{"id":755,"date":"2022-01-12T18:00:20","date_gmt":"2022-01-12T09:00:20","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=755"},"modified":"2024-04-11T10:14:25","modified_gmt":"2024-04-11T01:14:25","slug":"%e5%a4%aa%e9%99%bd%e9%87%8d%e5%8a%9b%e3%81%ab%e3%82%88%e3%82%8b%e5%85%89%e3%81%ae%e3%80%8c%e6%9b%b2%e3%81%8c%e3%82%8a%e8%a7%92%e3%80%8d","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e5%85%89%e3%81%ae%e4%bc%9d%e6%92%ad\/%e5%a4%aa%e9%99%bd%e9%87%8d%e5%8a%9b%e3%81%ab%e3%82%88%e3%82%8b%e5%85%89%e3%81%ae%e3%80%8c%e6%9b%b2%e3%81%8c%e3%82%8a%e8%a7%92%e3%80%8d\/","title":{"rendered":"\u592a\u967d\u91cd\u529b\u306b\u3088\u308b\u5149\u306e\u300c\u66f2\u304c\u308a\u89d2\u300d"},"content":{"rendered":"

\u592a\u967d\u306e\u8868\u9762\u3059\u308c\u3059\u308c\u3092\u304b\u3059\u3081\u3066\u3084\u3063\u3066\u304f\u308b\u5149\u306f\uff0c\u592a\u967d\u91cd\u529b\u306b\u3088\u3063\u3066\u3069\u308c\u304f\u3089\u3044\u66f2\u3052\u3089\u308c\u308b\u304b\uff1f<\/p>\n

\u885d\u7a81\u30d1\u30e9\u30e1\u30fc\u30bf $b$ \u3092\u592a\u967d\u534a\u5f84 $R$ \u3068\u3057\u3066\u5149\u306e\u300c\u66f2\u304c\u308a\u89d2<\/strong><\/span>\u300d
\n$$\\alpha = \\frac{4 G M}{R c^2}$$ \u306f\u89d2\u5ea6\u306b\u3059\u308c\u3070\u4f55\u79d2\u306b\u306a\u308b\u304b\u3002<\/p>\n

Maxima-Jupyter \u3067\u306e\u8a08\u7b97\u4f8b<\/h3>\n
\n
\n
<\/div>\n
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\n

\u592a\u967d\u306e\u8868\u9762\u3059\u308c\u3059\u308c\u3092\u304b\u3059\u3081\u3066\u3084\u3063\u3066\u304f\u308b\u5149\u306f\uff0c\u592a\u967d\u91cd\u529b\u306b\u3088\u3063\u3066\u3069\u308c\u304f\u3089\u3044\u66f2\u3052\u3089\u308c\u308b\u304b\uff1f<\/p>\n

