{"id":4356,"date":"2022-12-02T11:14:58","date_gmt":"2022-12-02T02:14:58","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4356"},"modified":"2023-12-05T15:04:30","modified_gmt":"2023-12-05T06:04:30","slug":"hubble-1929-%e3%81%ae%e3%83%87%e3%83%bc%e3%82%bf%e3%81%8b%e3%82%89-maxima-%e3%81%a7%e3%83%8f%e3%83%83%e3%83%96%e3%83%ab%e5%ae%9a%e6%95%b0%e3%82%92%e6%8e%a8%e5%ae%9a%e3%81%99%e3%82%8b","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4356\/","title":{"rendered":"Hubble (1929) \u306e\u30c7\u30fc\u30bf\u304b\u3089 Maxima \u3067\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u3092\u63a8\u5b9a\u3059\u308b"},"content":{"rendered":"
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Hubble (1929) \u306e\u30c7\u30fc\u30bf<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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Hubble (1929)<\/a> \u306e Table 1<\/a> \u306e\u30c7\u30fc\u30bf\u304b\u3089 Hubble \u5b9a\u6570\u3092\u63a8\u5b9a\u3059\u308b\u3002<\/p>\n

Hubble (1929) \u306e\u30aa\u30ea\u30b8\u30ca\u30eb\u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n

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\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5185\u5bb9\u306e hubble.dat<\/code> \u3092\u7528\u610f\u3059\u308b\u3002<\/p>\n

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1\u5217\u76ee    2\u5217\u76ee    2\u5217\u76ee\r\nname     r(Mpc)   v(km\/s)\r\n<\/pre>\n<\/div>\n
\u3068\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n
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\"S.Mag.\"   0.032  +170\r\n\"L.Mag.\"   0.034  +290\r\n\"6822\"     0.214  -130\r\n\"598\"      0.263   -70\r\n\"221\"      0.275  -185\r\n\"224\"      0.275  -220\r\n\"5457\"     0.45   +200\r\n\"4736\"     0.5    +290\r\n\"5194\"     0.5    +270\r\n\"4449\"     0.63   +200\r\n\"4214\"     0.8    +300\r\n\"3031\"     0.9     -30\r\n\"3627\"     0.9    +650\r\n\"4826\"     0.9    +150\r\n\"5236\"     0.9    +500\r\n\"1068\"     1.0    +920\r\n\"5055\"     1.1    +450\r\n\"7331\"     1.1    +500\r\n\"4258\"     1.4    +500\r\n\"4151\"     1.7    +960\r\n\"4382\"     2.0    +500\r\n\"4472\"     2.0    +850\r\n\"4486\"     2.0    +800\r\n\"4649\"     2.0   +1090\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u9280\u6cb3\u307e\u3067\u306e\u8ddd\u96e2\u3068\u5f8c\u9000\u901f\u5ea6\u306e\u30b0\u30e9\u30d5<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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\/* hubble.dat \u3092\u8aad\u307f\u8fbc\u307f... *\/<\/span>\r\ntmp<\/span>:<\/span> read_nested_list<\/span>(<\/span>\"hubble.dat\"<\/span>)<\/span>$\r\n\/* 2\u5217\u76ee r \u3068 3\u5217\u76ee v \u306e\u30ea\u30b9\u30c8\u3092\u3064\u304f\u308b\u3002*\/<\/span>\r\nrv<\/span>:<\/span> makelist<\/span>([<\/span>a<\/span>[<\/span>2]<\/span>,a<\/span>[<\/span>3]]<\/span>, a<\/span>, tmp<\/span>)<\/span>$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  font<\/span> =<\/span> \"Arial\"<\/span>, font_size<\/span> =<\/span> 16<\/span>,\r\n  title<\/span> =<\/span> \"Hubble (1929) Table 1.\"<\/span>,\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>0.4<\/span>, 2.