Abibcode%2F2003SPIE.4834..161D&rft.aulast=Davis&rft.aufirst=Marc&rft.au=DEEP2+collaboration&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_conference" title="Template:Cite conference">cite conference</a>}}</code>: CS1 maint: numeric names: authors list (<a href="/wiki/Category:CS1_maint:_numeric_names:_authors_list" title="Category:CS1 maint: numeric names: authors list">link</a>)</span></span> </li> <li id="cite_note-90"><span class="mw-cite-backlink"><b><a href="#cite_ref-90">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKuhnKoupelis2004" class="citation book cs1">Kuhn, Karl F.; Koupelis, Theo (2004). <i>In Quest of the Universe</i>. <a href="/wiki/Jones_%26_Bartlett_Publishers" class="mw-redirect" title="Jones & Bartlett Publishers">Jones & Bartlett Publishers</a>. pp. 122–3. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7637-0810-8" title="Special:BookSources/978-0-7637-0810-8"><bdi>978-0-7637-0810-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=In+Quest+of+the+Universe&rft.pages=122-3&rft.pub=Jones+%26+Bartlett+Publishers&rft.date=2004&rft.isbn=978-0-7637-0810-8&rft.aulast=Kuhn&rft.aufirst=Karl+F.&rft.au=Koupelis%2C+Theo&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-91"><span class="mw-cite-backlink"><b><a href="#cite_ref-91">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWoodhouse2017" class="citation book cs1">Woodhouse, Chris (2017-12-04). "M31 (Andromeda Galaxy)". <i>The Astrophotography Manual</i> (2nd ed.). Routledge. pp. 308–313. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4324%2F9781315159225-42">10.4324/9781315159225-42</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-315-15922-5" title="Special:BookSources/978-1-315-15922-5"><bdi>978-1-315-15922-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=M31+%28Andromeda+Galaxy%29&rft.btitle=The+Astrophotography+Manual&rft.pages=308-313&rft.edition=2nd&rft.pub=Routledge&rft.date=2017-12-04&rft_id=info%3Adoi%2F10.4324%2F9781315159225-42&rft.isbn=978-1-315-15922-5&rft.aulast=Woodhouse&rft.aufirst=Chris&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Aoki2005-92"><span class="mw-cite-backlink">^ <a href="#cite_ref-Aoki2005_92-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Aoki2005_92-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Aoki2005_92-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAokiKawaguchiOhta2005" class="citation journal cs1">Aoki, Kentaro; Kawaguchi, Toshihiro; Ohta, Kouji (January 2005). "The Largest Blueshifts of the [O III] Emission Line in Two Narrow-Line Quasars". <i>Astrophysical Journal</i>. <b>618</b> (2): 601–608. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0409546">astro-ph/0409546</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005ApJ...618..601A">2005ApJ...618..601A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F426075">10.1086/426075</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17680991">17680991</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astrophysical+Journal&rft.atitle=The+Largest+Blueshifts+of+the+%5BO+III%5D+Emission+Line+in+Two+Narrow-Line+Quasars&rft.volume=618&rft.issue=2&rft.pages=601-608&rft.date=2005-01&rft_id=info%3Aarxiv%2Fastro-ph%2F0409546&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17680991%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1086%2F426075&rft_id=info%3Abibcode%2F2005ApJ...618..601A&rft.aulast=Aoki&rft.aufirst=Kentaro&rft.au=Kawaguchi%2C+Toshihiro&rft.au=Ohta%2C+Kouji&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-R.N_1-93"><span class="mw-cite-backlink"><b><a href="#cite_ref-R.N_1_93-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNemiroff1993" class="citation web cs1">Nemiroff, R. J. (1993). <a rel="nofollow" class="external text" href="https://antwrp.gsfc.nasa.gov/htmltest/gifcity/nslens_math.html">"Gravitational Principles and Mathematics"</a>. <a href="/wiki/NASA" title="NASA">NASA</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Gravitational+Principles+and+Mathematics&rft.pub=NASA&rft.date=1993&rft.aulast=Nemiroff&rft.aufirst=R.+J.&rft_id=http%3A%2F%2Fantwrp.gsfc.nasa.gov%2Fhtmltest%2Fgifcity%2Fnslens_math.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-R.N_2-94"><span class="mw-cite-backlink"><b><a href="#cite_ref-R.N_2_94-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNemiroff1993" class="citation journal cs1">Nemiroff, R. J. (1993). "Visual distortions near a neutron star and black hole". <i>American Journal of Physics</i>. <b>61</b> (7): 619–632. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/9312003v1">astro-ph/9312003v1</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993AmJPh..61..619N">1993AmJPh..61..619N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.17224">10.1119/1.17224</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16640860">16640860</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Visual+distortions+near+a+neutron+star+and+black+hole&rft.volume=61&rft.issue=7&rft.pages=619-632&rft.date=1993&rft_id=info%3Aarxiv%2Fastro-ph%2F9312003v1&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A16640860%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1119%2F1.17224&rft_id=info%3Abibcode%2F1993AmJPh..61..619N&rft.aulast=Nemiroff&rft.aufirst=R.