\u885d\u7a81\u30d1\u30e9\u30e1\u30fc\u30bf $b$ \u3092\u592a\u967d\u534a\u5f84 $R$ \u3068\u3057\u3066\u5149\u306e\u300c\u66f2\u304c\u308a\u89d2\u300d
\n$$\\alpha = \\frac{4 G M}{R c^2}$$ \u306f\u89d2\u5ea6\u306b\u3059\u308c\u3070\u4f55\u79d2\u306b\u306a\u308b\u304b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
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In\u00a0[1]:<\/div>\n
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alpha<\/span> =<\/span> alpha<\/span>:<\/span> 4*<\/span>G<\/span>*<\/span>M<\/span>\/<\/span>(<\/span>R<\/span> *<\/span> c<\/span>**<\/span>2<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
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Out[1]:<\/div>\n
\\[\\tag{${\\it \\%o}_{1}$}\\alpha=\\frac{4\\,G\\,M}{R\\,c^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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\/* \u4e07\u6709\u5f15\u529b\u5b9a\u6570 *\/<\/span>\r\nG<\/span>:<\/span> 6.<\/span>674E<\/span>-<\/span>11$\r\n\/* \u592a\u967d\u8cea\u91cf *\/<\/span>\r\nM<\/span>:<\/span> 1.<\/span>9891E30<\/span>$\r\n\/* \u592a\u967d\u534a\u5f84 *\/<\/span>\r\nR<\/span>:<\/span> 6.<\/span>9551E8<\/span>$\r\n\/* \u5149\u901f *\/<\/span>\r\nc<\/span>:<\/span> 299792458$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
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In\u00a0[3]:<\/div>\n
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alpha<\/span> =<\/span> ev<\/span>(<\/span>alpha<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
\\[\\tag{${\\it \\%o}_{6}$}\\frac{4\\,G\\,M}{R\\,c^2}=8.494895222001688 \\times 10^{-6}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
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\u30e9\u30b8\u30a2\u30f3\u3092\u79d2\u306b\u306a\u304a\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
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In\u00a0[4]:<\/div>\n
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fpprintprec<\/span>:<\/span> 3$\r\nprint<\/span>(<\/span>float<\/span>(<\/span>ev<\/span>(<\/span>alpha<\/span>)<\/span> \/<\/span>%pi<\/span> *<\/span> 180<\/span> *<\/span> 60<\/span> *<\/span> 60<\/span>)<\/span>, \"\u79d2\u89d2\"<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
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<\/div>\n
\\(1.75\\) \u79d2\u89d2<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
Python \u3067\u5149\u306e\u66f2\u304c\u308a\u89d2\u306e\u8a08\u7b97<\/h3>\n
\n
<\/div>\n
\n
\n
\u592a\u967d\u306e\u8868\u9762\u3059\u308c\u3059\u308c\u3092\u304b\u3059\u3081\u3066\u3084\u3063\u3066\u304f\u308b\u5149\u306f\uff0c\u592a\u967d\u91cd\u529b\u306b\u3088\u3063\u3066\u3069\u308c\u304f\u3089\u3044\u66f2\u3052\u3089\u308c\u308b\u304b\uff1f\u885d\u7a81\u30d1\u30e9\u30e1\u30fc\u30bf $b$ \u3092\u592a\u967d\u534a\u5f84 $R$ \u3068\u3057\u3066\u5149\u306e\u300c\u66f2\u304c\u308a\u89d2\u300d<\/p>\n
$$\\alpha = \\frac{4GM}{c^2 R}$$<\/p>\n
\u306f\u89d2\u5ea6\u306b\u3059\u308c\u3070\u4f55\u79d2\u306b\u306a\u308b\u304b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u30e2\u30b8\u30e5\u30fc\u30eb\u306e import<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
\n
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In\u00a0[1]:<\/div>\n
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\n
# \u5186\u5468\u7387\u3068\u304b\u3092\u4f7f\u3044\u305f\u3044\u306e\u3067<\/span>\r\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
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In\u00a0[2]:<\/div>\n
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# \u4e07\u6709\u5f15\u529b\u5b9a\u6570 <\/span>\r\nG<\/span> =<\/span> 6.674E-11<\/span>\r\n# \u592a\u967d\u8cea\u91cf  <\/span>\r\nM<\/span> =<\/span> 1.9891E30<\/span>\r\n# \u592a\u967d\u534a\u5f84  <\/span>\r\nR<\/span> =<\/span> 6.9551E8<\/span>\r\n# \u5149\u901f  <\/span>\r\nc<\/span> =<\/span> 299792458<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[3]:<\/div>\n
\n
\n
\n
alpha<\/span> =<\/span> 4<\/span>*<\/span>G<\/span>*<\/span>M<\/span>\/<\/span>(<\/span>c<\/span>**<\/span>2<\/span> *<\/span> R<\/span>)<\/span>\r\nalpha<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
