{"title":"On the Approximation of the Attraction Field of a Rigid Body by the Attraction Field of Four Material Points of the Same Mass","authors":"A. A. Burov, E. A. Nikonova, V. I. Nikonov","doi":"10.1134/s1063454124700110","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study the problem of approximating the gravitational potential of a rigid body by the potential of a system of four identical point masses. Considering the potential as an expansion in terms of a parameter characterizing the ratio of the average size of a body to the distance to a test point in space, we propose an approach to constructing an approximate expression up to terms of the third order of smallness. This approach is used to build a model of the gravitational field of the nucleus of comet 67P/Churyumov–Gerasimenko.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454124700110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we study the problem of approximating the gravitational potential of a rigid body by the potential of a system of four identical point masses. Considering the potential as an expansion in terms of a parameter characterizing the ratio of the average size of a body to the distance to a test point in space, we propose an approach to constructing an approximate expression up to terms of the third order of smallness. This approach is used to build a model of the gravitational field of the nucleus of comet 67P/Churyumov–Gerasimenko.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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