On the Asymptotic Behavior of the Secular Perturbation Function in the Circular Restricted Three-Body Problem

IF 0.6 4区物理与天体物理 Q4 ASTRONOMY & ASTROPHYSICS Cosmic Research Pub Date : 2024-06-04 DOI:10.1134/s0010952524600252

P. S. Krasilnikov, A. V. Dobroslavskiy

{"title":"On the Asymptotic Behavior of the Secular Perturbation Function in the Circular Restricted Three-Body Problem","authors":"P. S. Krasilnikov, A. V. Dobroslavskiy","doi":"10.1134/s0010952524600252","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3>The asymptotic behavior of the secular perturbation function expanded in a power series in μ, the ratio of the semimajor axes of the massless point (asteroid) and Jupiter, is studied in the restricted spatial circular three-body problem. It is assumed that \\(\\mu < 1\\) (internal case). A new derivation of the expansion of a secular perturbation function into a power series with coefficients expressed through Gauss and Clausen functions is described based on Parseval’s formula. For different values of μ at fixed values of the Lidov-Kozai constant, the radius of convergence of the reduced series, the areas of convergence and divergence are described in the plane of osculating elements e, ω. It is shown that power series is asymptotic in the sense of Poincaré in divergence regions, and that truncating the series after a 70 number of terms provides an high value approximation to a secular perturbation function. It is shown that the asymptotic properties of the series deteriorate on the nonanalyticity curves of secular perturbation function and completely disappear in a small neighborhood of \\(\\mu = 1\\). The asymptotic nature of the series allows, using ordinary methods of perturbation theory, to study the evolution of Keplerian orbital elements for all values of \\(\\mu \\) from the interval [0, 1), excluding the case \\(\\mu \\approx 1\\).","PeriodicalId":56319,"journal":{"name":"Cosmic Research","volume":"2 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cosmic Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0010952524600252","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}

引用次数: 0

Abstract

The asymptotic behavior of the secular perturbation function expanded in a power series in μ, the ratio of the semimajor axes of the massless point (asteroid) and Jupiter, is studied in the restricted spatial circular three-body problem. It is assumed that \(\mu < 1\) (internal case). A new derivation of the expansion of a secular perturbation function into a power series with coefficients expressed through Gauss and Clausen functions is described based on Parseval’s formula. For different values of μ at fixed values of the Lidov-Kozai constant, the radius of convergence of the reduced series, the areas of convergence and divergence are described in the plane of osculating elements e, ω. It is shown that power series is asymptotic in the sense of Poincaré in divergence regions, and that truncating the series after a 70 number of terms provides an high value approximation to a secular perturbation function. It is shown that the asymptotic properties of the series deteriorate on the nonanalyticity curves of secular perturbation function and completely disappear in a small neighborhood of \(\mu = 1\). The asymptotic nature of the series allows, using ordinary methods of perturbation theory, to study the evolution of Keplerian orbital elements for all values of \(\mu \) from the interval [0, 1), excluding the case \(\mu \approx 1\).

Abstract Image

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

论圆形受限三体问题中的周期扰动函数的渐近行为

摘要在受限空间圆周三体问题中研究了以μ（无质量点（小行星）和木星的半长轴之比）为单位的幂级数展开的世俗扰动函数的渐近行为。假设\(\mu < 1\) （内部情况）。在帕瑟瓦尔公式的基础上，描述了将世俗扰动函数展开为幂级数的新推导，幂级数的系数通过高斯和克劳森函数表示。在 Lidov-Kozai 常数的固定值下，对于不同的 μ 值，描述了在循环元素 e, ω 平面上的还原序列收敛半径、收敛区域和发散区域。研究表明，在世俗扰动函数的非解析性曲线上，数列的渐近性质会恶化，并在\(\mu = 1\) 的小邻域内完全消失。数列的渐近性质允许使用扰动理论的普通方法来研究开普勒轨道元素在区间[0, 1]内所有\(\mu \)值的演化，不包括\(\mu \approx 1\) 的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Cosmic Research 地学天文-工程：宇航

CiteScore

1.10

自引率

33.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Cosmic Research publishes scientific papers covering all subjects of space science and technology, including the following: ballistics, flight dynamics of the Earth’s artificial satellites and automatic interplanetary stations; problems of transatmospheric descent; design and structure of spacecraft and scientific research instrumentation; life support systems and radiation safety of manned spacecrafts; exploration of the Earth from Space; exploration of near space; exploration of the Sun, planets, secondary planets, and interplanetary medium; exploration of stars, nebulae, interstellar medium, galaxies, and quasars from spacecraft; and various astrophysical problems related to space exploration. A chronicle of scientific events and other notices concerning the main topics of the journal are also presented.