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Out[3]:<\/div>\n
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8.49489522200169e-06<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
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\u30e9\u30b8\u30a2\u30f3\u3092\u89d2\u5ea6\u79d2\u306b\u306a\u304a\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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print<\/span>(<\/span>\"\u03b1 = <\/span>%.2f<\/span> \u79d2\u89d2\"<\/span> %<\/span> (<\/span>alpha<\/span>\/<\/span>np<\/span>.<\/span>pi<\/span>*<\/span>180<\/span>*<\/span>60<\/span>*<\/span>60<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
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<\/div>\n
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\u03b1 = 1.75 \u79d2\u89d2\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\u65e5\u98df\u6642\u306e\u89b3\u6e2c\u3067\u306f\u3069\u3053\u306e\u89d2\u5ea6\u3092\u89b3\u6e2c\u3057\u3066\u3044\u308b\u306e\u304b\uff1f<\/h3>\n
\u66f2\u304c\u308a\u89d2 \\(\\alpha\\) \u305d\u306e\u3082\u306e\u306f\u89b3\u6e2c\u91cf\u3067\u306f\u306a\u3044\u3002\uff08\u89b3\u6e2c\u8005\u306e\u3044\u308b\u5730\u70b9\u3067\u306e\u91cf\u3067\u306f\u306a\u3044\u304b\u3089\u3002\uff09\u3067\u306f\uff0c\u65e5\u98df\u6642\u306e\u89b3\u6e2c\u3067\u306f\uff0c\u3069\u306e\u89d2\u5ea6\u3092\u89b3\u6e2c\u3057\u3066\u4e00\u822c\u76f8\u5bfe\u6027\u8ad6\u306e\u4e88\u8a00\u3068\u4e00\u81f4\u3057\u305f\uff01\u3068\u8a00\u3063\u3066\u3044\u308b\u306e\u3067\u3042\u308d\u3046\u304b\uff1f<\/p>\n
\u8003\u3048\u65b9\u3068\u3057\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u56f3\u306e\u3088\u3046\u306b\u306a\u308b\u3002\uff08\u89d2\u5ea6\u306f\u5927\u3052\u3055\u306b\u306a\u3063\u3066\u307e\u3059\u3002\uff09<\/p>\n
\u307e\u305a\uff0c\u592a\u967d\u91cd\u529b\u306b\u3088\u308b\u5f71\u97ff\u3092\u53d7\u3051\u306a\u3044\u5834\u5408\uff0c\u9060\u65b9\u306e\u661f\u304c\u3042\u308b\u65b9\u5411 \\(P\\) \u306b\u898b\u3048\u305f\u3068\u3059\u308b\u3002<\/p>\n
\u65e5\u98df\u6642\u306f\uff0c\u592a\u967d\u304c\u9060\u65b9\u306e\u661f\u306e\u624b\u524d\u306b\u6765\u3066\uff0c\u672c\u6765\u306a\u3089\u3070\u661f\u304b\u3089\u306e\u5149\u306f\u906e\u3089\u308c\u3066\u898b\u3048\u306a\u3044\u3053\u3068\u306b\u306a\u308b\u304c\uff0c\u592a\u967d\u91cd\u529b\u306b\u3088\u308b\u5149\u306e\u66f2\u304c\u308a\u306b\u3088\u3063\u3066\uff0c\u3042\u305f\u304b\u3082\u65b9\u5411 \\(\\color{red}{Q}\\) \u306b\u3042\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002<\/p>\n
 <\/p>\n
\"\"<\/p>\n
\u65b9\u5411 \\(P\\) \u3068\u65b9\u5411 \\(\\color{red}{Q}\\) \u306e\u89d2\u5ea6\u5dee \\(\\theta\\) \u304c\u5b9f\u969b\u306e\u89b3\u6e2c\u304b\u3089\u5f97\u3089\u308c\u308b\u89d2\u5ea6\u3067\u3042\u308b\u3002\u4e0a\u56f3\u306e\u3088\u3046\u306b\uff0c\u5730\u7403\u304b\u3089\u592a\u967d\u307e\u3067\u306e\u8ddd\u96e2\u306b\u304f\u3089\u3079\u3066\uff0c\u9060\u65b9\u306e\u661f\u304c\u5341\u5206\u9060\u304f\u306b\u3042\u308c\u3070\uff0c\u307b\u307c\uff08\u5e73\u884c\u7dda\u306e\u540c\u4f4d\u89d2\u306f\u7b49\u3057\u3044\u3068\u3044\u3046\u3053\u3068\u304b\u3089\uff09
\n$$\\theta \\simeq \\color{red}{\\alpha}$$<\/p>\n
\u3068\u3057\u3066\u3088\u3044\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u4e00\u822c\u76f8\u5bfe\u8ad6\u306e\u4e88\u8a00\u3067\u3042\u308b \\(\\color{red}{\\alpha}\\) \u306e\u5024\u3092\u89b3\u6e2c\u306b\u3088\u3063\u3066\u691c\u8a3c\u3067\u304d\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u592a\u967d\u306e\u8868\u9762\u3059\u308c\u3059\u308c\u3092\u304b\u3059\u3081\u3066\u3084\u3063\u3066\u304f\u308b\u5149\u306f\uff0c\u592a\u967d\u91cd\u529b\u306b\u3088\u3063\u3066\u3069\u308c\u304f\u3089\u3044\u66f2\u3052\u3089\u308c\u308b\u304b\uff1f<\/p>\n
\u885d\u7a81\u30d1\u30e9\u30e1\u30fc\u30bf $b$ \u3092\u592a\u967d\u534a\u5f84 $R$ \u3068\u3057\u3066\u5149\u306e\u300c\u66f2\u304c\u308a\u89d2\u300d $$\\alpha = \\frac{4 G M}{R c^2}$$ \u306f\u89d2\u5ea6\u306b\u3059\u308c\u3070\u4f55\u79d2\u306b\u306a\u308b\u304b\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":83,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-755","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t