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<ul id="toc-Direct_measurement-sublist" class="vector-toc-list"> <li id="toc-Astronomical_unit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomical_unit"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Astronomical unit</span> </div> </a> <ul id="toc-Astronomical_unit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parallax" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parallax"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Parallax</span> </div> </a> <ul id="toc-Parallax-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Standard_candles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Standard_candles"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Standard candles</span> </div> </a> <button aria-controls="toc-Standard_candles-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 Standard candles subsection</span> </button> <ul id="toc-Standard_candles-sublist" class="vector-toc-list"> <li id="toc-Problems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Problems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Problems</span> </div> </a> <ul id="toc-Problems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Standard_siren" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Standard_siren"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Standard siren</span> </div> </a> <ul id="toc-Standard_siren-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Standard_ruler" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Standard_ruler"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Standard ruler</span> </div> </a> <ul id="toc-Standard_ruler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Galactic_distance_indicators" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Galactic_distance_indicators"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Galactic distance indicators</span> </div> </a> <button aria-controls="toc-Galactic_distance_indicators-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 Galactic distance indicators subsection</span> </button> <ul id="toc-Galactic_distance_indicators-sublist" class="vector-toc-list"> <li id="toc-Main_sequence_fitting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Main_sequence_fitting"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Main sequence fitting</span> </div> </a> <ul id="toc-Main_sequence_fitting-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Extragalactic_distance_scale" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Extragalactic_distance_scale"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Extragalactic distance scale</span> </div> </a> <button aria-controls="toc-Extragalactic_distance_scale-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 Extragalactic distance scale subsection</span> </button> <ul id="toc-Extragalactic_distance_scale-sublist" class="vector-toc-list"> <li id="toc-Wilson–Bappu_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Wilson–Bappu_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Wilson–Bappu effect</span> </div> </a> <ul id="toc-Wilson–Bappu_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Classical_Cepheids" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classical_Cepheids"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Classical Cepheids</span> </div> </a> <ul id="toc-Classical_Cepheids-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Supernovae" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Supernovae"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Supernovae</span> </div> </a> <ul id="toc-Supernovae-sublist" class="vector-toc-list"> <li id="toc-Measuring_a_supernova's_photosphere" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Measuring_a_supernova's_photosphere"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.1</span> <span>Measuring a supernova's photosphere</span> </div> </a> <ul id="toc-Measuring_a_supernova's_photosphere-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Type_Ia_light_curves" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Type_Ia_light_curves"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.2</span> <span>Type Ia light curves</span> </div> </a> <ul id="toc-Type_Ia_light_curves-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Novae_in_distance_determinations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Novae_in_distance_determinations"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.3</span> <span>Novae in distance determinations</span> </div> </a> <ul id="toc-Novae_in_distance_determinations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Globular_cluster_luminosity_function" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Globular_cluster_luminosity_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Globular cluster luminosity function</span> </div> </a> <ul id="toc-Globular_cluster_luminosity_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Planetary_nebula_luminosity_function" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Planetary_nebula_luminosity_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Planetary nebula luminosity function</span> </div> </a> <ul id="toc-Planetary_nebula_luminosity_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface_brightness_fluctuation_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surface_brightness_fluctuation_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Surface brightness fluctuation method</span> </div> </a> <ul id="toc-Surface_brightness_fluctuation_method-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sigma-D_relation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sigma-D_relation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.7</span> <span>Sigma-D relation</span> </div> </a> <ul id="toc-Sigma-D_relation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Overlap_and_scaling" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Overlap_and_scaling"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Overlap and scaling</span> </div> </a> <ul id="toc-Overlap_and_scaling-sublist" class="vector-toc-list"> </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">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-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">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </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">12</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">Cosmic distance ladder</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 31 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-31" 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">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D9%84%D9%85_%D8%A7%D9%84%D9%85%D8%B3%D8%A7%D9%81%D8%A7%D8%AA_%D8%A7%D9%84%D9%83%D9%88%D9%86%D9%8A%D8%A9" title="سلم المسافات الكونية – Arabic" lang="ar" hreflang="ar" data-title="سلم المسافات الكونية" 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/Escalera_de_distancies_c%C3%B3smiques" title="Escalera de distancies cósmiques – Asturian" lang="ast" hreflang="ast" data-title="Escalera de distancies cósmiques" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Escala_de_dist%C3%A0ncies_c%C3%B2smiques" title="Escala de distàncies còsmiques – Catalan" lang="ca" hreflang="ca" data-title="Escala de distàncies còsmiques" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C5%BDeb%C5%99%C3%ADk_kosmick%C3%BDch_vzd%C3%A1lenost%C3%AD" title="Žebřík kosmických vzdáleností – Czech" lang="cs" hreflang="cs" data-title="Žebřík kosmických vzdáleností" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kosmisk_afstandsstige" title="Kosmisk afstandsstige – Danish" lang="da" hreflang="da" data-title="Kosmisk afstandsstige" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Entfernungsleiter" title="Entfernungsleiter – German" lang="de" hreflang="de" data-title="Entfernungsleiter" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Escalera_de_distancias_c%C3%B3smicas" title="Escalera de distancias cósmicas – Spanish" lang="es" hreflang="es" data-title="Escalera de distancias cósmicas" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Distantzia_kosmikoen_eskailera" title="Distantzia kosmikoen eskailera – Basque" lang="eu" hreflang="eu" data-title="Distantzia kosmikoen eskailera" 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/%D9%86%D8%B1%D8%AF%D8%A8%D8%A7%D9%86_%D9%81%D8%A7%D8%B5%D9%84%D9%87_%DA%A9%DB%8C%D9%87%D8%A7%D9%86%DB%8C" title="نردبان فاصله کیهانی – Persian" lang="fa" hreflang="fa" data-title="نردبان فاصله کیهانی" 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/Mesure_des_distances_en_astronomie" title="Mesure des distances en astronomie – French" lang="fr" hreflang="fr" data-title="Mesure des distances en astronomie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9A%B0%EC%A3%BC_%EA%B1%B0%EB%A6%AC_%EC%82%AC%EB%8B%A4%EB%A6%AC" title="우주 거리 사다리 – Korean" lang="ko" hreflang="ko" data-title="우주 거리 사다리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Standardna_svije%C4%87a" title="Standardna svijeća – Croatian" lang="hr" hreflang="hr" data-title="Standardna svijeća" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Scala_delle_distanze_cosmiche" title="Scala delle distanze cosmiche – Italian" lang="it" hreflang="it" data-title="Scala delle distanze cosmiche" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BA%D0%B0%D0%BB%D0%B0_%D0%BD%D0%B0_%D0%B2%D1%81%D0%B5%D0%BB%D0%B5%D0%BD%D1%81%D0%BA%D0%B8_%D1%80%D0%B0%D1%81%D1%82%D0%BE%D1%98%D0%B0%D0%BD%D0%B8%D1%98%D0%B0" title="Скала на вселенски растојанија – Macedonian" lang="mk" hreflang="mk" data-title="Скала на вселенски растојанија" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tangga_jarak_kosmos" title="Tangga jarak kosmos – Malay" lang="ms" hreflang="ms" data-title="Tangga jarak kosmos" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Astronomische_afstandsmeting" title="Astronomische afstandsmeting – Dutch" lang="nl" hreflang="nl" data-title="Astronomische afstandsmeting" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%AE%87%E5%AE%99%E3%81%AE%E8%B7%9D%E9%9B%A2%E6%A2%AF%E5%AD%90" title="宇宙の距離梯子 – Japanese" lang="ja" hreflang="ja" data-title="宇宙の距離梯子" 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/Kosmisk_avstandsstige" title="Kosmisk avstandsstige – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kosmisk avstandsstige" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Drabina_odleg%C5%82o%C5%9Bci_kosmicznych" title="Drabina odległości kosmicznych – Polish" lang="pl" hreflang="pl" data-title="Drabina odległości kosmicznych" 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/Escala_de_dist%C3%A2ncias_c%C3%B3smicas" title="Escala de distâncias cósmicas – Portuguese" lang="pt" hreflang="pt" data-title="Escala de distâncias cósmicas" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/M%C4%83surarea_distan%C8%9Belor_%C3%AEn_astronomie" title="Măsurarea distanțelor în astronomie – Romanian" lang="ro" hreflang="ro" data-title="Măsurarea distanțelor în astronomie" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A8%D0%BA%D0%B0%D0%BB%D0%B0_%D1%80%D0%B0%D1%81%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%B8%D0%B9_%D0%B2_%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D0%B8" title="Шкала расстояний в астрономии – Russian" lang="ru" hreflang="ru" data-title="Шкала расстояний в астрономии" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Cosmic_distance_ladder" title="Cosmic distance ladder – Simple English" lang="en-simple" hreflang="en-simple" data-title="Cosmic distance ladder" 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-sr mw-list-item"><a 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Stellar_distance&redirect=no" class="mw-redirect" title="Stellar distance">Stellar distance</a>)</span></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">Succession of methods by which astronomers determine the distances to celestial objects</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">For various definitions of distance in cosmology, see <a href="/wiki/Distance_measures_(cosmology)" class="mw-redirect" title="Distance measures (cosmology)">Distance measures (cosmology)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Lead_too_short plainlinks metadata ambox ambox-content ambox-lead_too_short" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article's <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Length" title="Wikipedia:Manual of Style/Lead section">lead section</a> <b>may be too short to adequately <a href="/wiki/Wikipedia:Summary_style" title="Wikipedia:Summary style">summarize</a> the key points</b>.