{"title":"太阳系动力学ⅰ:轨道倾角和节点进动","authors":"R. G. Calvet","doi":"10.7546/giq-23-2022-1-38","DOIUrl":null,"url":null,"abstract":"The dynamic equations of the $n$-body problem are solved in relative coordinates and applied to the solar system, whence the mean variation rates of the longitudes of the ascending nodes and of the inclinations of the planetary orbits at J2000 have been calculated with respect to the ecliptic and to the Laplace invariable plane under the approximation of circular orbits. The theory so obtained supersedes the Lagrange-Laplace secular evolution theory. Formulas for the change from the equatorial and ecliptic coordinates to those of the Laplace invariable plane are also provided.","PeriodicalId":53425,"journal":{"name":"Geometry, Integrability and Quantization","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Dynamics of the Solar System I: Orbital Inclination and Nodal Precession\",\"authors\":\"R. G. Calvet\",\"doi\":\"10.7546/giq-23-2022-1-38\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The dynamic equations of the $n$-body problem are solved in relative coordinates and applied to the solar system, whence the mean variation rates of the longitudes of the ascending nodes and of the inclinations of the planetary orbits at J2000 have been calculated with respect to the ecliptic and to the Laplace invariable plane under the approximation of circular orbits. The theory so obtained supersedes the Lagrange-Laplace secular evolution theory. Formulas for the change from the equatorial and ecliptic coordinates to those of the Laplace invariable plane are also provided.\",\"PeriodicalId\":53425,\"journal\":{\"name\":\"Geometry, Integrability and Quantization\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry, Integrability and Quantization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/giq-23-2022-1-38\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry, Integrability and Quantization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/giq-23-2022-1-38","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
On the Dynamics of the Solar System I: Orbital Inclination and Nodal Precession
The dynamic equations of the $n$-body problem are solved in relative coordinates and applied to the solar system, whence the mean variation rates of the longitudes of the ascending nodes and of the inclinations of the planetary orbits at J2000 have been calculated with respect to the ecliptic and to the Laplace invariable plane under the approximation of circular orbits. The theory so obtained supersedes the Lagrange-Laplace secular evolution theory. Formulas for the change from the equatorial and ecliptic coordinates to those of the Laplace invariable plane are also provided.
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