<\/span>4]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>400<\/span>, 1400]<\/span>, \r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  xtics<\/span> =<\/span> 1<\/span>, ytics<\/span> =<\/span> 500<\/span>, grid<\/span> =<\/span> true<\/span>,\r\n  xlabel<\/span> =<\/span> \"r (Mpc)\"<\/span>, ylabel<\/span> =<\/span> \"v (km\/s)\"<\/span>,\r\n\r\n  point_type<\/span> =<\/span> 7<\/span>, point_size<\/span> =<\/span> 0.6<\/span>, color<\/span> =<\/span> \"purple\"<\/span>,\r\n  points<\/span>(<\/span>rv<\/span>)<\/span>\r\n )<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u308b\u30d5\u30a3\u30c3\u30c8<\/h3>\n
$v = H_0 r$ \u3092\u4eee\u5b9a\u3057\u3066\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u308a $H_0$ \u3092\u63a8\u5b9a\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\/* \u6700\u521d\u306b1\u5ea6\u3060\u3051\u8ffd\u52a0\u30d1\u30c3\u30b1\u30fc\u30b8\u3092 load \u3057\u3066\u304a\u304f\u3002*\/<\/span>\r\nload<\/span>(<\/span>lsquares<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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f<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> H0<\/span> *<\/span> x<\/span>$\r\n\/* \u30ea\u30b9\u30c8 rv \u3092\u884c\u5217\u306b\u5909\u63db\u3057\u3066\u304b\u3089 *\/<\/span>\r\nlsquares_estimates<\/span>(<\/span>apply<\/span>(<\/span>'<\/span>matrix<\/span>, rv<\/span>)<\/span>, [<\/span>x<\/span>, y<\/span>]<\/span>, y<\/span>=<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>H0<\/span>])<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{6}$}\\left[ H_{0}=\\frac{2502739000}{5903559} \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\/* \u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u5f97\u3089\u308c\u305f\u5024\u3092 H0 \u306b\u4ee3\u5165 *\/<\/span>\r\nH0<\/span>:<\/span> float<\/span>(<\/span>rhs<\/span>(<\/span>%<\/span>[<\/span>1]))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{7}$}423.9373232316303\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30d5\u30a3\u30c3\u30c8\u3057\u305f\u76f4\u7dda\u3082\u30b0\u30e9\u30d5\u306b\u63cf\u304f<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d<\/span>(<\/span>\r\n  font<\/span> =<\/span> \"Arial\"<\/span>, font_size<\/span> =<\/span> 16<\/span>,\r\n  title<\/span> =<\/span> \"Hubble (1929) Table 1.\"<\/span>,\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>0.4<\/span>, 2.<\/span>4]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>400<\/span>, 1400]<\/span>, \r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, \r\n  xtics<\/span> =<\/span> 1<\/span>, ytics<\/span> =<\/span> 500<\/span>, grid<\/span> =<\/span> true<\/span>,\r\n  xlabel<\/span> =<\/span> \"r (Mpc)\"<\/span>, ylabel<\/span> =<\/span> \"v (km\/s)\"<\/span>,\r\n\r\n  point_type<\/span> =<\/span> 7<\/span>, point_size<\/span> =<\/span> 0.6<\/span>, color<\/span> =<\/span> \"purple\"<\/span>,\r\n  points<\/span>(<\/span>rv<\/span>)<\/span>, \r\n\r\n  key<\/span> =<\/span> printf<\/span>(<\/span>false<\/span>, \"H_0 = ~5,1f\"<\/span>, H0<\/span>)<\/span>,\r\n  line_width<\/span> =<\/span> 2<\/span>, color<\/span> =<\/span> \"forest_green\"<\/span>,\r\n  explicit<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2.4<\/span>)<\/span>\r\n )<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30cf\u30c3\u30d6\u30eb\u5e74\u9f62\uff08$H_0$ \u306e\u9006\u6570\uff09\u3092\u6c42\u3081\u308b<\/h3>\n
