TTC-3: Tangent-Plane Curvature Consistency for Three-Angle Initial Orbit Determination with Detailed Derivation and 1000-Case Benchmark

TTC-3: Tangent-Plane Curvature Consistency for Three-Angle Initial Orbit Determination with Detailed Derivation and 1000-Case Benchmark | 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 TTC-3: Tangent-Plane Curvature Consistency for Three-Angle Initial Orbit Determination with Detailed Derivation and 1000-Case Benchmark Kürşat Yenidoğan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8904411/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 paper develops and validates a three-observation, angles-only initial orbit determination method named TTC-3 (Tangent-Plane Curvature Consistency). The method uses exactly three topocentric right-ascension/declination measurements, requires no range or range-rate data, and avoids global nonlinear fitting as a core solver stage. Its key equation is a scalar midpoint-range consistency relation F(rho_m)=u_tan(rho_m)-u_geom(rho_m)=0, where u_tan is obtained from tangent-plane dynamic projection and u_geom=mu/||r_m||^3 is the two-body geometric curvature. We provide line-by-line derivation of all intermediate equations, including explicit elimination of ddrho_m, rank conditions of the tangent system, and root-selection logic under multiple admissible solutions. The method is benchmarked against Gauss, Laplace, and Gooding implementations in Orekit using 1000 synthetic two-body cases generated from a single station at Anitkabir (Ankara), across LEO/SSO/MEO/GEO/GTO/MOLNIYA families, under 0 and 20 arcsec measurement noise. Results show that TTC-3 is competitive and often superior in angular consistency and medium/high-altitude families, while Gauss remains stronger in low-altitude fast passes under this strict three-angle setup. The derivation, implementation details, and reproducible experiment artifacts are all provided. initial orbit determination angles-only IOD three-observation IOD tangent-plane dynamics curvature consistency space surveillance 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-8904411","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599488341,"identity":"0a862e8b-0bf7-4115-b274-bb61b9347867","order_by":0,"name":"Kürşat Yenidoğan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBUlEQVRIiWNgGAWjYJCCAzwgkgfCkQOLPCBBi4ExWCSBkDXIWhIbQBQ+LQbHew8eeFNRK2/Oc8bs44+aP+nzww4/BNpiJ6fbgEPLmXMJB+ecOW64s7fHeDbPMYPcjbfTDIBako3NDuDQciPH4DBv2zHGDed5jJkZ2IBaZieAtBxI3IZLy/03YC32IC2MP/4ZpBvOTv+AX8sNHpCWmsQNZ3uMGXjbDBLkpXPw2yJ5JscA6JcDyRvOHCtm5u0zNtwgnVNwIMEAt1/4jp8x/vCmos52w5nkzYw/vsnJy89O3/zhQ4WdHC4tChDxw0hOBYsYYFcOAvINYKoOQ2QUjIJRMApGARwAALiIaeMmgb9TAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Kürşat","middleName":"","lastName":"Yenidoğan","suffix":""}],"badges":[],"createdAt":"2026-02-17 21:38:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8904411/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8904411/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106403408,"identity":"e44b59ba-165c-45aa-9a0e-66ff170302ab","added_by":"auto","created_at":"2026-04-08 09:14:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":845397,"visible":true,"origin":"","legend":"","description":"","filename":"YenidoganTTC3JASEditableSourcev1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8904411/v1_covered_6a2ec6fb-72a3-489e-82d8-900c0b8515fa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"TTC-3: Tangent-Plane Curvature Consistency for Three-Angle Initial Orbit Determination with Detailed Derivation and 1000-Case Benchmark","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":"initial orbit determination; angles-only IOD, three-observation IOD, tangent-plane dynamics, curvature consistency, space surveillance","lastPublishedDoi":"10.21203/rs.3.rs-8904411/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8904411/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper develops and validates a three-observation, angles-only initial orbit determination method named TTC-3 (Tangent-Plane Curvature Consistency). The method uses exactly three topocentric right-ascension/declination measurements, requires no range or range-rate data, and avoids global nonlinear fitting as a core solver stage. Its key equation is a scalar midpoint-range consistency relation F(rho_m)=u_tan(rho_m)-u_geom(rho_m)=0, where u_tan is obtained from tangent-plane dynamic projection and u_geom=mu/||r_m||^3 is the two-body geometric curvature. We provide line-by-line derivation of all intermediate equations, including explicit elimination of ddrho_m, rank conditions of the tangent system, and root-selection logic under multiple admissible solutions. The method is benchmarked against Gauss, Laplace, and Gooding implementations in Orekit using 1000 synthetic two-body cases generated from a single station at Anitkabir (Ankara), across LEO/SSO/MEO/GEO/GTO/MOLNIYA families, under 0 and 20 arcsec measurement noise. Results show that TTC-3 is competitive and often superior in angular consistency and medium/high-altitude families, while Gauss remains stronger in low-altitude fast passes under this strict three-angle setup. The derivation, implementation details, and reproducible experiment artifacts are all provided. 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