<span class="hide-when-compact"> Please consider expanding the lead to <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Provide_an_accessible_overview" title="Wikipedia:Manual of Style/Lead section">provide an accessible overview</a> of all important aspects of the article.</span> <span class="date-container"><i>(<span class="date">January 2023</span>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Extragalactic_Distance_Ladder_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Extragalactic_Distance_Ladder_en.svg/300px-Extragalactic_Distance_Ladder_en.svg.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Extragalactic_Distance_Ladder_en.svg/450px-Extragalactic_Distance_Ladder_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Extragalactic_Distance_Ladder_en.svg/600px-Extragalactic_Distance_Ladder_en.svg.png 2x" data-file-width="720" data-file-height="540" /></a><figcaption> <div><ul><li>Light green boxes: Technique applicable to <a href="/wiki/Galaxy_formation_and_evolution" title="Galaxy formation and evolution">star-forming galaxies</a>.</li><li>Light blue boxes: Technique applicable to <a href="/wiki/Population_II" class="mw-redirect" title="Population II">population II</a> galaxies.</li><li>Light Purple boxes: Geometric distance technique.</li><li>Light Red box: The <a href="/wiki/Planetary_nebula_luminosity_function" title="Planetary nebula luminosity function">planetary nebula luminosity function</a> technique is applicable to all populations of the <a href="/wiki/Virgo_Supercluster" title="Virgo Supercluster">Virgo Supercluster</a>.</li><li>Solid black lines: Well calibrated ladder step.</li><li>Dashed black lines: Uncertain calibration ladder step.</li></ul></div></figcaption></figure> <p>The <b>cosmic distance ladder</b> (also known as the <b>extragalactic distance scale</b>) is the succession of methods by which astronomers determine the distances to celestial objects. A <i>direct</i> distance measurement of an astronomical object is possible only for those objects that are "close enough" (within about a thousand <a href="/wiki/Parsec" title="Parsec">parsecs</a>) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known <a href="/wiki/Luminosity" title="Luminosity">luminosity</a>. </p><p>The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Direct_measurement">Direct measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=1" title="Edit section: Direct measurement"><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:The_Astronomer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/The_Astronomer.jpg/170px-The_Astronomer.jpg" decoding="async" width="170" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/The_Astronomer.jpg/255px-The_Astronomer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/The_Astronomer.jpg/340px-The_Astronomer.jpg 2x" data-file-width="1013" data-file-height="1600" /></a><figcaption>The sculpture <i>The Astronomer</i> shows the use of parallax to measure distance. It is made from parts of the Yale–Columbia Refractor telescope (1924) damaged when the <a href="/wiki/2003_Canberra_bushfires" title="2003 Canberra bushfires">2003 Canberra bushfires</a> burned out the <a href="/wiki/Mount_Stromlo_Observatory" title="Mount Stromlo Observatory">Mount Stromlo Observatory</a>; at <a href="/wiki/Questacon" title="Questacon">Questacon</a>, <a href="/wiki/Canberra" title="Canberra">Canberra</a>.<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></figcaption></figure> <p>At the base of the ladder are <i>fundamental</i> distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. The precise measurement of stellar positions is part of the discipline of <a href="/wiki/Astrometry" title="Astrometry">astrometry</a>. Early fundamental distances—such as the radii of the earth, moon and sun, and the distances between them—were well estimated with very low technology by the ancient Greeks.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Astronomical_unit">Astronomical unit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=2" title="Edit section: Astronomical unit"><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/Astronomical_unit" title="Astronomical unit">Astronomical unit</a></div> <p>Direct distance measurements are based upon the astronomical unit (AU), which is defined as the mean distance between the <a href="/wiki/Earth" title="Earth">Earth</a> and the <a href="/wiki/Sun" title="Sun">Sun</a>. <a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws</a> provide precise <a href="/wiki/Ratio" title="Ratio">ratios</a> of the orbit sizes of objects orbiting the Sun, but provide no measurement of the overall scale of the orbit system. <a href="/wiki/Radar" title="Radar">Radar</a> is used to measure the distance between the orbits of the Earth and of a second body. From that measurement and the ratio of the two orbit sizes, the size of Earth's orbit is calculated. The Earth's orbit is known with an absolute precision of a few meters and a relative precision of a few parts in 100 billion (<span class="nowrap"><span data-sort-value="6989100000000000000♠"></span>1<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−11</sup></span>). </p><p>Historically, observations of <a href="/wiki/Transit_of_Venus#Scientific_interest_in_transits" title="Transit of Venus">Venus transits</a> were crucial in determining the AU; in the first half of the 20th century, observations of <a href="/wiki/Asteroids" class="mw-redirect" title="Asteroids">asteroids</a> were also important. Presently the orbit of Earth is determined with high precision using <a href="/wiki/Radar" title="Radar">radar</a> measurements of distances to Venus and other nearby planets and asteroids,<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> and by tracking interplanetary spacecraft in their orbits around the Sun through the <a href="/wiki/Solar_System" title="Solar System">Solar System</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Parallax">Parallax</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=3" title="Edit section: Parallax"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="excerpt-block"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable dablink excerpt-hat selfref">This section is an excerpt from <a href="/wiki/Parallax_in_astronomy" title="Parallax in astronomy">Parallax in astronomy</a>.<span class="mw-editsection-like plainlinks"><span class="mw-editsection-bracket">[</span><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Parallax_in_astronomy&action=edit">edit</a><span class="mw-editsection-bracket">]</span></span></div><div class="excerpt"> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:ParallaxV2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/ParallaxV2.svg/220px-ParallaxV2.svg.png" decoding="async" width="220" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/ParallaxV2.svg/330px-ParallaxV2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/ParallaxV2.svg/440px-ParallaxV2.svg.png 2x" data-file-width="550" data-file-height="400" /></a><figcaption>Stellar parallax motion from annual parallax. Half the apex angle is the parallax angle.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Parallax_geo_or_helio_static.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Parallax_geo_or_helio_static.PNG/260px-Parallax_geo_or_helio_static.PNG" decoding="async" width="260" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Parallax_geo_or_helio_static.PNG/390px-Parallax_geo_or_helio_static.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/1/10/Parallax_geo_or_helio_static.PNG 2x" data-file-width="446" data-file-height="386" /></a><figcaption>Parallax is an angle subtended by a line on a point. In the upper diagram, the Earth in its orbit sweeps the parallax angle subtended on the Sun. The lower diagram shows an equal angle swept by the Sun in a geostatic model. A similar diagram can be drawn for a star except that the angle of parallax would be minuscule.</figcaption></figure> <p>The most important fundamental <a href="/wiki/Distance_measurement" class="mw-redirect" title="Distance measurement">distance measurements</a> in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> come from trigonometric <a href="/wiki/Parallax" title="Parallax">parallax</a>, as applied in the <i><a href="/wiki/Stellar_parallax_method" class="mw-redirect" title="Stellar parallax method">stellar parallax method</a></i>. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an <a href="/wiki/Isosceles_triangle" title="Isosceles triangle">isosceles triangle</a>, with 2 <a href="/wiki/Astronomical_unit" title="Astronomical unit">AU</a> (the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal-length legs. The amount of shift is quite small, even for the nearest stars, measuring 1 <a href="/wiki/Minute_and_second_of_arc" title="Minute and second of arc">arcsecond</a> for an object at 1 parsec's distance (3.26 <a href="/wiki/Light-year" title="Light-year">light-years</a>), and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of <i><a href="/wiki/Parsecs" class="mw-redirect" title="Parsecs">parsecs</a></i> (parallax arcseconds); light-years are used in popular media. </p><p>Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars which are near enough to have a parallax larger than a few times the <a href="/wiki/Accuracy_and_precision" title="Accuracy and precision">precision</a> of the measurement. In the 1990s, for example, the <a href="/wiki/Hipparcos" title="Hipparcos">Hipparcos</a> mission obtained parallaxes for over a hundred thousand stars with a precision of about a <a href="/wiki/Minute_of_arc" class="mw-redirect" title="Minute of arc">milliarcsecond</a>,<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> providing useful distances for stars out to a few hundred parsecs. The <a href="/wiki/Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble Space Telescope</a>'s <a href="/wiki/Wide_Field_Camera_3" title="Wide Field Camera 3">Wide Field Camera 3</a> has the potential to provide a precision of 20 to 40 <i>micro</i>arcseconds, enabling reliable distance measurements up to 5,000 parsecs (16,000 ly) for small numbers of stars.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><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> The <i><a href="/wiki/Gaia_(spacecraft)" title="Gaia (spacecraft)">Gaia</a></i> space mission provided similarly accurate distances to most stars brighter than 15th magnitude.<sup id="cite_ref-Parallax_in_astronomy_dr2_7-0" class="reference"><a href="#cite_note-Parallax_in_astronomy_dr2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Distances can be measured within 10% as far as the <a href="/wiki/Galactic_Center" title="Galactic Center">Galactic Center</a>, about 30,000 light years away. Stars have a velocity relative to the Sun that causes <a href="/wiki/Proper_motion" title="Proper motion">proper motion</a> (transverse across the sky) and <a href="/wiki/Radial_velocity" title="Radial velocity">radial velocity</a> (motion toward or away from the Sun). The former is determined by plotting the changing position of the stars over many years, while the latter comes from measuring the <a href="/wiki/Doppler_shift" class="mw-redirect" title="Doppler shift">Doppler shift</a> of the star's spectrum caused by motion along the line of sight. For a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from <a href="/wiki/Statistical_analysis" class="mw-redirect" title="Statistical analysis">statistical analysis</a> of the proper motions relative to their radial velocities. This <a href="/wiki/Statistical_parallax" class="mw-redirect" title="Statistical parallax">statistical parallax</a> method is useful for measuring the distances of bright stars beyond 50 parsecs and giant <a href="/wiki/Variable_star" title="Variable star">variable stars</a>, including <a href="/wiki/Cepheid_variable" title="Cepheid variable">Cepheids</a> and the <a href="/wiki/RR_Lyrae_variable" title="RR Lyrae variable">RR Lyrae variables</a>.