$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408\u306f\uff0c\u5b87\u5b99\u5e74\u9f62\u306e\u4e0a\u9650\u304c $\\displaystyle \\frac{1}{H_0}$ \u3068\u306a\u308b\u3002\u307e\u305f\uff0c$\\Omega_{\\rm m} = 1, \\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408\u306e\u5b87\u5b99\u5e74\u9f62\u306f $\\displaystyle \\frac{2}{3}\\frac{1}{H_0}$ \u3068\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\/* Mpc \u3092 km \u3067 *\/<\/span>\r\nMpc<\/span>:<\/span> 3.<\/span>0856775814127E19<\/span>$\r\n\r\n\/* 1\/H0 \u306f\u79d2\u306a\u306e\u3067\u300c\u5104\u5e74\u300d\u306b\u63db\u7b97 *\/<\/span>\r\nHinv<\/span>:<\/span> 1\/<\/span>H0<\/span> *<\/span> Mpc<\/span>$\r\nokunen<\/span>:<\/span> 60*<\/span>60*<\/span>24*3<\/span>65.<\/span>25*<\/span>1.<\/span>E8<\/span>$\r\n\r\nprintf<\/span>(<\/span>true<\/span>, \"~3,1f \u5104\u5e74\"<\/span>, Hinv<\/span>\/<\/span>okunen<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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23.1 \u5104\u5e74<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6f14\u7fd2<\/h3>\n
Hubble (1929) \u306e\u30c7\u30fc\u30bf\u304b\u3089\u5f97\u3089\u308c\u305f\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u5024\uff0c\u304a\u3088\u3073\u305d\u306e\u9006\u6570\u304b\u3089\u5f97\u3089\u308c\u308b\u5b87\u5b99\u5e74\u9f62\u306e\u4e0a\u9650\u306e\u5024\u306f\uff0c\u73fe\u5728\u6211\u3005\u304c\u77e5\u3063\u3066\u3044\u308b\u5730\u7403\u5e74\u9f62\uff08\u7d0446\u5104\u5e74\uff09\u3088\u308a\u3082\u77ed\u3044\u3060\u3051\u3067\u306a\u304f\uff0c\u5f53\u6642\uff0820\u4e16\u7d00\u524d\u534a\uff09\u306e\u77e5\u898b\u3067\u3082\u5730\u7403\u3088\u308a\u5b87\u5b99\u306e\u5e74\u9f62\u304c\u77ed\u304f\u306a\u308a\u305d\u3046\u306a\u5371\u3046\u3044\u72b6\u6cc1\u3067\u3042\u3063\u305f\u3002<\/p>\n
\u305d\u306e\u539f\u56e0\u306f\uff0c\u8ddd\u96e2\u306e\u63a8\u5b9a\u306e\u8aa4\u5dee\u3067\u3042\u3063\u305f\u3002<\/p>\n
\u73fe\u5728\uff0c\u6211\u3005\u306f\u4ee5\u4e0b\u306e\u30ea\u30f3\u30af\u304b\u3089\u305d\u308c\u305e\u308c\u306e\u9280\u6cb3\u306e\u8ddd\u96e2\uff08\u8ddd\u96e2\u306f\u30cf\u30c3\u30d6\u30eb\u306e\u6cd5\u5247\u4ee5\u5916\u306e\u624b\u6bb5\u3067\u6c42\u3081\u3089\u308c\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3057\u3088\u3046\uff09\u3068\u8d64\u65b9\u504f\u79fb\u3092\u78ba\u8a8d\u3067\u304d\u308b\u3002\u3053\u308c\u3089\u306e\u5024\u3092\u7528\u3044\u3066\u30cf\u30c3\u30d6\u30eb\u5b9a\u6570\u306e\u63a8\u5b9a\u3092\u884c\u3044\uff0c\u30cf\u30c3\u30d6\u30eb\u5e74\u9f62\u304c\u3044\u304f\u3089\u306b\u306a\u308b\u304b\u8abf\u3079\u3088\u3002<\/p>\n
\u4e00\u90e8\uff0c\u4ee5\u4e0b\u306e\u30ea\u30f3\u30af\u3067\u306f\u8ddd\u96e2\u306e\u30c7\u30fc\u30bf\u304c\u306a\u3044\u5929\u4f53\u3082\u3042\u308b\u3060\u308d\u3046\u3002\u305d\u306e\u5834\u5408\u306f\u300cngc 4214 distance\u300d\u306a\u3069\u3068\u30cd\u30c3\u30c8\u691c\u7d22\u3057\u3066\u307f\u3088\u3002<\/p>\n