New precession expressions, valid for long time intervals

<!DOCTYPE html>     <html class="no-js" lang="en">  <head> <title>New precession expressions, valid for long time intervals - ADS</title>  <link rel="apple-touch-icon" sizes="180x180" href="//styles/favicon/apple-touch-icon.png" /> <link rel="icon" type="image/png" sizes="32x32" href="//styles/favicon/favicon-32x32.png" /> <link rel="icon" type="image/png" sizes="16x16" href="//styles/favicon/favicon-16x16.png" /> <link rel="manifest" href="//styles/favicon/site.webmanifest" /> <link rel="mask-icon" href="//styles/favicon/safari-pinned-tab.svg" color="#5bbad5" /> <meta name="apple-mobile-web-app-title" content="ADS" /> <meta name="application-name" content="ADS" /> <meta name="msapplication-TileColor" content="#ffc40d" /> <meta name="theme-color" content="#ffffff" />   <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-NT2453N');</script>  <link rel="stylesheet" href="/styles/css/styles.css"> <meta name="robots" content="noarchive"> <link rel="canonical" href="http://ui.adsabs.harvard.edu/abs/2011A&A...534A..22V/abstract"/> <meta name="description" content="Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters 蠄<SUB>A</SUB>,蠅<SUB>A</SUB>, suitable for use over long time intervals. <BR /> Aims: The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries. <BR /> Methods: We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&amp;A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval 卤 200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval. <BR /> Results: Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the 卤 200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix. <P />The Appendix containing the computer code is available in electronic form at <A href="http://www.aanda.org">http://www.aanda.org</A>">  <meta property="og:type" content="article"> <meta property="og:title" content="New precession expressions, valid for long time intervals"> <meta property="og:site_name" content="ADS"> <meta property="og:description" content="Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters 蠄<SUB>A</SUB>,蠅<SUB>A</SUB>, suitable for use over long time intervals. <BR /> Aims: The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries. <BR /> Methods: We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&amp;A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval 卤 200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval. <BR /> Results: Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the 卤 200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix. <P />The Appendix containing the computer code is available in electronic form at <A href="http://www.aanda.org">http://www.aanda.org</A>"> <meta property="og:url" content="https://ui.adsabs.harvard.edu/abs/2011A&A...534A..22V/abstract"> <meta property="og:image" content="https://ui.adsabs.harvard.edu/styles/img/transparent_logo.svg"> <meta property="article:published_time" content="10/2011"> <meta property="article:author" content="Vondr谩k, J."> <meta property="article:author" content="Capitaine, N."> <meta property="article:author" content="Wallace, P.">  <meta name="citation_journal_title" content="Astronomy and Astrophysics"> <meta name="citation_authors" content="Vondr谩k, J.;Capitaine, N.;Wallace, P."> <meta name="citation_title" content="New precession expressions, valid for long time intervals"> <meta name="citation_date" content="10/2011"> <meta name="citation_volume" content="534"> <meta name="citation_firstpage" content="A22"> <meta name="citation_doi" content="10.1051/0004-6361/201117274"> <meta name="citation_issn" content="0004-6361"> <meta name="citation_language" content="en"> <meta name="citation_keywords" content="astrometry"> <meta name="citation_keywords" content="ephemerides"> <meta name="citation_keywords" content="reference systems"> <meta name="citation_abstract_html_url" content="https://ui.adsabs.harvard.edu/abs/2011A&A...534A..22V/abstract"> <meta name="citation_publication_date" content="10/2011"> <meta name="citation_pdf_url" content="https://ui.adsabs.harvard.edu/link_gateway/2011A&A...534A..22V/PUB_PDF"> <link title="schema(PRISM)" rel="schema.prism" href="http://prismstandard.org/namespaces/1.2/basic/" /> <meta name="prism.publicationDate" content="10/2011" /> <meta name="prism.publicationName" content="A&A" /> <meta name="prism.issn" content="0004-6361" /> <meta name="prism.volume" content="534" /> <meta name="prism.startingPage" content="A22" /> <link title="schema(DC)" rel="schema.dc" href="http://purl.org/dc/elements/1.1/" /> <meta name="dc.identifier" content="doi:10.1051/0004-6361/201117274" /> <meta name="dc.date" content="10/2011" /> <meta name="dc.source" content="A&A" /> <meta name="dc.title" content="New precession expressions, valid for long time intervals" /> <meta name="dc.creator" content="Vondr谩k, J."