<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> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cosmic_distance_ladder.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Cosmic_distance_ladder.jpg/330px-Cosmic_distance_ladder.jpg" decoding="async" width="330" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Cosmic_distance_ladder.jpg/495px-Cosmic_distance_ladder.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Cosmic_distance_ladder.jpg/660px-Cosmic_distance_ladder.jpg 2x" data-file-width="1280" data-file-height="832" /></a><figcaption>Parallax measurements may be an important clue to understanding three of the universe's most elusive components: <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a>, <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a> and <a href="/wiki/Neutrino" title="Neutrino">neutrinos</a>.<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></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg/220px-Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg" decoding="async" width="220" height="289" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg/330px-Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg/440px-Hubble_stretches_the_stellar_tape_measure_ten_times_further.jpg 2x" data-file-width="2400" data-file-height="3150" /></a><figcaption>Hubble Space Telescope precision stellar distance measurement has been extended 10 times further into the Milky Way.<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></figcaption></figure> <p>The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as <a href="/wiki/Stellar_parallax" title="Stellar parallax">secular parallax</a>. For stars in the <a href="/wiki/Milky_Way" title="Milky Way">Milky Way</a> disk, this corresponds to a mean baseline of 4 <a href="/wiki/Astronomical_unit" title="Astronomical unit">AU</a> per year, while for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of observed stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the uncertainty is inversely proportional to the <a href="/wiki/Square_root" title="Square root">square root</a> of the sample size.<sup id="cite_ref-Parallax_in_astronomy_popowski_11-0" class="reference"><a href="#cite_note-Parallax_in_astronomy_popowski-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Moving_cluster_parallax" class="mw-redirect" title="Moving cluster parallax">Moving cluster parallax</a> is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster. Only <a href="/wiki/Open_cluster" title="Open cluster">open clusters</a> are near enough for this technique to be useful. In particular the distance obtained for the <a href="/wiki/Hyades_(star_cluster)" title="Hyades (star cluster)">Hyades</a> has historically been an important step in the distance ladder. </p><p>Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a <a href="/wiki/Supernova_remnant" title="Supernova remnant">supernova remnant</a> or <a href="/wiki/Planetary_nebula" title="Planetary nebula">planetary nebula</a>, can be observed over time, then an <i>expansion parallax</i> distance to that cloud can be estimated. Those measurements however suffer from uncertainties in the deviation of the object from sphericity. <a href="/wiki/Binary_star" title="Binary star">Binary stars</a> which are both <a href="/wiki/Binary_star#Visual_binaries" title="Binary star">visual</a> and <a href="/wiki/Binary_star#Spectroscopic_binaries" title="Binary star">spectroscopic</a> binaries also can have their distance estimated by similar means, and do not suffer from the above geometric uncertainty. The common characteristic to these methods is that a measurement of angular motion is combined with a measurement of the absolute <a href="/wiki/Velocity" title="Velocity">velocity</a> (usually obtained via the <a href="/wiki/Doppler_effect#Astronomy" title="Doppler effect">Doppler effect</a>). The distance estimate comes from computing how far the object must be to make its observed absolute velocity appear with the observed angular motion. </p> Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio <a href="/wiki/Interferometry" title="Interferometry">interferometers</a> which can measure very small angular motions. These combine to provide fundamental distance estimates to supernovae in other galaxies.<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> Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.</div></div> <div class="mw-heading mw-heading2"><h2 id="Standard_candles">Standard candles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=4" title="Edit section: Standard candles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Almost all astronomical objects used as physical distance indicators belong to a class that has a known brightness. By comparing this known <a href="/wiki/Luminosity" title="Luminosity">luminosity</a> to an object's observed brightness, the distance to the object can be computed using the <a href="/wiki/Inverse-square_law" title="Inverse-square law">inverse-square law</a>. These objects of known brightness are termed <b>standard candles</b>, coined by <a href="/wiki/Henrietta_Swan_Leavitt" title="Henrietta Swan Leavitt">Henrietta Swan Leavitt</a>.<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> </p><p>The brightness of an object can be expressed in terms of its <a href="/wiki/Absolute_magnitude" title="Absolute magnitude">absolute magnitude</a>. This quantity is derived from the logarithm of its luminosity as seen from a distance of 10 parsecs. The <a href="/wiki/Apparent_magnitude" title="Apparent magnitude">apparent magnitude</a>, the magnitude as seen by the observer (an instrument called a <a href="/wiki/Bolometer" title="Bolometer">bolometer</a> is used), can be measured and used with the absolute magnitude to calculate the distance <i>d</i> to the object in parsecs<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> as follows: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5\cdot \log _{10}d=m-M+5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>⋅</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mi>d</mi> <mo>=</mo> <mi>m</mi> <mo>−</mo> <mi>M</mi> <mo>+</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5\cdot \log _{10}d=m-M+5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90c50e52fa0e7504e4b0974b7e663399eb9c97fb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.717ex; height:2.676ex;" alt="{\displaystyle 5\cdot \log _{10}d=m-M+5}"></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d=10^{(m-M+5)/5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mi>M</mi> <mo>+</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=10^{(m-M+5)/5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/532e814aafada80208db89caf8d726d535e20da3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.344ex; height:2.843ex;" alt="{\displaystyle d=10^{(m-M+5)/5}}"></span> where <i>m</i> is the apparent magnitude, and <i>M</i> the absolute magnitude. For this to be accurate, both magnitudes must be in the same frequency band and there can be no relative motion in the radial direction. Some means of correcting for interstellar <a href="/wiki/Extinction_(astronomy)" title="Extinction (astronomy)">extinction</a>, which also makes objects appear fainter and more red, is needed, especially if the object lies within a dusty or gaseous region.<sup id="cite_ref-ctypeia_15-0" class="reference"><a href="#cite_note-ctypeia-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The difference between an object's absolute and apparent magnitudes is called its <a href="/wiki/Distance_modulus" title="Distance modulus">distance modulus</a>, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way. </p> <div class="mw-heading mw-heading3"><h3 id="Problems">Problems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=5" title="Edit section: Problems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Two problems exist for any class of standard candle. The principal one is <a href="/wiki/Calibration" title="Calibration">calibration</a>, that is the determination of exactly what the absolute magnitude of the candle is. This includes defining the class well enough that members can be recognized, and finding enough members of that class with well-known distances to allow their true absolute magnitude to be determined with enough accuracy. The second problem lies in recognizing members of the class, and not mistakenly using a standard candle calibration on an object which does not belong to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious. </p><p>A significant issue with standard candles is the recurring question of how standard they are. For example, all observations seem to indicate that <a href="/wiki/Type_Ia_supernova" title="Type Ia supernova">Type Ia supernovae</a> that are of known distance have the same brightness, corrected by the shape of the light curve. The basis for this closeness in brightness is discussed below; however, the possibility exists that the distant Type Ia supernovae have different properties than nearby Type Ia supernovae. The use of Type Ia supernovae is crucial in determining the correct <a href="/wiki/Physical_cosmology" title="Physical cosmology">cosmological model</a>. If indeed the properties of Type Ia supernovae are different at large distances, i.e. if the extrapolation of their calibration to arbitrary distances is not valid, ignoring this variation can dangerously bias the reconstruction of the cosmological parameters, in particular the reconstruction of the matter <a href="/wiki/Friedmann_equations" title="Friedmann equations">density parameter</a>.<sup id="cite_ref-Lindenetal2009_16-0" class="reference"><a href="#cite_note-Lindenetal2009-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (August 2015)">clarification needed</span></a></i>]</sup> </p><p>That this is not merely a philosophical issue can be seen from the history of distance measurements using <a href="/wiki/Cepheid_variable" title="Cepheid variable">Cepheid variables</a>. In the 1950s, <a href="/wiki/Walter_Baade" title="Walter Baade">Walter Baade</a> discovered that the nearby Cepheid variables used to calibrate the standard candle were of a different type than the ones used to measure distances to nearby galaxies. The nearby Cepheid variables were <a href="/wiki/Stellar_population" title="Stellar population">population I</a> stars with much higher <a href="/wiki/Metallicity" title="Metallicity">metal</a> content than the distant <a href="/wiki/Stellar_population" title="Stellar population">population II</a> stars. As a result, the population II stars were actually much brighter than believed, and when corrected, this had the effect of doubling the estimates of distances to the globular clusters, the nearby galaxies, and the diameter of the Milky Way.<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. (January 2023)">citation needed</span></a></i>]</sup> </p><p>Most recently <a href="/wiki/Kilonova" title="Kilonova">kilonova</a> have been proposed as another type of standard candle. "Since kilonovae explosions are spherical,<sup id="cite_ref-Spher_17-0" class="reference"><a href="#cite_note-Spher-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> astronomers could compare the apparent size of a supernova explosion with its actual size as seen by the gas motion, and thus measure the rate of cosmic expansion at different distances."