{"title":"Application of the Hori–Deprit Method to the Analysis of the Cosmogonic Evolution of Weakly Perturbed Planetary Systems","authors":"D. V. Mikryukov, I. A. Balyaev","doi":"10.1134/S1063773722030045","DOIUrl":null,"url":null,"abstract":"<p>The dynamical evolution of nonresonant two-planet systems whose structure is nearly circular and coplanar is studied by the Hori–Deprit averaging method. The Poincaré astrocentric coordinates and the complex form of the second system of Poincaré canonical elements are used. The equations are averaged to the second order in planetary masses. The averaged system is integrated using one model two-planet system and the real two-planet system HD 12661 as examples. The constructed solution is compared with the solution of the averaged system of the first approximation and with the solution of the exact equations of motion in rectangular coordinates. In the case of both planetary systems, the second approximation is shown to agree better with the solution of the exact equations. According to the exact equations, the equations of the second approximation, and the equations of the first approximation, the oscillation period of the eccentricities in the HD 12661 system is 26 175, 26 309, and 26 391 years, respectively.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1063773722030045","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
The dynamical evolution of nonresonant two-planet systems whose structure is nearly circular and coplanar is studied by the Hori–Deprit averaging method. The Poincaré astrocentric coordinates and the complex form of the second system of Poincaré canonical elements are used. The equations are averaged to the second order in planetary masses. The averaged system is integrated using one model two-planet system and the real two-planet system HD 12661 as examples. The constructed solution is compared with the solution of the averaged system of the first approximation and with the solution of the exact equations of motion in rectangular coordinates. In the case of both planetary systems, the second approximation is shown to agree better with the solution of the exact equations. According to the exact equations, the equations of the second approximation, and the equations of the first approximation, the oscillation period of the eccentricities in the HD 12661 system is 26 175, 26 309, and 26 391 years, respectively.
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Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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