{"title":"柯克伍德峡谷的数学探索","authors":"J. Vrbik","doi":"10.3888/TMJ.14-1","DOIUrl":null,"url":null,"abstract":"We first solve the planar Kepler problem of an asteroidʼs motion, perturbed by the gravitational pull of Jupiter. Analyzing the resulting differential equations for its orbital elements, we demonstrate the mechanism for creating a gap at the 2:1 resonance (the asteroid making two orbits for Jupiterʼs one), and briefly mention the case of other resonances (3:2, 3:1, etc.). We also discuss reasons why the motion becomes chaotic at these resonances.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical Exploration of Kirkwood Gaps\",\"authors\":\"J. Vrbik\",\"doi\":\"10.3888/TMJ.14-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We first solve the planar Kepler problem of an asteroidʼs motion, perturbed by the gravitational pull of Jupiter. Analyzing the resulting differential equations for its orbital elements, we demonstrate the mechanism for creating a gap at the 2:1 resonance (the asteroid making two orbits for Jupiterʼs one), and briefly mention the case of other resonances (3:2, 3:1, etc.). We also discuss reasons why the motion becomes chaotic at these resonances.\",\"PeriodicalId\":91418,\"journal\":{\"name\":\"The Mathematica journal\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Mathematica journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3888/TMJ.14-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Mathematica journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3888/TMJ.14-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We first solve the planar Kepler problem of an asteroidʼs motion, perturbed by the gravitational pull of Jupiter. Analyzing the resulting differential equations for its orbital elements, we demonstrate the mechanism for creating a gap at the 2:1 resonance (the asteroid making two orbits for Jupiterʼs one), and briefly mention the case of other resonances (3:2, 3:1, etc.). We also discuss reasons why the motion becomes chaotic at these resonances.
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