<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Standard_siren">Standard siren</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=6" title="Edit section: Standard siren"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a> originating from the <a href="/wiki/Orbital_decay" title="Orbital decay">inspiral phase</a> of compact binary systems, such as <a href="/wiki/Neutron_star" title="Neutron star">neutron stars</a> or <a href="/wiki/Black_hole" title="Black hole">black holes</a>, have the useful property that energy emitted as gravitational radiation comes exclusively from the <a href="/wiki/Orbital_energy" class="mw-redirect" title="Orbital energy">orbital energy</a> of the pair, and the resultant shrinking of their orbits is directly observable as an increase in the frequency of the emitted gravitational waves. To <a href="/wiki/Leading_order" class="mw-redirect" title="Leading order">leading order</a>, the <a href="/wiki/Time_derivative" title="Time derivative">rate of change</a> of frequency <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> is given by<sup id="cite_ref-cf1994_19-0" class="reference"><a href="#cite_note-cf1994-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Holz2018_20-0" class="reference"><a href="#cite_note-Holz2018-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 38">: 38 </span></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {df}{dt}}={\frac {96\pi ^{8/3}(G{\mathcal {M}})^{\frac {5}{3}}f^{\frac {11}{3}}}{5\,c^{5}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>f</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>96</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>3</mn> </mfrac> </mrow> </msup> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>11</mn> <mn>3</mn> </mfrac> </mrow> </msup> </mrow> <mrow> <mn>5</mn> <mspace width="thinmathspace" /> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {df}{dt}}={\frac {96\pi ^{8/3}(G{\mathcal {M}})^{\frac {5}{3}}f^{\frac {11}{3}}}{5\,c^{5}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63eb0ece614f71b081ccd4a4fd57f3b99dc3704b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:26.155ex; height:7.176ex;" alt="{\displaystyle {\frac {df}{dt}}={\frac {96\pi ^{8/3}(G{\mathcal {M}})^{\frac {5}{3}}f^{\frac {11}{3}}}{5\,c^{5}}},}"></span> where <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> is the <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a>, <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>, and <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 {\mathcal {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc2abebd45ec020509a0ec548b67c9a2cb7cecd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.791ex; height:2.176ex;" alt="{\displaystyle {\mathcal {M}}}"></span> is a single (therefore computable<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup>) number called the <a href="/wiki/Chirp_mass" title="Chirp mass">chirp mass</a> of the system, a combination of the masses <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 (m_{1},m_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (m_{1},m_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8629f8e8223f9653eade35872fee4b5646bc1e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.033ex; height:2.843ex;" alt="{\displaystyle (m_{1},m_{2})}"></span> of the two objects<sup id="cite_ref-Schutz86_23-0" class="reference"><a href="#cite_note-Schutz86-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {M}}={\frac {(m_{1}m_{2})^{3/5}}{(m_{1}+m_{2})^{1/5}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>5</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}={\frac {(m_{1}m_{2})^{3/5}}{(m_{1}+m_{2})^{1/5}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae0f4ad41b5622d92954968f6e33362dbe65e5a0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:20.909ex; height:7.009ex;" alt="{\displaystyle {\mathcal {M}}={\frac {(m_{1}m_{2})^{3/5}}{(m_{1}+m_{2})^{1/5}}}.}"></span> By observing the waveform, the chirp mass can be computed and thence the <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> (rate of energy emission) of the gravitational waves. Thus, such a gravitational wave source is a <b>standard siren</b> of known loudness.<sup id="cite_ref-HendryWoan2007_24-0" class="reference"><a href="#cite_note-HendryWoan2007-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Holz2018_20-1" class="reference"><a href="#cite_note-Holz2018-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Just as with standard candles, given the emitted and received amplitudes, the inverse-square law determines the distance to the source. There are some differences with standard candles, however. Gravitational waves are not emitted isotropically, but measuring the polarisation of the wave provides enough information to determine the angle of emission. Gravitational wave detectors also have anisotropic antenna patterns, so the position of the source on the sky relative to the detectors is needed to determine the angle of reception. </p><p>Generally, if a wave is detected by a network of three detectors at different locations, the network will measure enough information to make these corrections and obtain the distance. Also unlike standard candles, gravitational waves need no calibration against other distance measures. The measurement of distance does of course require the calibration of the gravitational wave detectors, but then the distance is fundamentally given as a multiple of the wavelength of the laser light being used in the <a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">gravitational wave interferometer</a>. </p><p>There are other considerations that limit the accuracy of this distance, besides detector calibration. Fortunately, gravitational waves are not subject to <a href="/wiki/Extinction_(astronomy)" title="Extinction (astronomy)">extinction</a> due to an intervening absorbing medium. But they <i>are</i> subject to <a href="/wiki/Gravitational_lens" title="Gravitational lens">gravitational lensing</a>, in the same way as light. If a signal is <a href="/wiki/Strong_gravitational_lensing" title="Strong gravitational lensing">strongly lensed</a>, then it might be received as multiple events, separated in time, the analogue of multiple images of a quasar, for example. Less easy to discern and control for is the effect of <a href="/wiki/Weak_gravitational_lensing" title="Weak gravitational lensing">weak lensing</a>, where the signal's path through space is affected by many small magnification and demagnification events. This will be important for signals originating at cosmological <a href="/wiki/Redshift" title="Redshift">redshifts</a> greater than 1. It is difficult for detector networks to measure the polarization of a signal accurately if the binary system is observed nearly face-on.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Such signals suffer significantly larger errors in the distance measurement. Unfortunately, binaries radiate most strongly perpendicular to the orbital plane, so face-on signals are intrinsically stronger and the most commonly observed. </p><p>If the binary consists of a pair of neutron stars, their merger will be accompanied by a <a href="/wiki/Kilonova" title="Kilonova">kilonova</a>/<a href="/wiki/Hypernova" title="Hypernova">hypernova</a> explosion that may allow the position to be accurately identified by electromagnetic telescopes. In such cases, the redshift of the host galaxy allows a determination of the <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble constant</a> <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 H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span>.<sup id="cite_ref-Schutz86_23-1" class="reference"><a href="#cite_note-Schutz86-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> This was the case for <a href="/wiki/GW170817" title="GW170817">GW170817</a>, which was used to make the first such measurement.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Even if no electromagnetic counterpart can be identified for an ensemble of signals, it is possible to use a statistical method to infer the value of <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 H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span>.<sup id="cite_ref-Schutz86_23-2" class="reference"><a href="#cite_note-Schutz86-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Standard_ruler">Standard ruler</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=7" title="Edit section: Standard ruler"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Another class of physical distance indicator is the <a href="/wiki/Standard_ruler" title="Standard ruler">standard ruler</a>. In 2008, galaxy diameters have been proposed as a possible standard ruler for cosmological parameter determination.<sup id="cite_ref-Marinonietal2009_27-0" class="reference"><a href="#cite_note-Marinonietal2009-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> More recently the physical scale imprinted by <a href="/wiki/Baryon_acoustic_oscillations" title="Baryon acoustic oscillations">baryon acoustic oscillations</a> (BAO) in the early universe has been used. In the early universe (before <a href="/wiki/Recombination_(cosmology)" title="Recombination (cosmology)">recombination</a>) the baryons and photons scatter off each other, and form a tightly coupled fluid that can support sound waves. The waves are sourced by primordial density perturbations, and travel at speed that can be predicted from the baryon density and other cosmological parameters. </p><p>The total distance that these sound waves can travel before recombination determines a fixed scale, which simply expands with the universe after recombination. BAO therefore provide a standard ruler that can be measured in galaxy surveys from the effect of baryons on the clustering of galaxies. The method requires an extensive galaxy survey in order to make this scale visible, but has been measured with percent-level precision (see <a href="/wiki/Baryon_acoustic_oscillations" title="Baryon acoustic oscillations">baryon acoustic oscillations</a>). The scale does depend on cosmological parameters like the baryon and matter densities, and the number of neutrinos, so distances based on BAO are more dependent on cosmological model than those based on local measurements. </p><p><a href="/wiki/Light_echo" title="Light echo">Light echos</a> can be also used as standard rulers,<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> although it is challenging to correctly measure the source geometry.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Galactic_distance_indicators">Galactic distance indicators</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=8" title="Edit section: Galactic distance indicators"><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/Distance_measure" title="Distance measure">Distance measure</a></div> <p>With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance. </p><p>Physical distance indicators, used on progressively larger distance scales, include: </p> <ul><li><a href="/wiki/Dynamical_parallax" title="Dynamical parallax">Dynamical parallax</a>, uses orbital parameters of <a href="/wiki/Visual_binary" title="Visual binary">visual binaries</a> to measure the mass of the system, and hence use the <a href="/wiki/Mass%E2%80%93luminosity_relation#In_astronomy" title="Mass–luminosity relation">mass–luminosity relation</a> to determine the luminosity <ul><li><a href="/wiki/Binary_star" title="Binary star">Eclipsing binaries</a> — In the last decade, measurement of eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them as indicators of distance. Recently, they have been used to give direct distance estimates to the <a href="/wiki/Large_Magellanic_Cloud" title="Large Magellanic Cloud">Large Magellanic Cloud</a> (LMC), <a href="/wiki/Small_Magellanic_Cloud" title="Small Magellanic Cloud">Small Magellanic Cloud</a> (SMC), <a href="/wiki/Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a> and <a href="/wiki/Triangulum_Galaxy" title="Triangulum Galaxy">Triangulum Galaxy</a>. Eclipsing binaries offer a direct method to gauge the distance to galaxies to a new improved 5% level of accuracy which is feasible with current technology to a distance of around 3 Mpc (3 million parsecs).<sup id="cite_ref-Bonanos2006_32-0" class="reference"><a href="#cite_note-Bonanos2006-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li></ul></li> <li><a href="/wiki/RR_Lyrae_variable" title="RR Lyrae variable">RR Lyrae variables</a> — used for measuring distances within the <a href="/wiki/Milky_Way" title="Milky Way">galaxy</a> and in nearby <a href="/wiki/Globular_cluster" title="Globular cluster">globular clusters</a>.</li> <li>The following four indicators all use stars in the old stellar populations (Population II):<sup id="cite_ref-Ferrareseetal2000_33-0" class="reference"><a href="#cite_note-Ferrareseetal2000-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> <ul><li><a href="/wiki/Tip_of_the_red-giant_branch" title="Tip of the red-giant branch">Tip of the red-giant branch</a> (TRGB) distance indicator.