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> <li id="cite_note-Bonometto2002-95"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bonometto2002_95-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBonomettoGoriniMoschella2002" class="citation book cs1">Bonometto, Silvio; Gorini, Vittorio; Moschella, Ugo (2002). <i>Modern Cosmology</i>. <a href="/wiki/CRC_Press" title="CRC Press">CRC Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7503-0810-6" title="Special:BookSources/978-0-7503-0810-6"><bdi>978-0-7503-0810-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Cosmology&rft.pub=CRC+Press&rft.date=2002&rft.isbn=978-0-7503-0810-6&rft.aulast=Bonometto&rft.aufirst=Silvio&rft.au=Gorini%2C+Vittorio&rft.au=Moschella%2C+Ugo&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=21" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Articles">Articles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=22" title="Edit section: Articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in <i>Sky & Telescope</i> Feb. 2003; pp31–35 (This article is useful further reading in distinguishing between the 3 types of redshift and their causes.)</li> <li>Lineweaver, Charles H. and Tamara M. Davis, "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20070715030354/http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147">Misconceptions about the Big Bang</a>", <i><a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a></i>, March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Books">Books</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=23" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNussbaumerLydia_Bieri2009" class="citation book cs1">Nussbaumer, Harry; <a href="/wiki/Lydia_Bieri" title="Lydia Bieri">Lydia Bieri</a> (2009). <i>Discovering the Expanding Universe</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-51484-2" title="Special:BookSources/978-0-521-51484-2"><bdi>978-0-521-51484-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discovering+the+Expanding+Universe&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-51484-2&rft.aulast=Nussbaumer&rft.aufirst=Harry&rft.au=Lydia+Bieri&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBinneyMichael_Merrifeld1998" class="citation book cs1">Binney, James; Michael Merrifeld (1998). <i>Galactic Astronomy</i>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-02565-0" title="Special:BookSources/978-0-691-02565-0"><bdi>978-0-691-02565-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Galactic+Astronomy&rft.pub=Princeton+University+Press&rft.date=1998&rft.isbn=978-0-691-02565-0&rft.aulast=Binney&rft.aufirst=James&rft.au=Michael+Merrifeld&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarroll,_Bradley_W.Dale_A._Ostlie1996" class="citation book cs1">Carroll, Bradley W. & Dale A. Ostlie (1996). <i>An Introduction to Modern Astrophysics</i>. Addison-Wesley Publishing Company, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-54730-6" title="Special:BookSources/978-0-201-54730-6"><bdi>978-0-201-54730-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Modern+Astrophysics&rft.pub=Addison-Wesley+Publishing+Company%2C+Inc.&rft.date=1996&rft.isbn=978-0-201-54730-6&rft.au=Carroll%2C+Bradley+W.&rft.au=Dale+A.+Ostlie&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman,_RichardLeighton,_RobertSands,_Matthew1989" class="citation book cs1">Feynman, Richard; Leighton, Robert; Sands, Matthew (1989). <a href="/wiki/The_Feynman_Lectures_on_Physics" title="The Feynman Lectures on Physics"><i>Feynman Lectures on Physics. Vol. 1</i></a>. Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-51003-4" title="Special:BookSources/978-0-201-51003-4"><bdi>978-0-201-51003-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Feynman+Lectures+on+Physics.+Vol.+1&rft.pub=Addison-Wesley&rft.date=1989&rft.isbn=978-0-201-51003-4&rft.au=Feynman%2C+Richard&rft.au=Leighton%2C+Robert&rft.au=Sands%2C+Matthew&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrønHervik,_Sigbjørn2007" class="citation book cs1"><a href="/wiki/%C3%98yvind_Gr%C3%B8n" title="Øyvind Grøn">Grøn, Øyvind</a>; Hervik, Sigbjørn (2007). <i>Einstein's General Theory of Relativity</i>. New York: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-69199-2" title="Special:BookSources/978-0-387-69199-2"><bdi>978-0-387-69199-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Einstein%27s+General+Theory+of+Relativity&rft.place=New+York&rft.pub=Springer&rft.date=2007&rft.isbn=978-0-387-69199-2&rft.aulast=Gr%C3%B8n&rft.aufirst=%C3%98yvind&rft.au=Hervik%2C+Sigbj%C3%B8rn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarrison2000" class="citation book cs1">Harrison, Edward (2000). <i>Cosmology: The Science of the Universe</i> (2nd ed.). Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-66148-5" title="Special:BookSources/978-0-521-66148-5"><bdi>978-0-521-66148-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cosmology%3A+The+Science+of+the+Universe&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=2000&rft.isbn=978-0-521-66148-5&rft.aulast=Harrison&rft.aufirst=Edward&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKutner,_Marc2003" class="citation book cs1">Kutner, Marc (2003). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/astronomyphysica00kutn"><i>Astronomy: A Physical Perspective</i></a></span>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-52927-3" title="Special:BookSources/978-0-521-52927-3"><bdi>978-0-521-52927-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomy%3A+A+Physical+Perspective&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=978-0-521-52927-3&rft.au=Kutner%2C+Marc&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fastronomyphysica00kutn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMisnerThorne,_Kip_S.Wheeler,_John_Archibald1973" class="citation book cs1">Misner, Charles; Thorne, Kip S.; Wheeler, John Archibald (1973). <i>Gravitation</i>. San Francisco: W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-0344-0" title="Special:BookSources/978-0-7167-0344-0"><bdi>978-0-7167-0344-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravitation&rft.place=San+Francisco&rft.pub=W.+H.+Freeman&rft.date=1973&rft.isbn=978-0-7167-0344-0&rft.aulast=Misner&rft.aufirst=Charles&rft.au=Thorne%2C+Kip+S.&rft.au=Wheeler%2C+John+Archibald&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeebles1993" class="citation book cs1">Peebles, P. J. E. (1993). <a rel="nofollow" class="external text" href="https://archive.org/details/principlesofphys00pjep"><i>Principles of Physical Cosmology</i></a>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-01933-8" title="Special:BookSources/978-0-691-01933-8"><bdi>978-0-691-01933-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Physical+Cosmology&rft.pub=Princeton+University+Press&rft.date=1993&rft.isbn=978-0-691-01933-8&rft.aulast=Peebles&rft.aufirst=P.+J.+E.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fprinciplesofphys00pjep&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylorWheeler1992" class="citation book cs1">Taylor, Edwin F.; <a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler, John Archibald</a> (1992). <a rel="nofollow" class="external text" href="https://archive.org/details/spacetimephysics00edwi_0"><i>Spacetime Physics: Introduction to Special Relativity</i></a> (2nd ed.). W.H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-2327-1" title="Special:BookSources/978-0-7167-2327-1"><bdi>978-0-7167-2327-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spacetime+Physics%3A+Introduction+to+Special+Relativity&rft.edition=2nd&rft.pub=W.H.+Freeman&rft.date=1992&rft.isbn=978-0-7167-2327-1&rft.aulast=Taylor&rft.aufirst=Edwin+F.&rft.au=Wheeler%2C+John+Archibald&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fspacetimephysics00edwi_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeinberg1971" class="citation book cs1">Weinberg, Steven (1971). <a rel="nofollow" class="external text" href="https://archive.org/details/gravitationcosmo00stev_0"><i>Gravitation and Cosmology</i></a>. John Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-92567-5" title="Special:BookSources/978-0-471-92567-5"><bdi>978-0-471-92567-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravitation+and+Cosmology&rft.pub=John+Wiley&rft.date=1971&rft.isbn=978-0-471-92567-5&rft.aulast=Weinberg&rft.aufirst=Steven&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgravitationcosmo00stev_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li> <li>See also <a href="/wiki/Physical_cosmology#Textbooks" title="Physical cosmology">physical cosmology textbooks</a> for applications of the cosmological and gravitational redshifts.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Redshift&action=edit&section=24" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Redshift" class="extiw" title="commons:Redshift"><span style="font-style:italic; font-weight:bold;">Redshift</span></a>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/redshift" class="extiw" title="wiktionary:Special:Search/redshift">redshift</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/doppler.htm">Ned Wright's Cosmology tutorial</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051203093117/http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/redshift.html">Cosmic reference guide entry on redshift</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051121214031/http://www.asterism.org/tutorials/tut29-1.htm">Mike Luciuk's Astronomical Redshift tutorial</a></li> <li><a rel="nofollow" class="external text" href="http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/Images/hu_animexp.gif">Animated GIF of Cosmological Redshift</a> by Wayne Hu</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMerrifieldHill2009" class="citation web cs1">Merrifield, Michael; Hill, Richard (2009). <a rel="nofollow" class="external text" href="http://www.sixtysymbols.com/videos/redshift.htm">"Z Redshift"</a>. <i>SIXTψ SYMBΦLS</i>. <a href="/wiki/Brady_Haran" title="Brady Haran">Brady Haran</a> for the <a href="/wiki/University_of_Nottingham" title="University of Nottingham">University of Nottingham</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=SIXT%CF%88+SYMB%CE%A6LS&rft.atitle=Z+Redshift&rft.date=2009&rft.aulast=Merrifield&rft.aufirst=Michael&rft.au=Hill%2C+Richard&rft_id=http%3A%2F%2Fwww.sixtysymbols.com%2Fvideos%2Fredshift.