{"title":"Efficient Computations in Keplerian Motion and Kepler’s Equation","authors":"I. A. Moiseev, N. V. Emelyanov","doi":"10.1134/S1063772925701653","DOIUrl":null,"url":null,"abstract":"<p>In the paper, the main aspects of practical calculations by the formulas of Keplerian motion have been considered. The initial value under consideration is the mean anomaly and five other constant parameters. Much attention has been paid to solving the Kepler equation. An overview of the methods for solving has been given. A method for specifying the accuracy of calculations with allowance for the limited accuracy of representing numbers in a computer system has been considered. Examples of solving the Kepler equation and examples of motion trajectories have been provided. According to the considered concept, an optimal program for calculations has been compiled in the programming languages C/C++, Fortran, Python and offered on the Internet pages. The user has been given the opportunity to select a method for solving the Kepler equation from those considered in the paper.</p>","PeriodicalId":55440,"journal":{"name":"Astronomy Reports","volume":"69 3","pages":"228 - 242"},"PeriodicalIF":0.7000,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Astronomy Reports","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1063772925701653","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
In the paper, the main aspects of practical calculations by the formulas of Keplerian motion have been considered. The initial value under consideration is the mean anomaly and five other constant parameters. Much attention has been paid to solving the Kepler equation. An overview of the methods for solving has been given. A method for specifying the accuracy of calculations with allowance for the limited accuracy of representing numbers in a computer system has been considered. Examples of solving the Kepler equation and examples of motion trajectories have been provided. According to the considered concept, an optimal program for calculations has been compiled in the programming languages C/C++, Fortran, Python and offered on the Internet pages. The user has been given the opportunity to select a method for solving the Kepler equation from those considered in the paper.
期刊介绍：
Astronomy Reports is an international peer reviewed journal that publishes original papers on astronomical topics, including theoretical and observational astrophysics, physics of the Sun, planetary astrophysics, radio astronomy, stellar astronomy, celestial mechanics, and astronomy methods and instrumentation.
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