</li> <li><a href="/wiki/Planetary_nebula_luminosity_function" title="Planetary nebula luminosity function">Planetary nebula luminosity function</a> (PNLF)</li> <li><a href="/w/index.php?title=Globular_cluster_luminosity_function&action=edit&redlink=1" class="new" title="Globular cluster luminosity function (page does not exist)">Globular cluster luminosity function</a> (GCLF)</li> <li><a href="/wiki/Surface_brightness_fluctuation" title="Surface brightness fluctuation">Surface brightness fluctuation</a> (SBF)</li></ul></li> <li>In galactic astronomy, <a href="/wiki/X-ray_burster" title="X-ray burster">X-ray bursts</a> (thermonuclear flashes on the surface of a <a href="/wiki/Neutron_star" title="Neutron star">neutron star</a>) are used as standard candles. Observations of X-ray burst sometimes show X-ray spectra indicating radius expansion. Therefore, the X-ray flux at the peak of the burst should correspond to <a href="/wiki/Eddington_luminosity" title="Eddington luminosity">Eddington luminosity</a>, which can be calculated once the mass of the neutron star is known (1.5 solar masses is a commonly used assumption). This method allows distance determination of some low-mass <a href="/wiki/X-ray_binary" title="X-ray binary">X-ray binaries</a>. Low-mass X-ray binaries are very faint in the optical, making their distances extremely difficult to determine.</li> <li><a href="/wiki/Astrophysical_maser#Distance_determinations" title="Astrophysical maser">Interstellar masers</a> can be used to derive distances to galactic and some extragalactic objects that have maser emission.</li> <li><a href="/wiki/Cepheid_variable#Use_as_a_"standard_candle"" title="Cepheid variable">Cepheids</a> and <a href="/wiki/Nova#Novae_as_distance_indicators" title="Nova">novae</a></li> <li>The <a href="/wiki/Tully%E2%80%93Fisher_relation" title="Tully–Fisher relation">Tully–Fisher relation</a></li> <li>The <a href="/wiki/Faber%E2%80%93Jackson_relation" title="Faber–Jackson relation">Faber–Jackson relation</a></li> <li><a href="/wiki/Type_Ia_supernova" title="Type Ia supernova">Type Ia supernovae</a> that have a very well-determined maximum absolute magnitude as a function of the shape of their <a href="/wiki/Light_curve" title="Light curve">light curve</a> and are useful in determining extragalactic distances up to a few hundred Mpc.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> A notable exception is <a href="/wiki/SN_2003fg" title="SN 2003fg">SN 2003fg</a>, the "Champagne Supernova", a Type Ia supernova of unusual nature.</li> <li><a href="/wiki/Redshift" title="Redshift">Redshifts</a> and <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Main_sequence_fitting">Main sequence fitting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=9" title="Edit section: Main sequence fitting"><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/Spectroscopic_parallax" title="Spectroscopic parallax">Spectroscopic parallax</a></div> <p>When the absolute magnitude for a group of stars is plotted against the <a href="/wiki/Stellar_classification" title="Stellar classification">spectral classification</a> of the star, in a <a href="/wiki/Hertzsprung%E2%80%93Russell_diagram" title="Hertzsprung–Russell diagram">Hertzsprung–Russell diagram</a>, evolutionary patterns are found that relate to the mass, age and composition of the star. In particular, during their hydrogen burning period, stars lie along a curve in the diagram called the <a href="/wiki/Main_sequence" title="Main sequence">main sequence</a>. By measuring these properties from a star's spectrum, the position of a main sequence star on the H–R diagram can be determined, and thereby the star's absolute magnitude estimated. A comparison of this value with the apparent magnitude allows the approximate distance to be determined, after correcting for interstellar extinction of the luminosity because of gas and dust. </p><p>In a gravitationally-bound <a href="/wiki/Star_cluster" title="Star cluster">star cluster</a> such as the <a href="/wiki/Hyades_(star_cluster)" title="Hyades (star cluster)">Hyades</a>, the stars formed at approximately the same age and lie at the same distance. This allows relatively accurate main sequence fitting, providing both age and distance determination. </p> <div class="mw-heading mw-heading2"><h2 id="Extragalactic_distance_scale">Extragalactic distance scale</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=10" title="Edit section: Extragalactic distance scale"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="float:right; width:40%;"> <caption>Extragalactic distance indicators<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr valign="top"> <th>Method </th> <th>Uncertainty for Single Galaxy (mag) </th> <th>Distance to <a href="/wiki/Virgo_Cluster" title="Virgo Cluster">Virgo Cluster</a> (<a href="/wiki/Parsec" title="Parsec">Mpc</a>) </th> <th>Range (Mpc) </th></tr> <tr valign="top"> <td>Classical Cepheids </td> <td>0.16 </td> <td>15–25 </td> <td>29 </td></tr> <tr valign="top"> <td>Novae </td> <td>0.4 </td> <td>21.1 ± 3.9 </td> <td>20 </td></tr> <tr valign="top"> <td>Planetary Nebula Luminosity Function </td> <td>0.3 </td> <td>15.4 ± 1.1 </td> <td>50 </td></tr> <tr valign="top"> <td>Globular Cluster Luminosity Function </td> <td>0.4 </td> <td>18.8 ± 3.8 </td> <td>50 </td></tr> <tr valign="top"> <td>Surface Brightness Fluctuations </td> <td>0.3 </td> <td>15.9 ± 0.9 </td> <td>50 </td></tr> <tr valign="top"> <td>Sigma-D relation </td> <td>0.5 </td> <td>16.8 ± 2.4 </td> <td>> 100 </td></tr> <tr valign="top"> <td>Type Ia Supernovae </td> <td>0.10 </td> <td>19.4 ± 5.0 </td> <td>> 1000 </td></tr></tbody></table> <p>The extragalactic distance scale is a series of techniques used today by astronomers to determine the distance of cosmological bodies beyond our own galaxy, which are not easily obtained with traditional methods. Some procedures use properties of these objects, such as <a href="/wiki/Star" title="Star">stars</a>, <a href="/wiki/Globular_cluster" title="Globular cluster">globular clusters</a>, <a href="/wiki/Nebula" title="Nebula">nebulae</a>, and galaxies as a whole. Other methods are based more on the statistics and probabilities of things such as entire <a href="/wiki/Galaxy_cluster" title="Galaxy cluster">galaxy clusters</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Wilson–Bappu_effect"><span id="Wilson.E2.80.93Bappu_effect"></span>Wilson–Bappu effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=11" title="Edit section: Wilson–Bappu 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 article: <a href="/wiki/Wilson%E2%80%93Bappu_effect" title="Wilson–Bappu effect">Wilson–Bappu effect</a></div> <p>Discovered in 1956 by <a href="/wiki/Olin_Chaddock_Wilson" title="Olin Chaddock Wilson">Olin Wilson</a> and <a href="/wiki/Vainu_Bappu" title="Vainu Bappu">M.K. Vainu Bappu</a>, the <a href="/wiki/Wilson%E2%80%93Bappu_effect" title="Wilson–Bappu effect">Wilson–Bappu effect</a> uses the effect known as <a href="/wiki/Spectroscopic_parallax" title="Spectroscopic parallax">spectroscopic parallax</a>. Many stars have features in their <a href="/wiki/Astronomical_spectroscopy" title="Astronomical spectroscopy">spectra</a>, such as the <a href="/wiki/Fraunhofer_lines" title="Fraunhofer lines">calcium K-line</a>, that indicate their <a href="/wiki/Absolute_magnitude" title="Absolute magnitude">absolute magnitude</a>. The distance to the star can then be calculated from its <a href="/wiki/Apparent_magnitude" title="Apparent magnitude">apparent magnitude</a> using the <a href="/wiki/Distance_modulus" title="Distance modulus">distance modulus</a>. </p><p>There are major limitations to this method for finding stellar distances. The calibration of the spectral line strengths has limited accuracy and it requires a correction for <a href="/wiki/Interstellar_extinction" class="mw-redirect" title="Interstellar extinction">interstellar extinction</a>. Though in theory this method has the ability to provide reliable distance calculations to stars up to 7 megaparsecs (Mpc), it is generally only used for stars at hundreds of kiloparsecs (kpc). </p> <div class="mw-heading mw-heading3"><h3 id="Classical_Cepheids">Classical Cepheids</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=12" title="Edit section: Classical Cepheids"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Beyond the reach of the <a href="/wiki/Wilson%E2%80%93Bappu_effect" title="Wilson–Bappu effect">Wilson–Bappu effect</a>, the next method relies on the <a href="/wiki/Period-luminosity_relation" title="Period-luminosity relation">period-luminosity relation</a> of classical <a href="/wiki/Cepheid_variable" title="Cepheid variable">Cepheid variable</a> stars. The following relation can be used to calculate the distance to Galactic and extragalactic classical Cepheids: </p><p>     <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 5\log _{10}{d}=V+(3.34)\log _{10}{P}-(2.45)(V-I)+7.52\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> <mo>=</mo> <mi>V</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>3.34</mn> <mo stretchy="false">)</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> <mo>−</mo> <mo stretchy="false">(</mo> <mn>2.45</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>V</mi> <mo>−</mo> <mi>I</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>7.52</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5\log _{10}{d}=V+(3.34)\log _{10}{P}-(2.45)(V-I)+7.52\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d69299e53ae94c337bee9ced405320e626f63d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:53.439ex; height:2.843ex;" alt="{\displaystyle 5\log _{10}{d}=V+(3.34)\log _{10}{P}-(2.45)(V-I)+7.52\,.}"></span><sup id="cite_ref-benedict2007_36-0" class="reference"><a href="#cite_note-benedict2007-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> <br />      <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 5\log _{10}{d}=V+(3.37)\log _{10}{P}-(2.55)(V-I)+7.48\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> <mo>=</mo> <mi>V</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mn>3.37</mn> <mo stretchy="false">)</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> <mo>−</mo> <mo stretchy="false">(</mo> <mn>2.55</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>V</mi> <mo>−</mo> <mi>I</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>7.48</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5\log _{10}{d}=V+(3.37)\log _{10}{P}-(2.55)(V-I)+7.48\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3dcc80013823f00e7cf590ca26b54c9b6ff2787" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:53.439ex; height:2.843ex;" alt="{\displaystyle 5\log _{10}{d}=V+(3.37)\log _{10}{P}-(2.55)(V-I)+7.48\,.}"></span><sup id="cite_ref-majaess2011_37-0" class="reference"><a href="#cite_note-majaess2011-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>Several problems complicate the use of Cepheids as standard candles and are actively debated, chief among them are: the nature and linearity of the period-luminosity relation in various passbands and the impact of metallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending) and a changing (typically unknown) extinction law on Cepheid distances.<sup id="cite_ref-stanekudalski1999_38-0" class="reference"><a href="#cite_note-stanekudalski1999-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-udalski2001_39-0" class="reference"><a href="#cite_note-udalski2001-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ngeow2006_40-0" class="reference"><a href="#cite_note-ngeow2006-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-macri2006_41-0" class="reference"><a href="#cite_note-macri2006-41"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-bono2008_42-0" class="reference"><a href="#cite_note-bono2008-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-majaess2009b_43-0" class="reference"><a href="#cite_note-majaess2009b-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-madore2009_44-0" class="reference"><a href="#cite_note-madore2009-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-scowcroft2009_45-0" class="reference"><a href="#cite_note-scowcroft2009-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-majaess2010_46-0" class="reference"><a href="#cite_note-majaess2010-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p><p>These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc. Resolving this discrepancy is one of the foremost problems in astronomy since some cosmological parameters of the Universe may be constrained significantly better by supplying a precise value of the Hubble constant.