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARedshift" class="Z3988"></span></li></ul> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 0.2em;min-height:24px;line-height:24px}@media screen and (max-width:768px){.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;flex-flow:column wrap;align-items:baseline}.mw-parser-output .portal-bar-header{text-align:center;flex:0;padding-left:0.5em;margin:0 auto}.mw-parser-output .portal-bar-related{font-size:100%;align-items:flex-start}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;align-items:center;flex:0;column-gap:1em;border-top:1px solid #a2a9b1;margin:0 auto;list-style:none}.mw-parser-output .portal-bar-content-related{border-top:none;margin:0;list-style:none}}.mw-parser-output .navbox+link+.portal-bar,.mw-parser-output .navbox+style+.portal-bar,.mw-parser-output .navbox+link+.portal-bar-bordered,.mw-parser-output .navbox+style+.portal-bar-bordered,.mw-parser-output .sister-bar+link+.portal-bar,.mw-parser-output .sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/17px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/26px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/34px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/19px-Crab_Nebula.jpg" 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title="Portal:Stars">Stars</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/19px-RocketSunIcon.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/29px-RocketSunIcon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/38px-RocketSunIcon.svg.png 2x" data-file-width="128" data-file-height="128" /></span></span> </span><a href="/wiki/Portal:Spaceflight" title="Portal:Spaceflight">Spaceflight</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/21px-Earth-moon.jpg" decoding="async" width="21" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/32px-Earth-moon.jpg 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Gravitational_waves" title="Template:Gravitational waves"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Gravitational_waves" title="Template talk:Gravitational waves"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Gravitational_waves" title="Special:EditPage/Template:Gravitational waves"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Gravitational-wave_astronomy" style="font-size:114%;margin:0 4em"><a href="/wiki/Gravitational-wave_astronomy" title="Gravitational-wave astronomy">Gravitational-wave astronomy</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational wave</a></li> <li><a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">Gravitational-wave observatory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">Detectors</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Gravitational-wave_observatory#Weber_bars" title="Gravitational-wave observatory">Resonant mass<br /> antennas</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Active</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=NAUTILUS&action=edit&redlink=1" class="new" title="NAUTILUS (page does not exist)">NAUTILUS</a> (<a href="/w/index.php?title=International_Gravitational_Event_Collaboration&action=edit&redlink=1" class="new" title="International Gravitational Event Collaboration (page does not exist)">IGEC</a>)</li> <li><a href="/wiki/AURIGA" title="AURIGA">AURIGA</a> (<a href="/w/index.php?title=International_Gravitational_Event_Collaboration&action=edit&redlink=1" class="new" title="International Gravitational Event Collaboration (page does not exist)">IGEC</a>)</li> <li><a href="/wiki/MiniGrail" title="MiniGrail">MiniGRAIL</a></li> <li><a href="/wiki/Mario_Schenberg_(Gravitational_Wave_Detector)" title="Mario Schenberg (Gravitational Wave Detector)">Mario Schenberg</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=EXPLORER&action=edit&redlink=1" class="new" title="EXPLORER (page does not exist)">EXPLORER</a> (<a href="/w/index.php?title=International_Gravitational_Event_Collaboration&action=edit&redlink=1" class="new" title="International Gravitational Event Collaboration (page does not exist)">IGEC</a>)</li> <li><a href="/wiki/Allegro_gravitational-wave_detector" title="Allegro gravitational-wave detector">ALLEGRO</a> (<a href="/w/index.php?title=International_Gravitational_Event_Collaboration&action=edit&redlink=1" class="new" title="International