Eccentricity excitation equation and its underlying mechanism: Orbital precession mechanism

Eccentricity excitation equation and its underlying mechanism: Orbital precession mechanism | 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 Article Eccentricity excitation equation and its underlying mechanism: Orbital precession mechanism Yong-Feng Dai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5324837/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 study addresses the problem of orbit formation in planetary (including planet−moon), binary, and hierarchical triple systems by proposing an eccentricity excitation equation and investigating its underlying mechanism. The study introduces a synchronous orbit radius ratio and investigates the relationship between the semi-major axes and synchronous orbit radius ratios of known eccentric systems with similar mass ratio orders of magnitude and spin–orbit angles to discover the eccentricity excitation equation. In an eccentric system with a mass ratio order of magnitude higher than −7.5217, the semi-major axis exhibits a power-law distribution relationship with the product of mass ratio and square of rotation period ratio. By assuming that a gravitational field rotates along with the host celestial body, this study extends Einstein’s equivalence principle to analyze the mechanism underlying the eccentricity excitation equation. A frame exists in local physical space of a rotating gravitational field, which replaces gravity and exhibits a free-fall acceleration toward the host and an acceleration from an initial zero velocity to current velocity of the gravitational field. This frame can be divided into two subframes, one of which can be replaced by the drag force. The orbital eccentricity results from the combined effect of two drag forces caused by the gravitational field rotation of the primary and secondary bodies in a system. Moreover, a power-law relationship exists between the orbital velocity forming the semi-major axis caused by the drag force due to the gravitational field rotation of the secondary body and the ratio of the two drag forces. Orbital precession is driven by the drag force acting on the secondary body only in the aphelion region and is positively correlated with the eccentricity. Physical sciences/Astronomy and planetary science/Planetary science/Exoplanets Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/General relativity and gravity Physical sciences/Astronomy and planetary science/Planetary science/Giant planets Physical sciences/Astronomy and planetary science/Planetary science/Inner planets exoplanets planets and satellites: gaseous planets planets and satellites: formation planets and satellites: terrestrial planets (stars:) binaries: general (stars:) planetary systems Full Text Additional Declarations There is NO Competing Interest. 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-5324837","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":369911299,"identity":"30bc806c-e16a-4edc-85aa-2f52b115e67b","order_by":0,"name":"Yong-Feng Dai","email":"data:image/png;base64,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","orcid":"","institution":"Lishuling Institute of Physical Space Research","correspondingAuthor":true,"prefix":"","firstName":"Yong-Feng","middleName":"","lastName":"Dai","suffix":""}],"badges":[],"createdAt":"2024-10-24 10:05:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5324837/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5324837/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68226241,"identity":"8c59511f-10f7-42c3-90fd-556a44079a9a","added_by":"auto","created_at":"2024-11-05 03:38:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":998596,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5324837/v1_covered_d9d92287-81df-4502-8b29-09ab3e86f97b.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Eccentricity excitation equation and its underlying mechanism: Orbital precession mechanism","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"exoplanets, planets and satellites: gaseous planets, planets and satellites: formation, planets and satellites: terrestrial planets, (stars:) binaries: general, (stars:) planetary systems","lastPublishedDoi":"10.21203/rs.3.rs-5324837/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5324837/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study addresses the problem of orbit formation in planetary (including planet−moon), binary, and hierarchical triple systems by proposing an eccentricity excitation equation and investigating its underlying mechanism. The study introduces a synchronous orbit radius ratio and investigates the relationship between the semi-major axes and synchronous orbit radius ratios of known eccentric systems with similar mass ratio orders of magnitude and spin–orbit angles to discover the eccentricity excitation equation. In an eccentric system with a mass ratio order of magnitude higher than −7.5217, the semi-major axis exhibits a power-law distribution relationship with the product of mass ratio and square of rotation period ratio. By assuming that a gravitational field rotates along with the host celestial body, this study extends Einstein’s equivalence principle to analyze the mechanism underlying the eccentricity excitation equation. A frame exists in local physical space of a rotating gravitational field, which replaces gravity and exhibits a free-fall acceleration toward the host and an acceleration from an initial zero velocity to current velocity of the gravitational field. This frame can be divided into two subframes, one of which can be replaced by the drag force. The orbital eccentricity results from the combined effect of two drag forces caused by the gravitational field rotation of the primary and secondary bodies in a system. Moreover, a power-law relationship exists between the orbital velocity forming the semi-major axis caused by the drag force due to the gravitational field rotation of the secondary body and the ratio of the two drag forces. Orbital precession is driven by the drag force acting on the secondary body only in the aphelion region and is positively correlated with the eccentricity.","manuscriptTitle":"Eccentricity excitation equation and its underlying mechanism: Orbital precession mechanism","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-25 02:12:52","doi":"10.21203/rs.3.rs-5324837/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"7bf9ddf6-75fe-461a-af5a-8b1278b98ad5","owner":[],"postedDate":"October 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":39366348,"name":"Physical sciences/Astronomy and planetary science/Planetary science/Exoplanets"},{"id":39366349,"name":"Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/General relativity and gravity"},{"id":39366350,"name":"Physical sciences/Astronomy and planetary science/Planetary science/Giant planets"},{"id":39366351,"name":"Physical sciences/Astronomy and planetary science/Planetary science/Inner planets"}],"tags":[],"updatedAt":"2024-11-05T03:30:17+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-25 02:12:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5324837","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5324837","identity":"rs-5324837","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}