{"id":4037,"date":"2023-02-27T10:00:16","date_gmt":"2023-02-27T01:00:16","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4037"},"modified":"2023-03-14T16:46:45","modified_gmt":"2023-03-14T07:46:45","slug":"wikipedia-%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e3%82%b1%e3%83%97%e3%83%a9%e3%83%bc%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e7%b4%9a%e6%95%b0%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4037\/","title":{"rendered":"Wikipedia (en\/ja) \u306b\u304a\u3051\u308b\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u89e3\u306e\u5fae\u5999\u306a\u5dee\u7570"},"content":{"rendered":"<p>\uff08\u305d\u306e\u3046\u3061\u4fee\u6b63\u3055\u308c\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u306e\u3067\uff09\u672c\u65e5\u95b2\u89a7\u6642\u70b9\u3067\uff0cWikipedia \u65e5\u672c\u8a9e\u7248\u306e\u300c<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%82%B1%E3%83%97%E3%83%A9%E3%83%BC%E6%96%B9%E7%A8%8B%E5%BC%8F\">\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/a>\u300d\u306e\u9805\u3068\uff0c\u82f1\u8a9e\u7248\u300c<a href=\"https:\/\/en.wikipedia.org\/wiki\/Kepler%27s_equation\">Kepler&#8217;s equation<\/a>\u300d\u306e\u9805\u3067\uff0c\u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u3092\u4f7f\u3063\u305f\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u89e3\u304c\u5fae\u5999\u306b\u7570\u306a\u308b\u4ef6\u3002<\/p>\n<p>\u8ffd\u8a18\uff1a 2023-02-27<\/p>\n<p>\u4ee5\u4e0b\u306e\u4ef6\u306f\uff0c\u96e2\u5fc3\u7387\u306e\u5b9a\u7fa9\u304c\u82f1\u8a9e\u7248\u306b\u5408\u3046\u3088\u3046\u306b\u4fee\u6b63\u3055\u308c\uff0c\u5fae\u5999\u306a\u5dee\u7570\u306f\u89e3\u6d88\u3055\u308c\u305f\u3088\u3046\u3067\u3059\u3002<\/p>\n<ul>\n<li>Wikipedia \u65e5\u672c\u8a9e\u7248\u306e\u300c<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%82%B1%E3%83%97%E3%83%A9%E3%83%BC%E6%96%B9%E7%A8%8B%E5%BC%8F\">\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/a>\u300d<\/li>\n<\/ul>\n<p><!--more--><\/p>\n<h3><a href=\"https:\/\/en.wikipedia.org\/wiki\/Kepler%27s_equation\">Kepler&#8217;s equation &#8211; Wikipedia<\/a>\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u89e3<\/h3>\n<blockquote><p>Kepler&#8217;s equation is<\/p>\n<p>$$ M = E &#8211; e \\sin E$$<\/p>\n<p>Fourier series expansion (with respect to $M$ ) using Bessel functions is<\/p>\n<p>$$ E = M + \\sum_{m=1}^{\\infty} \\frac{2}{m} J_m(m e) \\sin(m M)$$<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4039\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-en-640x223.png\" alt=\"\" width=\"640\" height=\"223\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-en-640x223.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-en-300x105.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-en-750x262.png 750w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-en.png 1270w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p><\/blockquote>\n<h3><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%82%B1%E3%83%97%E3%83%A9%E3%83%BC%E6%96%B9%E7%A8%8B%E5%BC%8F\">\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f &#8211; Wikipedia<\/a>\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u89e3<\/h3>\n<blockquote><p>$$ M = E + \\epsilon\u00a0 \\sin E$$<\/p>\n<p>\u901a\u5e38\u306f\u3053\u306e\u5f62\u306e\u65b9\u7a0b\u5f0f\u3092<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3068\u547c\u3093\u3067\u3044\u308b\u3002<\/p>\n<p>\u7d50\u5c40<\/p>\n<p>$$E = M + \\sum_{n=1}^{\\infty} \\frac{2}{n} J_n(-n \\epsilon) \\sin n M$$\u304c\u53b3\u5bc6\u89e3\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4040\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-ja-640x192.png\" alt=\"\" width=\"640\" height=\"192\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-ja-640x192.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-ja-300x90.