Gravitational Event Collaboration (page does not exist)">IGEC</a>)</li> <li><a href="/wiki/NIOBE" title="NIOBE">NIOBE</a> (<a href="/w/index.php?title=International_Gravitational_Event_Collaboration&action=edit&redlink=1" class="new" title="International Gravitational Event Collaboration (page does not exist)">IGEC</a>)</li> <li><a href="/w/index.php?title=Stanford_gravitational_wave_detector&action=edit&redlink=1" class="new" title="Stanford gravitational wave detector (page does not exist)">Stanford gravitational wave detector</a></li> <li><a href="/w/index.php?title=ALTAIR_(gravitational_wave_detector)&action=edit&redlink=1" class="new" title="ALTAIR (gravitational wave detector) (page does not exist)">ALTAIR</a></li> <li><a href="/w/index.php?title=GEOGRAV&action=edit&redlink=1" class="new" title="GEOGRAV (page does not exist)">GEOGRAV</a></li> <li><a href="/w/index.php?title=AGATA_(gravitational_wave_detector)&action=edit&redlink=1" class="new" title="AGATA (gravitational wave detector) (page does not exist)">AGATA</a></li> <li><a href="/wiki/Weber_bar" title="Weber bar">Weber bar</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Proposed</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Torsion-bar_antenna" title="Torsion-bar antenna">TOBA</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past proposals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/MiniGrail" title="MiniGrail">GRAIL</a> (downsized to <a href="/wiki/MiniGrail" title="MiniGrail">MiniGRAIL</a>)</li> <li><a href="/w/index.php?title=Truncated_Icosahedral_Gravitational_Wave_Antenna&action=edit&redlink=1" class="new" title="Truncated Icosahedral Gravitational Wave Antenna (page does not exist)">TIGA</a></li> <li><a href="/w/index.php?title=SFERA&action=edit&redlink=1" class="new" title="SFERA (page does not exist)">SFERA</a></li> <li><a href="/wiki/Mario_Schenberg_(Gravitational_Wave_Detector)" title="Mario Schenberg (Gravitational Wave Detector)">Graviton</a> (downsized to <a href="/wiki/Mario_Schenberg_(Gravitational_Wave_Detector)" title="Mario Schenberg (Gravitational Wave Detector)">Mario Schenberg</a>)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ground-based_interferometric_gravitational-wave_search" title="Ground-based interferometric gravitational-wave search"> Ground-based<br />interferometers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Active</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AIGO" title="AIGO">AIGO</a> (<a href="/wiki/ACIGA" title="ACIGA">ACIGA</a>)</li> <li><a href="/wiki/CLIO" title="CLIO">CLIO</a></li> <li><a href="/wiki/Holometer" title="Holometer">Fermilab holometer</a></li> <li><a href="/wiki/GEO600" title="GEO600">GEO600</a></li> <li><a href="/wiki/LIGO" title="LIGO">Advanced LIGO</a> (<a href="/wiki/LIGO_Scientific_Collaboration" title="LIGO Scientific Collaboration">LIGO Scientific Collaboration</a>)</li> <li><a href="/wiki/KAGRA" title="KAGRA">KAGRA</a></li> <li><a href="/wiki/Virgo_interferometer" title="Virgo interferometer">Advanced Virgo</a> (<a href="/wiki/European_Gravitational_Observatory" title="European Gravitational Observatory">European Gravitational Observatory</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/TAMA_300" title="TAMA 300">TAMA 300</a></li> <li><a href="/wiki/TAMA_300" title="TAMA 300">TAMA 20, later known as LISM</a></li> <li><a href="/w/index.php?title=TENKO-100&action=edit&redlink=1" class="new" title="TENKO-100 (page does not exist)">TENKO-100</a></li> <li><a href="/wiki/LIGO#Background" title="LIGO">Caltech 40m interferometer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Planned</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indian_Initiative_in_Gravitational-wave_Observations" title="Indian Initiative in Gravitational-wave Observations">INDIGO (LIGO-India)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Proposed</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cosmic_Explorer_(gravitational_wave_observatory)" title="Cosmic Explorer (gravitational wave observatory)">Cosmic Explorer</a></li> <li><a href="/wiki/Einstein_Telescope" title="Einstein Telescope">Einstein Telescope</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past proposals</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/LIGO-Australia" class="mw-redirect" title="LIGO-Australia">LIGO-Australia</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Space-based<br />interferometers</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Planned</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Laser_Interferometer_Space_Antenna" title="Laser Interferometer Space Antenna">LISA</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Proposed</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Big_Bang_Observer" title="Big Bang Observer">Big Bang Observer</a></li> <li><a href="/wiki/Deci-hertz_Interferometer_Gravitational_wave_Observatory" title="Deci-hertz Interferometer Gravitational