<sup id="cite_ref-tammannsandage2008_47-0" class="reference"><a href="#cite_note-tammannsandage2008-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-freedman2010_48-0" class="reference"><a href="#cite_note-freedman2010-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Cepheid variable stars were the key instrument in Edwin Hubble's 1923 conclusion that <a href="/wiki/Andromeda_Galaxy" title="Andromeda Galaxy">M31</a> (Andromeda) was an external galaxy, as opposed to a smaller nebula within the Milky Way. He was able to calculate the distance of M31 to 285 kpc, today's value being 770 kpc.<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. (January 2023)">citation needed</span></a></i>]</sup> </p><p>As detected thus far, NGC 3370, a spiral galaxy in the constellation Leo, contains the farthest Cepheids yet found at a distance of 29 Mpc. Cepheid variable stars are in no way perfect distance markers: at nearby galaxies they have an error of about 7% and up to a 15% error for the most distant.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Supernovae">Supernovae</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=13" title="Edit section: Supernovae"><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:SN1994D.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/SN1994D.jpg/220px-SN1994D.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/SN1994D.jpg/330px-SN1994D.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/SN1994D.jpg/440px-SN1994D.jpg 2x" data-file-width="1280" data-file-height="1280" /></a><figcaption><a href="/wiki/SN_1994D" title="SN 1994D">SN 1994D</a> (bright spot on the lower left) in the <a href="/wiki/NGC_4526" title="NGC 4526">NGC 4526</a> galaxy. Image by <a href="/wiki/NASA" title="NASA">NASA</a>, <a href="/wiki/ESA" class="mw-redirect" title="ESA">ESA</a>, The Hubble Key Project Team, and The High-Z Supernova Search Team</figcaption></figure> <p>There are several different methods for which <a href="/wiki/Supernova" title="Supernova">supernovae</a> can be used to measure extragalactic distances. </p> <div class="mw-heading mw-heading4"><h4 id="Measuring_a_supernova's_photosphere"><span id="Measuring_a_supernova.27s_photosphere"></span>Measuring a supernova's photosphere</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=14" title="Edit section: Measuring a supernova's photosphere"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>We can assume that a supernova expands in a spherically symmetric manner. If the supernova is close enough such that we can measure the angular extent, <i>θ</i>(<i>t</i>), of its <a href="/wiki/Photosphere" title="Photosphere">photosphere</a>, we can use the equation </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\frac {\Delta \theta }{\Delta t}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>θ</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ={\frac {\Delta \theta }{\Delta t}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60a690d5d03e2a6d24c69841b58ef81647591c14" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.441ex; height:5.509ex;" alt="{\displaystyle \omega ={\frac {\Delta \theta }{\Delta t}}\,,}"></span> where <i>ω</i> is angular velocity, <i>θ</i> is angular extent. In order to get an accurate measurement, it is necessary to make two observations separated by time Δ<i>t</i>. Subsequently, we can use </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ d={\frac {V_{ej}}{\omega }}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>j</mi> </mrow> </msub> <mi>ω</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ d={\frac {V_{ej}}{\omega }}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59b760d9947fc8e9fc00712f1deee6fef4a1ba88" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.796ex; height:5.509ex;" alt="{\displaystyle \ d={\frac {V_{ej}}{\omega }}\,,}"></span> where d is the distance to the supernova, <i>V<sub>ej</sub></i> is the supernova's ejecta's radial velocity (it can be assumed that <i>V<sub>ej</sub></i> equals <i>V<sub>θ</sub></i> if spherically symmetric). </p><p>This method works only if the supernova is close enough to be able to measure accurately the photosphere. Similarly, the expanding shell of gas is in fact not perfectly spherical nor a perfect blackbody. Also interstellar extinction can hinder the accurate measurements of the photosphere. This problem is further exacerbated by core-collapse supernova. All of these factors contribute to the distance error of up to 25%. </p> <div class="mw-heading mw-heading4"><h4 id="Type_Ia_light_curves">Type Ia light curves</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=15" title="Edit section: Type Ia light curves"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Type_Ia_supernovae" class="mw-redirect" title="Type Ia supernovae">Type Ia supernovae</a> are some of the best ways to determine extragalactic distances. Ia's occur when a binary white dwarf star begins to accrete matter from its companion star. As the white dwarf gains matter, eventually it reaches its <a href="/wiki/Chandrasekhar_limit" title="Chandrasekhar limit">Chandrasekhar limit</a> of <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 1.4M_{\odot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1.4</mn> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊙</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1.4M_{\odot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0486beb272d1250c581788cdfa4f0e46beba7d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.737ex; height:2.509ex;" alt="{\displaystyle 1.4M_{\odot }}"></span>. </p><p>Once reached, the star becomes unstable and undergoes a runaway nuclear fusion reaction. Because all Type Ia supernovae explode at about the same mass, their absolute magnitudes are all the same. This makes them very useful as standard candles. All Type Ia supernovae have a standard blue and visual magnitude of </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ M_{B}\approx M_{V}\approx -19.3\pm 0.3\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>≈</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msub> <mo>≈</mo> <mo>−</mo> <mn>19.3</mn> <mo>±</mo> <mn>0.3</mn> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ M_{B}\approx M_{V}\approx -19.3\pm 0.3\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7418f8923b7389f1f3b60bcadfa4c3b625fd5de1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.05ex; height:2.509ex;" alt="{\displaystyle \ M_{B}\approx M_{V}\approx -19.3\pm 0.3\,.}"></span> Therefore, when observing a Type Ia supernova, if it is possible to determine what its peak magnitude was, then its distance can be calculated. It is not intrinsically necessary to capture the supernova directly at its peak magnitude; using the <b>multicolor light curve shape</b> method (<b>MLCS</b>), the shape of the light curve (taken at any reasonable time after the initial explosion) is compared to a family of parameterized curves that will determine the absolute magnitude at the maximum brightness. This method also takes into effect interstellar extinction/dimming from dust and gas. </p><p>Similarly, the <b>stretch method</b> fits the particular supernovae magnitude light curves to a template light curve. This template, as opposed to being several light curves at different wavelengths (MLCS) is just a single light curve that has been stretched (or compressed) in time. By using this <i>Stretch Factor</i>, the peak magnitude can be determined.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p><p>Using Type Ia supernovae is one of the most accurate methods, particularly since supernova explosions can be visible at great distances (their luminosities rival that of the galaxy in which they are situated), much farther than Cepheid Variables (500 times farther). Much time has been devoted to the refining of this method. The current uncertainty approaches a mere 5%, corresponding to an uncertainty of just 0.1 magnitudes. </p> <div class="mw-heading mw-heading4"><h4 id="Novae_in_distance_determinations">Novae in distance determinations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=16" title="Edit section: Novae in distance determinations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Nova" title="Nova">Novae</a> can be used in much the same way as supernovae to derive extragalactic distances. There is a direct relation between a nova's max magnitude and the time for its visible light to decline by two magnitudes. This relation is shown to be: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ M_{V}^{\max }=-9.96-2.31\log _{10}{\dot {x}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msubsup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo movablelimits="true" form="prefix">max</mo> </mrow> </msubsup> <mo>=</mo> <mo>−</mo> <mn>9.96</mn> <mo>−</mo> <mn>2.31</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ M_{V}^{\max }=-9.96-2.31\log _{10}{\dot {x}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1eed5d4967b03c8707b63f0b738f85310f611ce" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:30.372ex; height:2.843ex;" alt="{\displaystyle \ M_{V}^{\max }=-9.96-2.31\log _{10}{\dot {x}}\,.}"></span> Where <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 {\dot {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a82c85f33714da82ab42d6b69eae07ab7e5e234b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.176ex;" alt="{\displaystyle {\dot {x}}}"></span> is the time derivative of the nova's mag, describing the average rate of decline over the first 2 magnitudes. </p><p>After novae fade, they are about as bright as the most luminous Cepheid variable stars, therefore both these techniques have about the same max distance: ~ 20 Mpc. The error in this method produces an uncertainty in magnitude of about ±0.4 </p> <div class="mw-heading mw-heading3"><h3 id="Globular_cluster_luminosity_function">Globular cluster luminosity function</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=17" title="Edit section: Globular cluster luminosity function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Cosmic_distance_ladder" title="Special:EditPage/Cosmic distance ladder">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">July 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Based on the method of comparing the luminosities of globular clusters (located in galactic halos) from distant galaxies to that of the <a href="/wiki/Virgo_Cluster" title="Virgo Cluster">Virgo Cluster</a>, the <a href="/w/index.php?title=Globular_cluster_luminosity_function&action=edit&redlink=1" class="new" title="Globular cluster luminosity function (page does not exist)">globular cluster luminosity function</a> carries an uncertainty of distance of about 20% (or 0.4 magnitudes). </p><p>US astronomer William Alvin Baum first attempted to use globular clusters to measure distant elliptical galaxies. He compared the brightest globular clusters in Virgo A galaxy with those in Andromeda, assuming the luminosities of the clusters were the same in both. Knowing the distance to Andromeda, Baum has assumed a direct correlation and estimated Virgo A's distance. </p><p>Baum used just a single globular cluster, but individual formations are often poor standard candles. Canadian astronomer <a href="/wiki/Ren%C3%A9_Racine" title="René Racine">René Racine</a> assumed the use of the globular cluster luminosity function (GCLF) would lead to a better approximation. The number of globular clusters as a function of magnitude is given by: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \Phi (m)=Ae^{(m-m_{0})^{2}/2\sigma ^{2}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi mathvariant="normal">Φ</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \Phi (m)=Ae^{(m-m_{0})^{2}/2\sigma ^{2}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdfa056786817b969a4f268d73be3b0f068aaddd" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.176ex; height:3.676ex;" alt="{\displaystyle \ \Phi (m)=Ae^{(m-m_{0})^{2}/2\sigma ^{2}}\,}"></span> where <i>m</i><sub>0</sub> is the turnover magnitude, <i>M</i><sub>0</sub> is the magnitude of the Virgo cluster, and sigma is the dispersion ~ 1.4 mag. </p><p>It is assumed that globular clusters all have roughly the same luminosities within the <a href="/wiki/Universe" title="Universe">universe</a>. There is no universal globular cluster luminosity function that applies to all galaxies. </p> <div class="mw-heading mw-heading3"><h3 id="Planetary_nebula_luminosity_function">Planetary nebula luminosity function</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=18" title="Edit section: Planetary nebula luminosity function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Cosmic_distance_ladder" title="Special:EditPage/Cosmic distance ladder">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">July 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Like the GCLF method, a similar numerical analysis can be used for <a href="/wiki/Planetary_nebula" title="Planetary nebula">planetary nebulae</a> within far off galaxies. The <a href="/wiki/Planetary_nebula_luminosity_function" title="Planetary nebula luminosity function">planetary nebula luminosity function</a> (PNLF) was first proposed in the late 1970s by Holland Cole and David Jenner. They suggested that all planetary nebulae might all have similar maximum intrinsic brightness, now calculated to be M = −4.53. This would therefore make them potential standard candles for determining extragalactic distances. </p><p>Astronomer George Howard Jacoby and his colleagues later proposed that the PNLF function equaled: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ N(M)\propto e^{0.307M}(1-e^{3(M^{*}-M)})\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>N</mi> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.307</mn> <mi>M</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>−</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ N(M)\propto e^{0.307M}(1-e^{3(M^{*}-M)})\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa08e4b88bf3a5654b9ff05dc560d9a907863012" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.649ex; height:3.343ex;" alt="{\displaystyle \ N(M)\propto e^{0.307M}(1-e^{3(M^{*}-M)})\,.}"></span> Where N(M) is number of planetary nebula, having absolute magnitude M. M* is equal to the nebula with the brightest magnitude. </p> <div class="mw-heading mw-heading3"><h3 id="Surface_brightness_fluctuation_method">Surface brightness fluctuation method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=19" title="Edit section: Surface brightness fluctuation method"><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:Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg/220px-Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg" decoding="async" width="220" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg/330px-Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg/440px-Galaxy_cluster_Abell_2218_gravitaitonal_lens.jpg 2x" data-file-width="1837" data-file-height="1336" /></a><figcaption>Galaxy cluster</figcaption></figure> <p>The following method deals with the overall inherent properties of galaxies. These methods, though with varying error percentages, have the ability to make distance estimates beyond 100 Mpc, though it is usually applied more locally. </p><p>The <a href="/wiki/Surface_brightness_fluctuation" title="Surface brightness fluctuation">surface brightness fluctuation</a> (SBF) method takes advantage of the use of <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">CCD</a> cameras on telescopes. Because of spatial fluctuations in a galaxy's surface brightness, some pixels on these cameras will pick up more stars than others. As distance increases, the picture will become increasingly smoother. Analysis of this describes a magnitude of the pixel-to-pixel variation, which is directly related to a galaxy's distance.<sup id="cite_ref-tonry2001_51-0" class="reference"><a href="#cite_note-tonry2001-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Sigma-D_relation">Sigma-D relation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=20" title="Edit section: Sigma-D relation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Sigma-D_relation" title="Sigma-D relation">Sigma-D relation</a> (or Σ-D relation), used in <a href="/wiki/Elliptical_galaxy" title="Elliptical galaxy">elliptical galaxies</a>, relates the angular diameter (D) of the galaxy to its <a href="/wiki/Velocity_dispersion" title="Velocity dispersion">velocity dispersion</a>. It is important to describe exactly what D represents, in order to understand this method. It is, more precisely, the galaxy's angular diameter out to the <a href="/wiki/Surface_brightness" title="Surface brightness">surface brightness</a> level of 20.75 B-mag arcsec<sup>−2</sup>. This surface brightness is independent of the galaxy's actual distance from us. Instead, D is inversely proportional to the galaxy's distance, represented as d. Thus, this relation does not employ standard candles. Rather, D provides a standard ruler. This relation between D and Σ is </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log(D)=1.333\log(\Sigma )+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1.333</mn> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Σ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log(D)=1.333\log(\Sigma )+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7602eaf6e1a7f2c2f58716f9f6d47c37145e3a2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.553ex; height:2.843ex;" alt="{\displaystyle \log(D)=1.333\log(\Sigma )+C}"></span> where C is a constant which depends on the distance to the galaxy clusters.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p>This method has the potential to become one of the strongest methods of galactic distance calculators, perhaps exceeding the range of even the Tully–Fisher method. As of today, however, elliptical galaxies are not bright enough to provide a calibration for this method through the use of techniques such as Cepheids. Instead, calibration is done using more crude methods. </p> <div class="mw-heading mw-heading2"><h2 id="Overlap_and_scaling">Overlap and scaling</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=21" title="Edit section: Overlap and scaling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A succession of distance indicators, which is the distance ladder, is needed for determining distances to other galaxies. The reason is that objects bright enough to be recognized and measured at such distances are so rare that few or none are present nearby, so there are too few examples close enough with reliable trigonometric parallax to calibrate the indicator. For example, Cepheid variables, one of the best indicators for nearby <a href="/wiki/Spiral_galaxy" title="Spiral galaxy">spiral galaxies</a>, cannot yet be satisfactorily calibrated by parallax alone, though the Gaia space mission can now weigh in on that specific problem. The situation is further complicated by the fact that different stellar populations generally do not have all types of stars in them. </p><p>Cepheids in particular are massive stars, with short lifetimes, so they will only be found in places where stars have very recently been formed. Consequently, because <a href="/wiki/Elliptical_galaxy" title="Elliptical galaxy">elliptical galaxies</a> usually have long ceased to have large-scale star formation, they will not have Cepheids. Instead, distance indicators whose origins are in an older stellar population (like novae and RR Lyrae variables) must be used. RR Lyrae variables are less luminous than Cepheids, and novae are unpredictable and an intensive monitoring program—and luck during that program—is needed to gather enough novae in the target galaxy for a good distance estimate. </p><p>Because the more distant steps of the cosmic distance ladder depend upon the nearer ones, the more distant steps include the effects of <a href="/wiki/Error" title="Error">errors</a> in the nearer steps, both systematic and statistical ones. The result of these <a href="/wiki/Propagation_of_uncertainty" title="Propagation of uncertainty">propagating errors</a> means that distances in astronomy are rarely known to the same level of precision as measurements in the other sciences, and that the precision necessarily is poorer for more distant types of object. </p><p>Another concern, especially for the very brightest standard candles, is their "standardness": how homogeneous the objects are in their true absolute magnitude. For some of these different standard candles, the homogeneity is based on theories about the <a href="/wiki/Star_formation" title="Star formation">formation</a> and <a href="/wiki/Stellar_evolution" title="Stellar evolution">evolution</a> of stars and galaxies, and is thus also subject to uncertainties in those aspects. For the most luminous of distance indicators, the Type Ia supernovae, this homogeneity is known to be poor.<sup id="cite_ref-Gilfanov2010_53-0" class="reference"><a href="#cite_note-Gilfanov2010-53"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (August 2015)">clarification needed</span></a></i>]</sup> However, no other class of object is bright enough to be detected at such large distances, so the class is useful simply because there is no real alternative. </p><p>The observational result of Hubble's law, the <a href="/wiki/Proportionality_(mathematics)" title="Proportionality (mathematics)">proportional</a> relationship between distance and the speed with which a galaxy is moving away from us, usually referred to as redshift, is a product of the cosmic distance ladder. <a href="/wiki/Edwin_Hubble" title="Edwin Hubble">Edwin Hubble</a> observed that fainter galaxies are more redshifted. Finding the value of the Hubble constant was the result of decades of work by many astronomers, both in amassing the measurements of galaxy redshifts and in calibrating the steps of the distance ladder. Hubble's law is the primary means we have for estimating the distances of <a href="/wiki/Quasar" title="Quasar">quasars</a> and distant galaxies in which individual distance indicators cannot be seen. </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=Cosmic_distance_ladder&action=edit&section=22" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/32px-Earth-moon.jpg" decoding="async" width="32" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/48px-Earth-moon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/64px-Earth-moon.jpg 2x" data-file-width="3000" data-file-height="2400" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Space" class="mw-redirect" title="Portal:Space">Space portal</a></span></li></ul> <ul><li><a href="/wiki/Araucaria_Project" title="Araucaria Project">Araucaria Project</a></li> <li><a href="/wiki/Distance_measure" title="Distance measure">Distance measure</a></li> <li><a href="/wiki/Orders_of_magnitude_(length)#Astronomical" title="Orders of magnitude (length)">Orders of magnitude (length)#Astronomical</a></li> <li><a href="/wiki/Standard_ruler" title="Standard ruler">Standard ruler</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cosmic_distance_ladder&action=edit&section=23" title="Edit section: Footnotes"><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 reflist-lower-alpha"> <ol class="references"> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">If the signal were to depend on the individual masses separately, there would not be enough observable information in the signal at the lowest order to infer its intrinsic loudness. This degeneracy between the masses therefore is crucial for the loudness measurement, but it is no accident: It has a fundamental origin in the scale-free nature of gravity in Einstein's general relativity.<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></span> </li> </ol></div> <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=Cosmic_distance_ladder&action=edit&section=24" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 25em;"> <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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.questacon.edu.au/visiting/galleries/outdoor/exhibits/the-astronomer">"The Astronomer"</a>. 