Fully analytical propagator for lunar satellite orbits in closed form]{Fully analytical propagator for lunar satellite orbits in closed form

Fully analytical propagator for lunar satellite orbits in closed form]{Fully analytical propagator for lunar satellite orbits in closed form | 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 Fully analytical propagator for lunar satellite orbits in closed form]{Fully analytical propagator for lunar satellite orbits in closed form Rita Mastroianni, Edoardo Legnaro, Christos Efthymiopoulos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8804548/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract We present a fully analytical propagator for the long-term motion of lunar artificial satellites, based on a lunar gravity and third-body model sufficiently accurate for many practical applications. The model includes the twelve most important lunar gravity harmonics together with the Earth's quadrupole tidal perturbation, computed using a precise representation of the Earth's lunicentric ephemeris. Numerical tests indicate a satisfactory precision with respect to high-order (GRAIL) gravity models for all trajectories at altitudes ranging from approximately 300 km to 3000 km above the lunar surface, or frozen orbits at lower altitudes. Additional gravitational terms can be incorporated in a straightforward manner using the analytical framework here developed. Our theory yields an analytical solution of the secular equations of motion through a Hamiltonian normal-form approach in 'closed form'. Two successive transformations are employed together with their inverses: from osculating to mean orbital elements, and from mean to proper elements. Hence, the method allows to recover analytically the satellite's cartesian position and velocity in the lunicentric frame (PALRF) for any future or past time $t$ without any intermediate numerical propagation of the initial conditions. The propagator is valid over timescales of several decades for all non-impacting orbits, except within narrow regions associated with specific secular resonances. Numerical comparisons with full Cartesian propagation are used to assess the accuracy of the method. Lunar satellite dynamics Analytical orbit propagation Secular perturbation theory Hamiltonian Mechanics Celestial Mechanics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 03 Apr, 2026 Reviews received at journal 01 Apr, 2026 Reviews received at journal 30 Mar, 2026 Reviews received at journal 22 Mar, 2026 Reviewers agreed at journal 16 Feb, 2026 Reviewers agreed at journal 13 Feb, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers invited by journal 11 Feb, 2026 Editor assigned by journal 10 Feb, 2026 Submission checks completed at journal 10 Feb, 2026 First submitted to journal 06 Feb, 2026 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. 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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-8804548","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":591160151,"identity":"0df46998-af9f-4b74-9667-43c884bbfd6e","order_by":0,"name":"Rita Mastroianni","email":"","orcid":"","institution":"European Space Research and Technology Centre","correspondingAuthor":false,"prefix":"","firstName":"Rita","middleName":"","lastName":"Mastroianni","suffix":""},{"id":591160152,"identity":"b5d7344b-0548-4dbc-81dd-71273542866c","order_by":1,"name":"Edoardo Legnaro","email":"data:image/png;base64,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","orcid":"","institution":"University of Genoa","correspondingAuthor":true,"prefix":"","firstName":"Edoardo","middleName":"","lastName":"Legnaro","suffix":""},{"id":591160154,"identity":"5cee9069-8a05-4cbe-a0cb-8e06d79b5411","order_by":2,"name":"Christos Efthymiopoulos","email":"","orcid":"","institution":"University of Padua","correspondingAuthor":false,"prefix":"","firstName":"Christos","middleName":"","lastName":"Efthymiopoulos","suffix":""}],"badges":[],"createdAt":"2026-02-06 08:38:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8804548/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8804548/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102749634,"identity":"d46e491f-8d82-437c-9e8c-ae2a38033606","added_by":"auto","created_at":"2026-02-16 09:12:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7728604,"visible":true,"origin":"","legend":"","description":"","filename":"CelMechSubmissionarchive.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8804548/v1_covered_1d752598-0b9c-42fd-a88f-4a2e2bc1ebff.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fully analytical propagator for lunar satellite orbits in closed form]{Fully analytical propagator for lunar satellite orbits in closed form","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"celestial-mechanics-and-dynamical-astronomy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cele","sideBox":"Learn more about [Celestial Mechanics and Dynamical Astronomy](http://link.springer.com/journal/10569)","snPcode":"10569","submissionUrl":"https://submission.nature.com/new-submission/10569/3","title":"Celestial Mechanics and Dynamical Astronomy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Lunar satellite dynamics, Analytical orbit propagation, Secular perturbation theory, Hamiltonian Mechanics, Celestial Mechanics","lastPublishedDoi":"10.21203/rs.3.rs-8804548/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8804548/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present a fully analytical propagator for the long-term motion of lunar artificial satellites, based on a lunar gravity and third-body model sufficiently accurate for many practical applications. 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