> <meta name="dc.creator" content="Capitaine, N."> <meta name="dc.creator" content="Wallace, P.">  <meta name="twitter:card" content="summary_large_image"/> <meta name="twitter:description" content="Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters 蠄<SUB>A</SUB>,蠅<SUB>A</SUB>, suitable for use over long time intervals. <BR /> Aims: The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries. <BR /> Methods: We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&amp;A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval 卤 200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval. <BR /> Results: Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the 卤 200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix. <P />The Appendix containing the computer code is available in electronic form at <A href="http://www.aanda.org">http://www.aanda.org</A>"/> <meta name="twitter:title" content="New precession expressions, valid for long time intervals"/> <meta name="twitter:site" content="@adsabs"/> <meta name="twitter:domain" content="ADS"/> <meta name="twitter:image:src" content="https://ui.adsabs.harvard.edu/styles/img/transparent_logo.svg"/> <meta name="twitter:creator" content="@adsabs"/> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <base href="/"> <style> .btn-full-ads { color: #fff !important; background-color: #1a1a1a !important; border-color: #1a1a1a !important; margin-top: 9px !important; padding-bottom: 10px !important; padding-top: 10px !important; } .btn-full-ads:hover, .btn-full-ads:focus, .btn-full-ads:active, .btn-full-ads.active, .open>.dropdown-toggle.btn-full-ads { color: #000 !important; 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<li class="author"><a href="/search/?q=author%3A%22Capitaine%2C+N.%22">Capitaine, N.</a> </li>; <li class="author"><a href="/search/?q=author%3A%22Wallace%2C+P.%22">Wallace, P.</a> </li> </ul> </div> <div class="s-abstract-text"> <h4 class="sr-only">Abstract</h4> <p> Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters 蠄<SUB>A</SUB>,蠅<SUB>A</SUB>, suitable for use over long time intervals. <BR /> Aims: The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries. <BR /> Methods: We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval 卤 200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval. <BR /> Results: Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the 卤 200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix. <P />The Appendix containing the computer code is available in electronic form at <A href="http://www.aanda.org">http://www.aanda.org</A> </p> </div> <br> <dl class="s-abstract-dl-horizontal"> <dt>Publication:</dt> <dd> <div id="article-publication">Astronomy and Astrophysics</div> </dd> <dt>Pub Date:</dt> <dd>October 2011</dd> <dt>DOI:</dt> <dd> <p class="doi-p"> <a href="/link_gateway/2011A&A...534A..22V/doi:10.1051/0004-6361/201117274" target="_blank" rel="noreferrer noopener">10.1051/0004-6361/201117274</a> <i class="fa fa-external-link"></i> </p> </dd> <dt>Bibcode:</dt> <dd> <a href="/abs/2011A%26A...534A..22V/abstract"> 2011A&A...534A..22V </a> <i class="icon-help" title="The bibcode is assigned by the ADS as a unique identifier for the paper."></i> </dd> <dt>Keywords:</dt> <dd> <ul class="list-inline"> <li>astrometry;</li> <li>ephemerides;</li> <li>reference systems</li> </ul> </dd> </dl> </article> </div> <div data-widget="ShowCitations"></div> <div data-widget="ShowReferences"></div> <div data-widget="ShowCoreads"></div> <div data-widget="ShowSimilar"></div> <div data-widget="ShowTableofcontents"></div> <div data-widget="ShowGraphics"></div> <div data-widget="ShowExportcitation" data-origin="abstract"></div> <div data-widget="ShowMetrics" data-allow-redirect="false"></div> <div data-widget="MetaTagsWidget"></div> </div> </div> </div> <div class="s-right-col-container col-xs-12 col-sm-12 col-md-3 col-lg-2 s-right-column" id="right-col-container" > <div data-widget="ShowResources"> <div data-reactroot="" class="s-right-col-widget-container" style="padding: 10px" > <div> <div class="resources__container"> <div class="resources__full__list"> <div class="resources__header__row"> <i class="fa fa-file-text-o" aria-hidden="true"> </i> <div class="resources__header__title">full text sources</div> </div> <div class="resources__content"> <div class="resources__content__title"> Publisher </div> <div class="resources__content__links"> <span> <a