Spacecraft Relative Motion with Respect to a Spinning Chief Body Frame

Spacecraft Relative Motion with Respect to a Spinning Chief Body Frame | 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 Spacecraft Relative Motion with Respect to a Spinning Chief Body Frame Afrah Ghedira, Hanspeter Schaub This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8118398/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 Relative motion between orbiting spacecraft is commonly modeled in the Hill frame due to its analytical first-order solutions and the intuitive geometry of the resulting trajectories. However, the Hill frame is not ideal for mission scenarios involving constraints defined in the body frame of a spinning chief, such as collision avoidance during close-proximity operations or docking within a keep-in zone. This paper investigates relative motion from the perspective of the rotating body frame of the chief, focusing on three fundamental spin cases. In each case, the body frame is initially aligned with the Hill frame and undergoes constant rotation about one of the Hill frame principal axes: radial, along-track, and cross-track direction. Closed-form solutions to the Clohessy-Wiltshire equations are used to derive analytical expressions for the relative motion in the chief body frame, assuming circular chief orbits and small separation distances. The resulting trajectories are described using geometrically meaningful invariants of motion, providing intuitive insights into the trajectory shapes and locations. These trajectories are characterized as parametric epitrochoid or hypotrochoid curves. The analysis considers both bounded and drifting motion, and includes both resonant cases, where the spin rate equals the orbital rate, and non-resonant spin cases. Spacecraft relative motion Body frame Spinning chief Circular chief orbits 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. 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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-8118398","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":560221300,"identity":"97703f2c-e92b-439d-9fff-73a7a5ca3e76","order_by":0,"name":"Afrah Ghedira","email":"data:image/png;base64,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","orcid":"","institution":"University of Colorado Boulder","correspondingAuthor":true,"prefix":"","firstName":"Afrah","middleName":"","lastName":"Ghedira","suffix":""},{"id":560221302,"identity":"076ddb4c-ae76-4a9c-9705-12cc42f5ce7f","order_by":1,"name":"Hanspeter Schaub","email":"","orcid":"","institution":"University of Colorado Boulder","correspondingAuthor":false,"prefix":"","firstName":"Hanspeter","middleName":"","lastName":"Schaub","suffix":""}],"badges":[],"createdAt":"2025-11-14 22:53:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8118398/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8118398/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98409918,"identity":"e5321f36-eeb1-46da-a927-d319defecd29","added_by":"auto","created_at":"2025-12-17 13:37:48","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4122,"visible":true,"origin":"","legend":"","description":"","filename":"1a4a6c26fcee4383aeed050d351f1d55.json","url":"https://assets-eu.researchsquare.com/files/rs-8118398/v1/728955aa38f0c6bd2c6d1af4.json"},{"id":98441994,"identity":"d3875677-3462-4a89-a5c9-1da36261f068","added_by":"auto","created_at":"2025-12-17 17:06:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":16191553,"visible":true,"origin":"","legend":"","description":"","filename":"JASGhediraSchaub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8118398/v1_covered_e1e1f59f-f2d8-44e8-ae9e-013c70484f8c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spacecraft Relative Motion with Respect to a Spinning Chief Body Frame","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":"Spacecraft relative motion, Body frame, Spinning chief, Circular chief orbits","lastPublishedDoi":"10.21203/rs.3.rs-8118398/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8118398/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Relative motion between orbiting spacecraft is commonly modeled in the Hill frame due to its analytical first-order solutions and the intuitive geometry of the resulting trajectories. 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