Harmonic Expansion of Sector-Area Residuals and Implications for Orbital Precession: A Modern Reappraisal

Harmonic Expansion of Sector-Area Residuals and Implications for Orbital Precession: A Modern Reappraisal | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (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-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Harmonic Expansion of Sector-Area Residuals and Implications for Orbital Precession: A Modern Reappraisal Juntao Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6912664/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We revisit the harmonic expansion of the sector-area residual in elliptical orbits and clarify several historical and methodological inconsistencies associated with precession estimates. Through a modern derivation, we demonstrate that both full-period and half-period Fourier expansions yield the same first harmonic coefficient b 1 = −e when properly normalized. The apparent discrepancy in classical ephemerides is attributed not to a true doubling, but to accumulated errors in normalization, drift extraction, and harmonic truncation. We derive the correspondence between the leading harmonic and inverse-cubic secular perturbation, incorporate high-order terms into the drift function, and validate the corrected model using VLBI-based ephemeris drift data. A complete error budget analysis confirms that normalization mismatches dominate the historical overestimates of perihelion precession. Full Text Additional Declarations No competing interests reported. Supplementary Files driftutils.py mercurydriftpipeline.py Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6912664","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":472453996,"identity":"b442f172-673a-405a-a750-5212fec4df7c","order_by":0,"name":"Juntao Xu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYBACxgYQWQHEB8AIKoBfCzOQPEOKFgYGoBbGNogWhLV4NczIPybNO++wPN/xM4YHfzDYyG44QMhhM5KZjXm3HTaceSbH4DAPQ5oxMVoYHwO1JBgcSEs4zMBwOJEYLQyHeecAtZx/lgB02H+itABtaQBquZF84AAPwwEitPQ8NjaccyzdcOaNxwcO8xgkG88kpMWwPfGZxJsaa3m+84nNH39U2Mn2EdTSgMI1IKAcBOSJUDMKRsEoGAUjHQAAzDtJXYrLbwgAAAAASUVORK5CYII=","orcid":"","institution":"University of California","correspondingAuthor":true,"prefix":"","firstName":"Juntao","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2025-06-17 09:23:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6912664/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6912664/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86797336,"identity":"91eb79ee-24cd-4762-bc33-d7414dcccaa5","added_by":"auto","created_at":"2025-07-15 16:01:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":776871,"visible":true,"origin":"","legend":"","description":"","filename":"HarmonicExpansionofSectorAreaResidualsandImplicationsforOrbitalPrecessionAModernReappraisal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6912664/v1_covered_d2878073-1b37-4776-bf57-4bc5e17573ba.pdf"},{"id":84846830,"identity":"9a600be4-9438-43bf-a867-928992deb2dd","added_by":"auto","created_at":"2025-06-18 03:17:01","extension":"py","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1571,"visible":true,"origin":"","legend":"","description":"","filename":"driftutils.py","url":"https://assets-eu.researchsquare.com/files/rs-6912664/v1/9eb562d4c5cc19c21ad1b6e2.py"},{"id":84846829,"identity":"6eab5c1b-1758-4a39-8e99-ded90a72275b","added_by":"auto","created_at":"2025-06-18 03:17:01","extension":"py","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":5876,"visible":true,"origin":"","legend":"","description":"","filename":"mercurydriftpipeline.py","url":"https://assets-eu.researchsquare.com/files/rs-6912664/v1/728688fe60053b4df9359f7f.py"}],"financialInterests":"No competing interests reported.","formattedTitle":"Harmonic Expansion of Sector-Area Residuals and Implications for Orbital Precession: A Modern Reappraisal","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6912664/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6912664/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We revisit the harmonic expansion of the sector-area residual in elliptical orbits and clarify several historical and methodological inconsistencies associated with precession estimates. 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