A Unified Hamiltonian Framework for Lunar Frozen Orbit Analysis Including Higher-Order Harmonics

A Unified Hamiltonian Framework for Lunar Frozen Orbit Analysis Including Higher-Order Harmonics | 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 A Unified Hamiltonian Framework for Lunar Frozen Orbit Analysis Including Higher-Order Harmonics Grigory Nikitin, Kyle Alfriend This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8835590/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 Although higher-order zonal harmonics have been considered in early Earth frozen-orbit analyses, the lunar frozen-orbit problem differs fundamentally due to the comparable magnitudes of multiple lunar gravity harmonics. As a result, most analytic lunar frozen-orbit studies rely on low-order gravity models and simplified averaging assumptions. This research provides a new method for finding frozen orbits through a long-period canonical transformation with the inclusion of higher-order harmonics, which allows frozen orbit conditions to be derived from the structure of the doubly-averaged Hamiltonian rather than through the use of the Lagrange Planetary Equations. This paper compares the frozen orbit parameters of lunar orbits obtained with gravitational harmonics up to \((C_{6,6})\) to those from a simpler model and demonstrates the importance of higher-order harmonics for lower-altitude orbits. Frozen orbits Lunar orbits Gravitational harmonics Third-body effects Long-period transformation Full Text Additional Declarations No competing interests reported. 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-8835590","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":593084453,"identity":"b8f7ab69-da13-4232-8fe7-e3e787e33995","order_by":0,"name":"Grigory Nikitin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7UlEQVRIiWNgGAWjYFACxgYQySPBzMBwgKECKshDnBZmoJYzBsRogQIJBqA1jG1EaJGPPtz84uOeOzKS7fwHDxfO+yOvOyOB8cHbNtxaDM8ltlnOePaMRxrosMMztxkYbruRwGw4F5+WHsY2Y54Dh3nkQFp4txkwArWwSfMSr2WOgT1QC/tvfFrkeRibH4O0gB3G22CQCLKFGZ8WAx7GNsYZQC2SzcwGh3mOGSdvO/OwWXLOOTy29LA//vDhwGF7ifMHH3/mqZGz3XY8+eCHN2V4bDnAwCaBJgaJXNy2NDAwf8CrYhSMglEwCkYBAFO9UJ+CTK41AAAAAElFTkSuQmCC","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":true,"prefix":"","firstName":"Grigory","middleName":"","lastName":"Nikitin","suffix":""},{"id":593084456,"identity":"4654122c-4aa9-4c78-a5ae-0614ea4e3f23","order_by":1,"name":"Kyle Alfriend","email":"","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":false,"prefix":"","firstName":"Kyle","middleName":"","lastName":"Alfriend","suffix":""}],"badges":[],"createdAt":"2026-02-10 02:53:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8835590/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8835590/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103090542,"identity":"66282f7e-1b9c-4f7b-afe5-603c5c71fe2b","added_by":"auto","created_at":"2026-02-20 16:40:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":506704,"visible":true,"origin":"","legend":"","description":"","filename":"AUnifiedHamiltonianFrameworkforLunarFrozenOrbitAnalysisIncludingHigherOrderHarmonics.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8835590/v1_covered_b2387c1a-6196-4609-a1f5-095c20b86fc1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Unified Hamiltonian Framework for Lunar Frozen Orbit Analysis Including Higher-Order Harmonics","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Frozen orbits, Lunar orbits, Gravitational harmonics, Third-body effects, Long-period transformation","lastPublishedDoi":"10.21203/rs.3.rs-8835590/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8835590/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAlthough higher-order zonal harmonics have been considered in early Earth frozen-orbit analyses, the lunar frozen-orbit problem differs fundamentally due to the comparable magnitudes of multiple lunar gravity harmonics. 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