wave Observatory">DECIGO</a></li> <li><a href="/wiki/TianQin" title="TianQin">TianQin</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pulsar_timing_array" title="Pulsar timing array">Pulsar timing arrays</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/European_Pulsar_Timing_Array" title="European Pulsar Timing Array">EPTA</a></li> <li><a href="/wiki/International_Pulsar_Timing_Array" title="International Pulsar Timing Array">IPTA</a></li> <li><a href="/wiki/North_American_Nanohertz_Observatory_for_Gravitational_Waves" title="North American Nanohertz Observatory for Gravitational Waves">NANOGrav</a></li> <li><a href="/wiki/Parkes_Observatory" title="Parkes Observatory">PPTA</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Data analysis</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Einstein@Home" title="Einstein@Home">Einstein@Home</a></li> <li><a href="/wiki/PyCBC" title="PyCBC">PyCBC</a></li> <li><a href="/wiki/Zooniverse" title="Zooniverse">Zooniverse</a>: Gravity Spy</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Observations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Events</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_gravitational_wave_observations" title="List of gravitational wave observations">List of observations</a></li> <li><a href="/wiki/First_observation_of_gravitational_waves" title="First observation of gravitational waves">First observation (GW150914)</a></li> <li><a href="/wiki/GW151226" title="GW151226">GW151226</a></li> <li><a href="/wiki/GW170104" title="GW170104">GW170104</a></li> <li><a href="/wiki/GW170608" title="GW170608">GW170608</a></li> <li><a href="/wiki/GW170814" title="GW170814">GW170814</a></li> <li><a href="/wiki/GW170817" title="GW170817">GW170817</a> (first <a href="/wiki/Neutron_star_merger" title="Neutron star merger">neutron star merger</a>)</li> <li><a href="/wiki/GW190412" title="GW190412">GW190412</a></li> <li><a href="/wiki/GW190521" title="GW190521">GW190521</a> (first-ever possible light from bh-bh merger)</li> <li><a href="/wiki/GW190814" title="GW190814">GW190814</a> (first-ever "mass gap" collision)</li> <li><a href="/w/index.php?title=GW200105&action=edit&redlink=1" class="new" title="GW200105 (page does not exist)">GW200105</a> (first black hole - neutron star merger)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Methods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Direct detection <ul><li><a href="/wiki/Interferometric_gravitational-wave_detector" class="mw-redirect" title="Interferometric gravitational-wave detector">Laser interferometers</a></li> <li>Resonant mass detectors</li> <li><i>Proposed: <a href="/wiki/Atom_interferometer" title="Atom interferometer">Atom interferometers</a></i></li></ul></li> <li>Indirect detection <ul><li><a href="/wiki/Cosmic_microwave_background#B-modes" title="Cosmic microwave background">B-modes</a> of <a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">CMB</a></li> <li><a href="/wiki/Pulsar_timing_array" title="Pulsar timing array">Pulsar timing array</a></li> <li><a href="/wiki/Binary_pulsar" title="Binary pulsar">Binary pulsar</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_relativity" title="General relativity">General relativity</a></li> <li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Tests of general relativity</a></li> <li><a href="/wiki/Alternatives_to_general_relativity" title="Alternatives to general relativity">Metric theories</a></li> <li><a href="/wiki/Graviton" title="Graviton">Graviton</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Effects / properties</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gravitational_wave#Effects_of_passing" title="Gravitational wave">Polarization</a></li> <li><a href="/wiki/Spin-flip" title="Spin-flip">Spin-flip</a></li> <li><a class="mw-selflink selflink">Redshift</a></li> <li>Travel with <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a></li> <li>h strain</li> <li>Chirp signal (<a href="/wiki/Chirp_mass" title="Chirp mass">chirp mass</a>)</li> <li>Carried <a href="/wiki/Energy" title="Energy">energy</a></li> <li><a href="/wiki/Gravitational_wave_background" title="Gravitational wave background">Gravitational wave background</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types / sources</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stochastic" title="Stochastic">Stochastic</a> <ul><li><a href="/wiki/Cosmic_inflation" title="Cosmic inflation">Cosmic inflation</a>-<a href="/wiki/Quantum_fluctuation" title="Quantum fluctuation">quantum fluctuation</a></li> <li><a href="/wiki/Phase_transition" title="Phase transition">Phase transition</a></li></ul></li> <li>Binary inspiral <ul><li><a href="/wiki/Supermassive_black_hole" title="Supermassive black hole">Supermassive black holes</a></li> <li><a href="/wiki/Stellar_black_hole" title="Stellar black hole">Stellar black holes</a></li> <li><a href="/wiki/Neutron_star" title="Neutron star">Neutron stars</a></li> <li><a