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-ja-750x225.png 750w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/keplereq-ja.png 1326w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p><\/blockquote>\n<h3>\u9055\u3046\u306e\u304b\u9055\u308f\u306a\u3044\u306e\u304b<\/h3>\n<p>\u4e00\u77ac\uff0c\u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u306e\u4e2d\u8eab\u306e\u6b63\u8ca0\u304c\u7570\u306a\u308b\u306e\u3067\uff0c\u3048\uff0c\u3048\u30fc\u3063\uff01\u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u306f $n$ \u304c\u5947\u6570\u306a\u3089\u5947\u95a2\u6570\uff0c$n$\u00a0 \u304c\u5076\u6570\u306a\u3089\u5076\u95a2\u6570\u3060\u3063\u305f\u3088\u306a\u3041&#8230; \u3053\u308c\u3058\u3083\u3042\u7b54\u3048\u304c\u9055\u3046\u3053\u3068\u306b\u306a\u308b\u305e&#8230; \u306a\u3069\u3068\u601d\u3063\u305f\u304c\uff0c\u3088\u304f\u898b\u308b\u3068\u6700\u521d\u306e\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3067 $\\sin E$ \u306e\u524d\u306e\u7b26\u53f7\u304c\u7570\u306a\u308b\u3002\u3064\u307e\u308a\uff0c<\/p>\n<p>$$ \\epsilon \\Rightarrow &#8211; e$$<\/p>\n<p>\u3068\u3059\u308c\u3070\u540c\u3058\u5f0f\u3002Wikipedia \u65e5\u672c\u8a9e\u7248\u306e\u8a18\u4e8b\u304c\u306a\u305c\uff0c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u975e\u6a19\u6e96\u7684\u306a\u8868\u8a18\u3092\u3057\u305f\u306e\u304b\u4e0d\u660e\u3002<\/p>\n<p>\u300c<a href=\"https:\/\/astro-dic.jp\/keplers-equation\/\">\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f|\u5929\u6587\u5b66\u8f9e\u5178<\/a>\u300d\u3067\u3082<\/p>\n<p>$$u(t) &#8211; e \\sin u(t) = M(t)$$<\/p>\n<p>\u3060\u3057\uff0c\u79c1\u306e\u8a18\u4e8b\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/1881\/\">\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c2\u6cd5\u5247\u3092\u8996\u899a\u7684\u306b\u78ba\u8a8d\u3059\u308b<\/a>\u300d\u306e\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u306e\u9805\u3067\u3082\uff0c$e$ \u3092\u96e2\u5fc3\u7387\u3068\u3059\u308c\u3070<\/p>\n<p>$$u &#8211; e \\sin u = \\frac{2\\pi}{T} t$$<\/p>\n<p>\u3068\u306a\u308b\u3053\u3068\u304c\u5c0e\u304b\u308c\u3066\u3044\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uff08\u305d\u306e\u3046\u3061\u4fee\u6b63\u3055\u308c\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u306e\u3067\uff09\u672c\u65e5\u95b2\u89a7\u6642\u70b9\u3067\uff0cWikipedia \u65e5\u672c\u8a9e\u7248\u306e\u300c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u300d\u306e\u9805\u3068\uff0c\u82f1\u8a9e\u7248\u300cKepler&#8217;s equation\u300d\u306e\u9805\u3067\uff0c\u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u3092\u4f7f\u3063\u305f\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u89e3\u304c\u5fae\u5999\u306b\u7570\u306a\u308b\u4ef6\u3002<\/p>\n<p>\u8ffd\u8a18\uff1a 2023-02-27<\/p>\n<p>\u4ee5\u4e0b\u306e\u4ef6\u306f\uff0c\u96e2\u5fc3\u7387\u306e\u5b9a\u7fa9\u304c\u82f1\u8a9e\u7248\u306b\u5408\u3046\u3088\u3046\u306b\u4fee\u6b63\u3055\u308c\uff0c\u5fae\u5999\u306a\u5dee\u7570\u306f\u89e3\u6d88\u3055\u308c\u305f\u3088\u3046\u3067\u3059\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4037\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>Wikipedia \u65e5\u672c\u8a9e\u7248\u306e\u300c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u300d<\/li>\n<\/ul>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[18],"tags":[],"class_list":["post-4037","post","type-post","status-publish","format-standard","hentry","category-18","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/4037","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=4037"}],"version-history":[{"count":13,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/4037\/revisions"}],"predecessor-version":[{"id":5403,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/4037\/revisions\/5403"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=4037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=4037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=4037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}