Encke-based orbit propagation and impulsive control under J2 perturbations: a comparison with RK45 and directional correction strategies

Encke-based orbit propagation and impulsive control under J2 perturbations: a comparison with RK45 and directional correction strategies | 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 Encke-based orbit propagation and impulsive control under J2 perturbations: a comparison with RK45 and directional correction strategies Minh Nguyen Cong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9514739/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract This paper presents a computationally efficient framework for orbit maintenance under dominant $J_2$ perturbations, combining Encke-based propagation with discrete impulsive control. The propagation performance is first evaluated against the Runge–Kutta–Fehlberg (RK45) method, showing comparable accuracy while enabling significantly larger integration time steps. The accuracy is further validated through the evolution of the right ascension of the ascending node (RAAN), which closely matches the theoretical secular drift induced by $J_2$. Based on this framework, a time-triggered impulsive control strategy is developed to mitigate perturbation-induced deviations. Two correction schemes are investigated: a multi-directional approach that compensates all components of the velocity error, and a dominant-direction approach that corrects only the largest component. Numerical results reveal a clear trade-off: the multi-directional strategy achieves faster convergence and lower cumulative $\Delta v$, whereas the dominant-direction strategy exhibits slower convergence and higher fuel consumption but yields smoother steady-state behavior. These findings highlight the potential of reduced-dimensional impulsive control for scenarios with directional constraints or limited actuation. Encke-based propagation J2 perturbation impulsive control directional correction RK45 comparison Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 13 May, 2026 Reviewers agreed at journal 11 May, 2026 Reviewers invited by journal 06 May, 2026 Editor assigned by journal 28 Apr, 2026 Submission checks completed at journal 27 Apr, 2026 First submitted to journal 24 Apr, 2026 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. 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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-9514739","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":630806665,"identity":"7a4a46d4-da7f-42d3-a619-ac11e58c8e15","order_by":0,"name":"Minh Nguyen Cong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsElEQVRIiWNgGAWjYJCCA4wNNhAWDwla0kjUwsDYcJgELebspxMPF+44n7hdIoHxwds2hsTthLRY9uRuODzzzO3EnTMSmA3nArXsbCCgxeAG74bDvG23jQ1uJLBJ87YxGBscIE7LOZAW9t+kaDkgB7KFGahFjrCWM7kgLclyBmceNkvOOSdBhJbjZzd/5m2z4zE4nnzww5syGx6CWpAAYwOQkCBe/SgYBaNgFIwC3AAAjPFBw1Z51ywAAAAASUVORK5CYII=","orcid":"","institution":"Vietnam National University, Hanoi","correspondingAuthor":true,"prefix":"","firstName":"Minh","middleName":"Nguyen","lastName":"Cong","suffix":""}],"badges":[],"createdAt":"2026-04-24 09:25:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9514739/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9514739/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108182846,"identity":"bd34d5ab-abfc-4ab9-88a9-188911b8a9ff","added_by":"auto","created_at":"2026-04-30 08:59:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4283631,"visible":true,"origin":"","legend":"","description":"","filename":"Enckebasedorbitpropagation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9514739/v1_covered_85f0d200-59d7-4fd2-a1ba-87e352e18a36.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Encke-based orbit propagation and impulsive control under J2 perturbations: a comparison with RK45 and directional correction strategies","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"ceas-space-journal","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ceas","sideBox":"Learn more about [CEAS Space Journal](http://link.springer.com/journal/12567)","snPcode":"12567","submissionUrl":"https://submission.nature.com/new-submission/12567/3","title":"CEAS Space Journal","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Encke-based propagation, J2 perturbation, impulsive control, directional correction, RK45 comparison","lastPublishedDoi":"10.21203/rs.3.rs-9514739/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9514739/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper presents a computationally efficient framework for orbit maintenance under dominant $J_2$ perturbations, combining Encke-based propagation with discrete impulsive control. 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