href="/wiki/Extreme_mass_ratio_inspiral" title="Extreme mass ratio inspiral">EMRI</a></li></ul></li> <li>Continuous <ul><li>Rotating neutron star</li></ul></li> <li>Burst <ul><li><a href="/wiki/Supernova" title="Supernova">Supernova</a> or from <i>unknown</i> sources</li></ul></li> <li>Hypothesis <ul><li>Colliding <a href="/wiki/Cosmic_string" title="Cosmic string">cosmic string</a> and <i>other unknown</i> sources</li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Cosmology" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Cosmology_topics" title="Template:Cosmology topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Cosmology_topics" title="Template talk:Cosmology topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Cosmology_topics" title="Special:EditPage/Template:Cosmology topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Cosmology" style="font-size:114%;margin:0 4em"><a href="/wiki/Cosmology" title="Cosmology">Cosmology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Age_of_the_universe" title="Age of the universe">Age of the universe</a></li> <li><a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a></li> <li><a href="/wiki/Chronology_of_the_universe" title="Chronology of the universe">Chronology of the universe</a></li> <li><a href="/wiki/Universe" title="Universe">Universe</a></li> <li><a href="/wiki/Observable_universe" title="Observable universe">Observable universe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">History of<br />cosmological theories</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Discovery of cosmic microwave background</a></li> <li><a href="/wiki/History_of_the_Big_Bang_theory" title="History of the Big Bang theory">History of the Big Bang theory</a></li> <li><a href="/wiki/Religious_interpretations_of_the_Big_Bang_theory" title="Religious interpretations of the Big Bang theory">Religious interpretations of the Big Bang</a></li> <li><a href="/wiki/Timeline_of_cosmological_theories" title="Timeline of cosmological theories">Timeline of cosmological theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Past universe</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cosmic_microwave_background" title="Cosmic microwave background">Cosmic microwave background</a></li> <li><a href="/wiki/Cosmic_neutrino_background" title="Cosmic neutrino background">Cosmic neutrino background</a></li> <li><a href="/wiki/Gravitational_wave_background" title="Gravitational wave background">Gravitational wave background</a></li> <li><a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">Inflation</a></li> <li><a href="/wiki/Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Nucleosynthesis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Present universe</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW metric</a></li> <li><a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a></li> <li><a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a></li> <li><a href="/wiki/Expansion_of_the_universe" title="Expansion of the universe">Expansion of the universe</a></li> <li><a href="/wiki/Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">Accelerating expansion</a></li> <li><a class="mw-selflink selflink">Redshift</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Future universe</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Future_of_an_expanding_universe" title="Future of an expanding universe">Future of an expanding universe</a></li> <li><a href="/wiki/Ultimate_fate_of_the_universe" title="Ultimate fate of the universe">Ultimate fate of the universe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dark_energy" title="Dark energy">Dark energy</a></li> <li><a href="/wiki/Dark_fluid" title="Dark fluid">Dark fluid</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Quintessence_(physics)" title="Quintessence (physics)">Quintessence</a></li> <li><a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Structure formation</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Galaxy_filament" title="Galaxy filament">Galaxy filament</a></li> <li><a href="/wiki/Galaxy_formation_and_evolution" title="Galaxy formation and evolution">Galaxy formation</a></li> <li><a href="/wiki/Large_quasar_group" title="Large quasar group">Large quasar group</a></li> <li><a href="/wiki/Large-scale_structure_of_the_cosmos" class="mw-redirect" title="Large-scale structure of the cosmos">Large-scale structure</a></li> <li><a href="/wiki/Reionization" title="Reionization">Reionization</a></li> <li><a href="/wiki/Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></li> <li><a href="/wiki/Structure_formation" title="Structure formation">Structure formation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/2dF_Galaxy_Redshift_Survey" title="2dF Galaxy Redshift Survey">2dF</a></li> <li><a href="/wiki/6dF_Galaxy_Survey" title="6dF Galaxy Survey">6dF</a></li> <li><a href="/wiki/BOOMERanG_experiment" title="BOOMERanG experiment">BOOMERanG</a></li> <li><a