{"title":"稍微扁圆的椭球上的射线路径和焦散","authors":"M. Longuet-Higgins","doi":"10.1098/rspa.1990.0035","DOIUrl":null,"url":null,"abstract":"We investigate the ray paths from a point-source S on a slightly oblate ellipsoidal shell. The caustics are found to form a 4-star, i.e. a regular, 4-cusped hypocycloid, centred on the point antipodal to S. The length-scale of the 4-star varies as ϵ cos2λ, where ϵ is the eccentricity and λ is the latitude of the antipodal point.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"32 1","pages":"283 - 290"},"PeriodicalIF":0.0000,"publicationDate":"1990-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Ray paths and caustics on a slightly oblate ellipsoid\",\"authors\":\"M. Longuet-Higgins\",\"doi\":\"10.1098/rspa.1990.0035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the ray paths from a point-source S on a slightly oblate ellipsoidal shell. The caustics are found to form a 4-star, i.e. a regular, 4-cusped hypocycloid, centred on the point antipodal to S. The length-scale of the 4-star varies as ϵ cos2λ, where ϵ is the eccentricity and λ is the latitude of the antipodal point.\",\"PeriodicalId\":20605,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"volume\":\"32 1\",\"pages\":\"283 - 290\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.1990.0035\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1990.0035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ray paths and caustics on a slightly oblate ellipsoid
We investigate the ray paths from a point-source S on a slightly oblate ellipsoidal shell. The caustics are found to form a 4-star, i.e. a regular, 4-cusped hypocycloid, centred on the point antipodal to S. The length-scale of the 4-star varies as ϵ cos2λ, where ϵ is the eccentricity and λ is the latitude of the antipodal point.
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