Semi-Analytical Time Series Solutions to the Circular Restricted Three-Body Problem

Semi-Analytical Time Series Solutions to the Circular Restricted Three-Body Problem | 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 Semi-Analytical Time Series Solutions to the Circular Restricted Three-Body Problem Ryan J. Menges, Daniel J. Scheeres This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7574811/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 work develops and verifies a semi-analytical propagation framework for the circular restricted three-body problem that represents the state as an explicit polynomial in time. The coefficient expressions are derived symbolically from the equations of motion, and the state transition matrix is obtained by differentiating the same truncated series so that state and sensitivity remain consistent. An adaptive step size follows from Taylor’s remainder integral and the method applies on intervals where the required derivatives exist and remain bounded. Validation across planar, spatial, and non-periodic Earth–Moon trajectories shows the expected truncation-error behavior and preserves invariants such as the Jacobi constant. Application studies use the same time-series model for both orbit propagation and STM construction. In impulsive targeting the STM maps terminal-state corrections to small adjustments at the initial epoch. In relative navigation with range, range-rate, and optical-angle measurements, the Extended Kalman Filter advances the state with the time-series propagation and carries the covariance and linearized measurement sensitivities with the analytical STM, while the Unscented Kalman Filter advances sigma points and predicted measurements with the same time-series dynamics. The results demonstrate accurate guidance and estimation performance in nonlinear cislunar dynamics with a consistent closed-form treatment of state and sensitivity. Semi-analytical propagation Cislunar dynamics CR3BP 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-7574811","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":518966208,"identity":"edb3b17f-5eb0-4f87-84ca-0825cf08ec40","order_by":0,"name":"Ryan J. 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