href="/wiki/Cosmic_Background_Explorer" title="Cosmic Background Explorer">COBE</a></li> <li><a href="/wiki/Illustris_project" title="Illustris project">Illustris project</a></li> <li><a href="/wiki/Observational_cosmology" title="Observational cosmology">Observational cosmology</a></li> <li><a href="/wiki/Planck_(spacecraft)" title="Planck (spacecraft)">Planck</a></li> <li><a href="/wiki/Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">SDSS</a></li> <li><a href="/wiki/Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">WMAP</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/16px-Crab_Nebula.jpg" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/24px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/32px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">astronomy portal</a></b></div></td></tr></tbody></table></div>    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[\"CITEREFGoldhaberGroomKimAldering2001\"] = 1,\n [\"CITEREFGrishchuk2005\"] = 1,\n [\"CITEREFGrønHervik,_Sigbjørn2007\"] = 1,\n [\"CITEREFHarrison1992\"] = 1,\n [\"CITEREFHarrison2000\"] = 1,\n [\"CITEREFHoggBaldryBlantonEisenstein2002\"] = 1,\n [\"CITEREFHubble1929\"] = 1,\n [\"CITEREFHuchra\"] = 2,\n [\"CITEREFHuggins1868\"] = 1,\n [\"CITEREFIvesStilwell1938\"] = 1,\n [\"CITEREFKarachentsevMakarovSharinaDolphin2003\"] = 1,\n [\"CITEREFKempner2022\"] = 1,\n [\"CITEREFKoupelisKuhn2007\"] = 1,\n [\"CITEREFKuhnKoupelis2004\"] = 1,\n [\"CITEREFKutner,_Marc2003\"] = 1,\n [\"CITEREFLehnertNesvadbaCubySwinbank2010\"] = 1,\n [\"CITEREFLesgourguesPastor2006\"] = 1,\n [\"CITEREFLewisFrancisBarnesKwan2008\"] = 1,\n [\"CITEREFLibbrecht1988\"] = 1,\n [\"CITEREFLineweaverDavis2005\"] = 1,\n [\"CITEREFLongair1998\"] = 1,\n [\"CITEREFMaulik2005\"] = 1,\n [\"CITEREFMerrifieldHill2009\"] = 1,\n [\"CITEREFMisnerThorne,_Kip_S.Wheeler,_John_Archibald1973\"] = 1,\n [\"CITEREFNaozNoterBarkana2006\"] = 1,\n [\"CITEREFNemiroff1993\"] = 2,\n [\"CITEREFNussbaumerLydia_Bieri2009\"] = 1,\n [\"CITEREFO\u0026#039;ConnorRobertson1998\"] = 1,\n [\"CITEREFOeschBrammervan_DokkumIllingworth2016\"] = 1,\n [\"CITEREFOort1970\"] = 1,\n [\"CITEREFOverbye2015\"] = 1,\n [\"CITEREFPannekoek1961\"] = 1,\n [\"CITEREFPeebles1993\"] = 1,\n [\"CITEREFPoundRebka1960\"] = 1,\n [\"CITEREFReber1995\"] = 1,\n [\"CITEREFRybickiLightman1979\"] = 1,\n [\"CITEREFSachsWolfe1967\"] = 1,\n [\"CITEREFSalvaterraValleCampanaChincarini2009\"] = 1,\n [\"CITEREFSaxena2018\"] = 1,\n [\"CITEREFSlipher1912\"] = 1,\n [\"CITEREFSlipher1915\"] = 2,\n [\"CITEREFSmail,_IanOwen,_F._N.Morrison,_G._E.Keel,_W._C.2002\"] = 1,\n [\"CITEREFSobralMattheeDarvishSchaerer2015\"] = 1,\n [\"CITEREFStaff2015\"] = 1,\n [\"CITEREFStaff2018\"] = 1,\n [\"CITEREFStaff2022\"] = 1,\n [\"CITEREFTaylorWheeler1992\"] = 1,\n [\"CITEREFTotani,_TomonoriYoshii,_YuzuruIwamuro,_FumihideMaihara,_Toshinori2001\"] = 1,\n [\"CITEREFWalterBertoldiCarilliCox2003\"] = 1,\n [\"CITEREFWatsonChristensenKnudsenRichard2015\"] = 1,\n [\"CITEREFWeinberg1971\"] = 1,\n [\"CITEREFWeinberg1993\"] = 1,\n [\"CITEREFWeinberg2008\"] = 1,\n [\"CITEREFWoodhouse2017\"] = 1,\n [\"CITEREFde_Sitter1934\"] = 1,\n}\ntemplate_list = table#1 {\n [\"!\"] = 1,\n [\"=\"] = 19,\n [\"About\"] = 1,\n [\"Authority control\"] = 1,\n [\"Blockquote\"] = 1,\n [\"Cite OED\"] = 1,\n [\"Cite arXiv\"] = 1,\n [\"Cite book\"] = 29,\n [\"Cite conference\"] = 2,\n [\"Cite journal\"] = 51,\n [\"Cite news\"] = 2,\n [\"Cite web\"] = 14,\n [\"Cn\"] = 9,\n [\"Commons\"] = 1,\n [\"Cosmology topics\"] = 1,\n [\"Featured article\"] = 1,\n [\"General relativity sidebar\"] = 1,\n [\"Gravitational waves\"] = 1,\n [\"Harvnb\"] = 1,\n [\"ISBN\"] = 1,\n [\"Main\"] = 4,\n [\"Math\"] = 60,\n [\"Page needed\"] = 1,\n [\"Physical cosmology\"] = 1,\n [\"Portal bar\"] = 1,\n [\"Redirect\"] = 1,\n [\"Reflist\"] = 1,\n [\"See also\"] = 1,\n [\"Short description\"] = 1,\n [\"Special relativity sidebar\"] = 1,\n [\"Sup\"] = 3,\n [\"Webarchive\"] = 2,\n [\"Wiktionary\"] = 1,\n}\narticle_whitelist = table#1 {\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\n","limitreport-profile":[["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::gsub","180","17.6"],["?","120","11.8"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::callParserFunction","120","11.8"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::find","120","11.8"],["recursiveClone \u003CmwInit.lua:45\u003E","60","5.9"],["makeMessage \u003Cmw.message.lua:76\u003E","40","3.9"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::match","40","3.9"],["is_set \u003CModule:Citation/CS1/Utilities:23\u003E","40","3.9"],["dataWrapper 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Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2001-11-19T19:54:21Z","dateModified":"2024-11-23T19:09:38Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/6\/6a\/Redshift.svg","headline":"relative increase in wavelength of electromagnetic radiation in the emission spectrum of astronomical objects"}</script> </body> </html>