Orbital Dynamics of Lunar Frozen Orbits around Triaxial Moon in the Presence of Third Body Influences

Orbital Dynamics of Lunar Frozen Orbits around Triaxial Moon in the Presence of Third Body Influences | 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 Orbital Dynamics of Lunar Frozen Orbits around Triaxial Moon in the Presence of Third Body Influences osama ramla, fawzy Abdelsalam, Walid Rahoma, Elamira Khattab This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9085564/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 This research explores the existence of some new families of frozen orbits for satellites orbiting the triaxial Moon. The Hamiltonian of the problem incorporates the Moon's gravitational zonal harmonic coefficients up to J6, along with the most significant triaxiality terms J22, J31, J32, J33, and the third-body perturbation due to Earth. By applying canonical Lie transforms, the short periodic terms are eliminated from the Hamiltonian, retaining the long periodic terms up to the second order. This study uncovers new families of critical inclination roots, with one set close to polar orbits and another near the typical critical inclination. It examines the dynamical variations in critical inclination due to changes in eccentricity, semi-major axis, and argument of periapsis. A family of frozen orbits with a fixed apsidal line is derived and graphically represented. To ensure the stability of these orbits, the periapsis argument solution imposes specific restrictions on selecting the inclination that satisfies the frozen argument of periapsis condition. Perturbations in the critical inclination become notably significant for high lunar orbits due to 3rd body perturbation from Earth. Frozen orbits Triaxial Moon 3rd body perturbation Critical inclination Lunar orbiters 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-9085564","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":605788664,"identity":"1adbb974-d88e-42cb-86f8-d3c0f7c0b0ef","order_by":0,"name":"osama ramla","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYLCCBww2YFqCeC0JDGmkazlMghZ+6cNPNyTUnJc3OMB88DYPg41dAyEtkn1pZjcSjt023HCALdmahyEtmaAWgzMMQC1stxMMDvCYSfMwHE4m6DCDM+zfbiT8OwfUwv8NqOU/MVp4zG4kth0A2cIG1HLAjqAWyR6eshuJfcmGMw+zGVvOMUhOIKiFn4d9240P3+zk+Y43P7zxpsLOnqAWBGAGu5MhsYEEPRBAii2jYBSMglEwQgAAWo85RSOrEvwAAAAASUVORK5CYII=","orcid":"","institution":"Cairo University","correspondingAuthor":true,"prefix":"","firstName":"osama","middleName":"","lastName":"ramla","suffix":""},{"id":605788665,"identity":"eada8c64-f32b-4844-a5a0-b1c8d8efa428","order_by":1,"name":"fawzy Abdelsalam","email":"","orcid":"","institution":"Cairo University","correspondingAuthor":false,"prefix":"","firstName":"fawzy","middleName":"","lastName":"Abdelsalam","suffix":""},{"id":605788666,"identity":"7298e1f7-4169-4701-bd02-6d1e5146d1ca","order_by":2,"name":"Walid Rahoma","email":"","orcid":"","institution":"Cairo University","correspondingAuthor":false,"prefix":"","firstName":"Walid","middleName":"","lastName":"Rahoma","suffix":""},{"id":605788667,"identity":"15e419d1-1433-426b-af84-b21cf6afc8ca","order_by":3,"name":"Elamira Khattab","email":"","orcid":"","institution":"Cairo University","correspondingAuthor":false,"prefix":"","firstName":"Elamira","middleName":"","lastName":"Khattab","suffix":""}],"badges":[],"createdAt":"2026-03-10 15:08:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9085564/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9085564/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107146728,"identity":"9112091d-69a2-4d5c-82d1-b19f47add001","added_by":"auto","created_at":"2026-04-17 09:58:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1589547,"visible":true,"origin":"","legend":"","description":"","filename":"OrbitalDynamicsofLunarFrozenOrbitsaroundTriaxialMooninthePresenceofThirdBodyInfluences.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9085564/v1_covered_47966238-e97b-4c5c-aeb9-ac62fab4a415.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Orbital Dynamics of Lunar Frozen Orbits around Triaxial Moon in the Presence of Third Body Influences","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, Triaxial Moon, 3rd body perturbation, Critical inclination, Lunar orbiters","lastPublishedDoi":"10.21203/rs.3.rs-9085564/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9085564/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This research explores the existence of some new families of frozen orbits for satellites orbiting the triaxial Moon. 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