16 April 2013. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210509022646/https://www.questacon.edu.au/visiting/galleries/outdoor/exhibits/the-astronomer">Archived</a> from the original on 9 May 2021<span class="reference-accessdate">. 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Retrieved <span class="nowrap">2015-10-18</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Light+echoes+whisper+the+distance+to+a+star&rft.pub=European+Southern+Observatory&rft.date=2008-02-11&rft_id=http%3A%2F%2Fwww.eso.org%2Fpublic%2Fnews%2Feso0805%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+distance+ladder" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKervellaMérandSzabadosFouqué2008" class="citation journal cs1">Kervella, Pierre; Mérand, Antoine; Szabados, László; Fouqué, Pascal; Bersier, David; Pompei, Emanuela; Perrin, Guy (2 March 2008). <a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%3A20078961">"The long-period Galactic Cepheid RS Puppis I. A geometric distance from its light echoes"</a>. <i><a href="/wiki/Astronomy_and_Astrophysics" class="mw-redirect" title="Astronomy and Astrophysics">Astronomy and Astrophysics</a></i>. <b>480</b> (1): 167–178. <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/0802.1501">0802.1501</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/2008A&A...480..167K">2008A&A...480..167K</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/10.1051%2F0004-6361%3A20078961">10.1051/0004-6361:20078961</a></span>. <q>we derive a geometric distance of <span class="nowrap"><span data-sort-value="7019614666974228264♠"></span>1992<span style="margin-left:0.3em;margin-right:0.15em;">±</span>28 pc</span> to RS Pup</q></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+long-period+Galactic+Cepheid+RS+Puppis+I.+A+geometric+distance+from+its+light+echoes&rft.volume=480&rft.issue=1&rft.pages=167-178&rft.date=2008-03-02&rft_id=info%3Aarxiv%2F0802.1501&rft_id=info%3Adoi%2F10.1051%2F0004-6361%3A20078961&rft_id=info%3Abibcode%2F2008A%26A...480..167K&rft.aulast=Kervella&rft.aufirst=Pierre&rft.au=M%C3%A9rand%2C+Antoine&rft.au=Szabados%2C+L%C3%A1szl%C3%B3&rft.au=Fouqu%C3%A9%2C+Pascal&rft.au=Bersier%2C+David&rft.au=Pompei%2C+Emanuela&rft.au=Perrin%2C+Guy&rft_id=https%3A%2F%2Fdoi.org%2F10.1051%252F0004-6361%253A20078961&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+distance+ladder" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBondSparks2009" class="citation journal cs1">Bond, Howard E.; Sparks, William B. (4 March 2009). <a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%3A200810280">"On geometric distance determination to the Cepheid RS Puppis from its light echoes"</a>. <i><a href="/wiki/Astronomy_and_Astrophysics" class="mw-redirect" title="Astronomy and Astrophysics">Astronomy and Astrophysics</a></i>. <b>495</b> (2): 371–377. <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/0811.2943">0811.2943</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/2009A&A...495..371B">2009A&A...495..371B</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/10.1051%2F0004-6361%3A200810280">10.1051/0004-6361:200810280</a></span>. <q>We conclude that most of the knots are in fact likely to lie in front of the plane of the sky, thus invalidating the Kervella et al. result. [...] Although the Kervella et al. distance result is invalidated, we show that high-resolution polarimetric imaging has the potential to yield a valid geometric distance to this important Cepheid.</q></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=On+geometric+distance+determination+to+the+Cepheid+RS+Puppis+from+its+light+echoes&rft.volume=495&rft.issue=2&rft.pages=371-377&rft.date=2009-03-04&rft_id=info%3Aarxiv%2F0811.2943&rft_id=info%3Adoi%2F10.1051%2F0004-6361%3A200810280&rft_id=info%3Abibcode%2F2009A%26A...495..371B&rft.aulast=Bond&rft.aufirst=Howard+E.&rft.au=Sparks%2C+William+B.&rft_id=https%3A%2F%2Fdoi.org%2F10.1051%252F0004-6361%253A200810280&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+distance+ladder" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKervellaBondCracraftSzabados2014" class="citation journal cs1">Kervella, Pierre; Bond, Howard E.; Cracraft, Misty; Szabados, László; Breitfelder, Joanne; Mérand2, Antoine; Sparks, William B.; Gallenne, Alexandre; Bersier, David; Fouqué, Pascal; Anderson, Richard I. (December 2014). <a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%2F201424395">"The long-period Galactic Cepheid RS Puppis. III. A geometric distance from HST polarimetric imaging of its light echoes"</a>. <i><a href="/wiki/Astronomy_and_Astrophysics" class="mw-redirect" title="Astronomy and Astrophysics">Astronomy and Astrophysics</a></i>. <b>572</b>: A7 (13 pp.). <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/1408.1697">1408.1697</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/2014A&A...572A...7K">2014A&A...572A...7K</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/10.1051%2F0004-6361%2F201424395">10.1051/0004-6361/201424395</a></span>. <q>We obtain a distance of <span class="nowrap"><span data-sort-value="7019589364418060233♠"></span>1910<span style="margin-left:0.3em;margin-right:0.15em;">±</span>80 pc</span> (4.2%)</q></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+long-period+Galactic+Cepheid+RS+Puppis.+III.+A+geometric+distance+from+HST+polarimetric+imaging+of+its+light+echoes&rft.volume=572&rft.pages=A7+%2813+pp.%29&rft.date=2014-12&rft_id=info%3Aarxiv%2F1408.1697&rft_id=info%3Adoi%2F10.1051%2F0004-6361%2F201424395&rft_id=info%3Abibcode%2F2014A%26A...572A...7K&rft.aulast=Kervella&rft.aufirst=Pierre&rft.au=Bond%2C+Howard+E.&rft.au=Cracraft%2C+Misty&rft.au=Szabados%2C+L%C3%A1szl%C3%B3&rft.au=Breitfelder%2C+Joanne&rft.au=M%C3%A9rand2%2C+Antoine&rft.au=Sparks%2C+William+B.&rft.au=Gallenne%2C+Alexandre&rft.au=Bersier%2C+David&rft.au=Fouqu%C3%A9%2C+Pascal&rft.au=Anderson%2C+Richard+I.&rft_id=https%3A%2F%2Fdoi.org%2F10.1051%252F0004-6361%252F201424395&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+distance+ladder" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</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-Bonanos2006-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bonanos2006_32-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBonanos2006" class="citation journal cs1">Bonanos, A. 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Harlow, United Kingdom: <a href="/wiki/Pearson_Education_Limited" class="mw-redirect" title="Pearson Education Limited">Pearson Education Limited</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-292-02293-2" title="Special:BookSources/978-1-292-02293-2"><bdi>978-1-292-02293-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Modern+Astrophysics&rft.place=Harlow%2C+United+Kingdom&rft.pub=Pearson+Education+Limited&rft.date=2014&rft.isbn=978-1-292-02293-2&rft.aulast=Carroll&rft.aufirst=Bradley+W.&rft.au=Ostlie%2C+Dale+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+distance+ladder" class="Z3988"></span></li> <li><i>Measuring the Universe The Cosmological Distance Ladder</i>, Stephen Webb, copyright 2001.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPasachoffFilippenko2013" class="citation book cs1"><a href="/wiki/Jay_Pasachoff" title="Jay Pasachoff">Pasachoff, J.M.</a>; <a href="/wiki/Alexei_Filippenko" class="mw-redirect" title="Alexei Filippenko">Filippenko, A.</a> (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=tZsoAAAAQBAJ"><i>The Cosmos: Astronomy in the New Millennium</i></a> (4th ed.). Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-68756-1" title="Special:BookSources/978-1-107-68756-1"><bdi>978-1-107-68756-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cosmos%3A+Astronomy+in+the+New+Millennium&rft.place=Cambridge&rft.edition=4th&rft.pub=Cambridge+University+Press&rft.date=2013&rft.isbn=978-1-107-68756-1&rft.aulast=Pasachoff&rft.aufirst=J.M.&rft.au=Filippenko%2C+A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DtZsoAAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACosmic+distance+ladder" class="Z3988"></span></li> <li><i>The Astrophysical Journal</i>, <i>The Globular Cluster Luminosity Function as a Distance Indicator: Dynamical Effects</i>, Ostriker and Gnedin, May 5, 1997.</li> <li><i>An Introduction to Distance Measurement in Astronomy</i>, Richard de Grijs, Chichester: John Wiley & Sons, 2011, <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/978-0-470-51180-0" title="Special:BookSources/978-0-470-51180-0">978-0-470-51180-0</a>.</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=Cosmic_distance_ladder&action=edit&section=26" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/distance.htm">The ABC's of distances (UCLA)</a></li> <li><a rel="nofollow" class="external text" href="http://www.astr.ua.edu/keel/galaxies/distance.html">The Extragalactic Distance Scale</a> by Bill Keel</li> <li><a rel="nofollow" class="external text" href="http://www.ipac.caltech.edu/H0kp/">The Hubble Space Telescope Key Project on the Extragalactic Distance Scale</a></li> <li><a rel="nofollow" class="external text" href="http://cfa-www.harvard.edu/~huchra/hubble/">The Hubble Constant</a>, a historical discussion</li> <li><a rel="nofollow" class="external text" href="https://heasarc.gsfc.nasa.gov/docs/cosmic/">NASA Cosmic Distance Scale</a></li> <li><a rel="nofollow" class="external text" href="http://www.noao.edu/jacoby/pnlf/pnlf.html">PNLF information database</a></li> <li><a rel="nofollow" class="external text" href="http://iopscience.iop.org/0004-637X">The Astrophysical Journal</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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href="/wiki/Template:Units_of_length_used_in_Astronomy" title="Template:Units of length used in Astronomy"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Units_of_length_used_in_Astronomy" title="Template talk:Units of length used in Astronomy"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Units_of_length_used_in_Astronomy" title="Special:EditPage/Template:Units of length used in Astronomy"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Units_of_length_used_in_Astronomy" style="font-size:114%;margin:0 4em"><a href="/wiki/Unit_of_length" title="Unit of length">Units of length</a> used in <a href="/wiki/Astronomy" title="Astronomy">Astronomy</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Astronomical_system_of_units" title="Astronomical system of units">Astronomical system of units</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Earth_radius_(unit)" class="mw-redirect" title="Earth radius (unit)">Earth radius</a> (<var>R</var><sub>🜨</sub> or <i>R<sub>E</sub></i>)</li> <li><a href="/wiki/Light-second" title="Light-second">Light-second</a> (ls)</li> <li><a href="/wiki/Solar_radius" title="Solar radius">Solar radius</a> (<var>R</var><sub>☉</sub>)</li> <li><a href="/wiki/Gigametre" class="mw-redirect" title="Gigametre">gigametre</a> (Gm)</li> <li><a href="/wiki/Astronomical_unit" title="Astronomical unit">Astronomical unit</a> (au)</li> <li><a href="/wiki/Terametre" class="mw-redirect" title="Terametre">terametre</a> (Tm)</li> <li><a href="/wiki/Light-year" title="Light-year">light-year</a> (ly)</li> <li><a href="/wiki/Parsec" title="Parsec">parsec</a> (pc)</li> <li><a href="/wiki/Kiloparsec" class="mw-redirect" title="Kiloparsec">kiloparsec</a> (kpc)</li> <li><a href="/wiki/Megaparsec" class="mw-redirect" title="Megaparsec">megaparsec</a> (Mpc)</li> <li><a href="/wiki/Gigaparsec" class="mw-redirect" title="Gigaparsec">gigaparsec</a> (Gpc)</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <dl><dt>See also</dt> <dd><a class="mw-selflink selflink">Cosmic distance ladder</a></dd> <dd><a href="/wiki/Orders_of_magnitude_(length)" title="Orders of magnitude (length)">Orders of magnitude (length)</a></dd> <dd><a href="/wiki/Conversion_of_units" title="Conversion of units">Conversion of units</a></dd></dl> </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"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox 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