href="/link_gateway/2011A&A...534A..22V/PUB_PDF" rel="noopener" class="resources__content__link unlock" > <i class="fa fa-file-pdf-o" aria-hidden="true"> </i> </a> <div class="resources__content__link__separator">|</div> </span> <span> <a href="/link_gateway/2011A&A...534A..22V/PUB_HTML" rel="noopener" class="resources__content__link unlock" > <i class="fa fa-file-text" aria-hidden="true"> </i> </a> </span> </div> </div> </div> </div> <div data-widget="ShowAssociated"> <div data-reactroot="" class="resources__container"> <div class="resources__header__row"> <i class="fa fa-folder-open"></i> <div class="resources__header__title"> Related Materials (1) </div> </div> <div> <div style=" font-size: 1em; border-left: 3px solid grey; padding-left: 5px; margin-left: 7px; " class="resources__content" > <a href="/abs/2012A%26A...541C...1V/abstract" class="resources__content__link" >Erratum: 2012A&A...541C...1V</a > </div> </div> </div> </div> </div> </div> </div> <div data-widget="ShowGraphicsSidebar"> <div class="s-graphics-sidebar graphics-sidebar"> <div class="s-right-col-widget-container"> <div class="graphics-container s-graphics-container"> <h4 class="s-right-col-widget-title">Graphics</h4> <div class="grid-cell"> <a href="/abs/2011A%26A...534A..22V/graphics" > <img src="https://s3.amazonaws.com/adsabs-thumbnails/seri/A%2BA/0534/aa17274-11/aa17274-11-fig1.jpg" alt="figure from paper" class="grid-cell__image" /> <p><i>Click to view more</i></p> </a> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div id="footer-container"> <div data-widget="FooterWidget"> <div class="footer s-footer"> <footer> <div class="__footer_wrapper"> <div class="__footer_brand"> 漏 The SAO Astrophysics Data System <div class="__footer_brand_extra"> <p> <i class="fa fa-envelope"></i> adshelp[at]cfa.harvard.edu </p> <p> The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement <em>NNX16AC86A</em> </p> </div> <div class="__footer_brand_logos"> <div class="logo1"> <a href="http://www.si.edu" target="_blank" rel="noreferrer noopener"> <img id="smithsonian-logo" src="//styles/img/smithsonian-logo.svg" alt="Smithsonian logo" /> </a> </div> <div class="logo2"> <a href="https://www.cfa.harvard.edu/" target="_blank" rel="noreferrer noopener"> <img src="//styles/img/cfa.png" alt="Harvard Center for Astrophysics logo" id="cfa-logo" /> </a> </div> <div class="logo3"> <a href="http://www.nasa.gov" target="_blank" rel="noreferrer noopener"> <img src="//styles/img/nasa-partner.svg" alt="NASA logo" id="nasa-logo" /> </a> </div> <div class="__footer_brand_disclaimer"> *The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. 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b.innerHTML += autoValues[i].match.substr(val.length); } // Insert a input field that will hold the current array item's value: b.innerHTML += "<input type='hidden' value='" + autoValues[i].value + "'>"; // Listen to clicks on the item value (DIV element): b.addEventListener("click", function(e) { var terms = searchBox.value.split(/\s+/); // Remove the current part of the input used for matching terms.pop(); // Insert the value for the autocomplete text field: terms.push(this.getElementsByTagName("input")[0].value); searchBox.value = terms.join(" "); // Move cursor position inside quotes/parenthesis if needed searchBox.focus(); if (searchBox.value[searchBox.value.length-1] === '"' || searchBox.value[searchBox.value.length-1] === ')') { searchBox.setSelectionRange(searchBox.value.length-1, searchBox.value.length-1); } // Close the list of autocompleted values closeAllLists(); }); a.appendChild(b); } } if (a.children.length > 0) { // By default, enter will select the first entry currentFocus = 0; addActive(a.children); } }); /*execute a function presses a key on the keyboard:*/ searchBox.addEventListener("keydown", function(e) { var x = document.getElementById(this.id + "autocomplete-list"); if (x) x = x.getElementsByTagName("div"); if (e.keyCode == 40) { // If the arrow DOWN key is pressed, increase the currentFocus variable: currentFocus++; addActive(x); } else if (e.keyCode == 38) { //up // If the arrow UP key is pressed, decrease the currentFocus variable: currentFocus--; /*and and make the current item more visible:*/ addActive(x); } else if (e.keyCode == 13) { // If the ENTER key is pressed: if (currentFocus > -1) { // Prevent the form from being submitted: e.preventDefault(); // Simulate a click on the "active" item: if (x) x[currentFocus].click(); currentFocus = -1; } } }); function addActive(x) { // Classify an item as "active": if (!x) return false; // Remove the "active" class on all items: removeActive(x); if (currentFocus >= x.length) currentFocus = 0; if (currentFocus < 0) currentFocus = (x.length - 1); // Add class "autocomplete-active": x[currentFocus].classList.add("autocomplete-active"); } function removeActive(x) { // Remove the "active" class from all autocomplete items: for (var i = 0; i < x.length; i++) { x[i].classList.remove("autocomplete-active"); } } function closeAllLists(elmnt) { // Close all autocomplete lists in the document, except the one passed as an argument: var x = document.getElementsByClassName("autocomplete-items"); for (var i = 0; i < x.length; i++) { if (elmnt != x[i] && elmnt != searchBox) { x[i].parentNode.removeChild(x[i]); } } } // Any other clicks in the document: document.addEventListener("click", function (e) { closeAllLists(e.target); }); } var autoList = [ { value: 'author:""', label: 'Author', match: 'author:"' }, { value: 'author:"^"', label: 'First Author', match: 'first author' }, { value: 'author:"^"', label: 'First Author', match: 'author:"^' }, { value: 'bibcode:""', label: 'Bibcode', desc: 'e.g. bibcode:1989ApJ...342L..71R', match: 'bibcode:"' }, { value: 'bibstem:""', label: 'Publication', desc: 'e.g. bibstem:ApJ', match: 'bibstem:"' }, { value: 'bibstem:""', label: 'Publication', desc: 'e.g. bibstem:ApJ', match: 'publication (bibstem)' }, { value: 'arXiv:', label: 'arXiv ID', match: 'arxiv:' }, { value: 'doi:', label: 'DOI', match: 'doi:' }, { value: 'full:""', label: 'Full text search', desc: 'title, abstract, and body', match: 'full:' }, { value: 'full:""', label: 'Full text search', desc: 'title, abstract, and body', match: 'fulltext' }, { value: 'full:""', label: 'Full text search', desc: 'title, abstract, and body', match: 'text' }, { value: 'year:', label: 'Year', match: 'year' }, { value: 'year:1999-2005', label: 'Year Range', desc: 'e.g. 1999-2005', match: 'year range' }, { value: 'aff:""', label: 'Affiliation', match: 'aff:' }, { value: 'abs:""', label: 'Search abstract + title + keywords', match: 'abs:' }, { value: 'database:astronomy', label: 'Limit to papers in the astronomy database', match: 'database:astronomy' }, { value: 'database:physics', label: 'Limit to papers in the physics database', match: 'database:physics' }, { value: 'title:""', label: 'Title', match: 'title:"' }, { value: 'orcid:', label: 'ORCiD identifier', match: 'orcid:' }, { value: 'object:', label: 'SIMBAD object (e.g. object:LMC)', match: 'object:' }, { value: 'property:refereed', label: 'Limit to refereed', desc: '(property:refereed)', match: 'refereed' }, { value: 'property:refereed', label: 'Limit to refereed', desc: '(property:refereed)', match: 'property:refereed' }, { value: 'property:notrefereed', label: 'Limit to non-refereed', desc: '(property:notrefereed)', match: 'property:notrefereed' }, { value: 'property:notrefereed', label: 'Limit to non-refereed', desc: '(property:notrefereed)', match: 'notrefereed' }, { value: 'property:eprint', label: 'Limit to eprints', desc: '(property:eprint)', match: 'eprint' }, { value: 'property:eprint', label: 'Limit to eprints', desc: '(property:eprint)', match: 'property:eprint' }, { value: 'property:openaccess', label: 'Limit to open access', desc: '(property:openaccess)', match: 'property:openaccess' }, { value: 'property:openaccess', label: 'Limit to open access', desc: '(property:openaccess)', match: 'openaccess' }, { value: 'doctype:software', label: 'Limit to software', desc: '(doctype:software)', match: 'software' }, { value: 'doctype:software', label: 'Limit to software', desc: '(doctype:software)', match: 'doctype:software' }, { value: 'property:inproceedings', label: 'Limit to papers in conference proceedings', desc: '(property:inproceedings)', match: 'proceedings' }, { value: 'property:inproceedings', label: 'Limit to papers in conference proceedings', desc: '(property:inproceedings)', match: 'property:inproceedings' }, { value: 'citations()', label: 'Citations', desc: 'Get papers citing your search result set', match: 'citations(' }, { value: 'references()', label: 'References', desc: 'Get papers referenced by your search result set', match: 'references(' }, { value: 'trending()', label: 'Trending', desc: 'Get papers most read by users who recently read your search result set', match: 'trending(' }, { value: 'reviews()', label: 'Review Articles', desc: 'Get most relevant papers that cite your search result set', match: 'reviews(' }, { value: 'useful()', label: 'Useful', desc: 'Get papers most frequently cited by your search result set', match: 'useful(' }, { value: 'similar()', label: 'Similar', desc: 'Get papers that have similar full text to your search result set', match: 'similar(' }, ]; 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