{"id":4342,"date":"2022-12-01T17:55:05","date_gmt":"2022-12-01T08:55:05","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4342"},"modified":"2023-03-14T16:51:01","modified_gmt":"2023-03-14T07:51:01","slug":"hubble-1929-%e3%81%ae%e3%83%87%e3%83%bc%e3%82%bf%e3%81%8b%e3%82%89-gnuplot-%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\/4342\/","title":{"rendered":"Hubble (1929) \u306e\u30c7\u30fc\u30bf\u304b\u3089 gnuplot \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<\/div>\n<\/div>\n<\/div>\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   3\u5217\u76ee\r\nname      r(Mpc)  v(km\/s)\r\n<\/pre>\n<\/div>\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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In\u00a0[1]:<\/div>\n
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%gnu<\/span>plot<\/span> inline<\/span> svg<\/span> size<\/span> 640<\/span>,<\/span>480<\/span> fixed<\/span> enhanced<\/span> font<\/span> ',16'<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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set<\/span> xrange<\/span> [<\/span>-0<\/span>.4<\/span>:<\/span>2.4<\/span>]<\/span>\r\nset<\/span> yrange<\/span> [<\/span>-400<\/span>:<\/span>1400<\/span>]<\/span>\r\nset<\/span> xtics<\/span> 1<\/span>\r\nset<\/span> ytics<\/span> 500<\/span>\r\nset<\/span> zeroaxis<\/span>\r\nset<\/span> grid<\/span>\r\nset<\/span> xlabel<\/span> \"r (Mpc)\"<\/span>\r\nset<\/span> ylabel<\/span> \"v (km\/s)\"<\/span>\r\nset<\/span> title<\/span> \"Hubble (1929) Table 1.\"<\/span>\r\n\r\nplot<\/span> \"hubble.dat\"<\/span> using<\/span> 2<\/span>:<\/span>3<\/span> pt<\/span> 7<\/span> ps<\/span> 0.6<\/span> notitle<\/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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In\u00a0[4]:<\/div>\n
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f<\/span>(<\/span>x<\/span>)<\/span> =<\/span> H0<\/span> *<\/span> x<\/span>\r\nfit<\/span> f<\/span>(<\/span>x<\/span>)<\/span> \"hubble.dat\"<\/span> using<\/span> 2<\/span>:<\/span>3<\/span> via<\/span> H0<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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iter      chisq       delta\/lim  lambda   H0           \r\n   0 6.4864271278e+06   0.00e+00  1.11e+00    1.000000e+00\r\n   1 1.2148506771e+06  -4.34e+05  1.11e-01    4.070198e+02\r\n   2 1.2064026394e+06  -7.00e+02  1.11e-02    4.239303e+02\r\n   3 1.2064026380e+06  -1.21e-04  1.11e-03    4.239373e+02\r\niter      chisq       delta\/lim  lambda   H0           \r\n\r\nAfter 3 iterations the fit converged.\r\nfinal sum of squares of residuals : 1.2064e+06\r\nrel. change during last iteration : -1.21473e-09\r\n\r\ndegrees of freedom    (FIT_NDF)                        : 23\r\nrms of residuals      (FIT_STDFIT) = sqrt(WSSR\/ndf)    : 229.025\r\nvariance of residuals (reduced chisquare) = WSSR\/ndf   : 52452.3\r\n\r\nFinal set of parameters            Asymptotic Standard Error\r\n=======================            ==========================\r\nH0              = 423.937          +\/- 42.15        (9.943%)\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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print<\/span> sprintf<\/span>(<\/span>\"H0 = %4.1f\"<\/span>,<\/span> H0<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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H0 = 423.9\r\n<\/pre>\n<\/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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In\u00a0[6]:<\/div>\n
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plot<\/span> \"hubble.dat\"<\/span> using<\/span> 2<\/span>:<\/span>3<\/span> pt<\/span> 7<\/span> ps<\/span> 0.6<\/span> notitle<\/span>,<\/span> \\\r\n     [<\/span>0<\/span>:<\/span>2.4<\/span>]<\/span> f<\/span>(<\/span>x<\/span>)<\/span> lw<\/span> 2<\/span> title<\/span> sprintf<\/span>(<\/span>\"H0 = %4.1f\"<\/span>,<\/span> H0<\/span>)<\/span>\r\n<\/pre>\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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In\u00a0[8]:<\/div>\n
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# Mpc \u3092 km \u3067<\/span>\r\nMpc<\/span> =<\/span> 3.0856775814127E19<\/span>\r\n\r\n# km\/(s Mpc)<\/span>\r\nHinv<\/span> =<\/span> 1<\/span>\/<\/span>H0<\/span> *<\/span> Mpc<\/span>\r\n# 1\/H0 \u306f\u79d2\u306a\u306e\u3067\u300c\u5104\u5e74\u300d\u306b\u63db\u7b97\u3059\u308b<\/span>\r\nokunen<\/span> =<\/span> 60<\/span>*<\/span>60<\/span>*<\/span>24<\/span>*<\/span>365.25<\/span>*<\/span>1.E8<\/span>\r\nprint<\/span> sprintf<\/span>(<\/span>\"%3.1f \u5104\u5e74\"<\/span>,<\/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\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6f14\u7fd2\u554f\u984c\uff1a\u73fe\u5728\u306e\u30c7\u30fc\u30bf\u304b\u3089 $H_0$ \u3092\u63a8\u5b9a\u3059\u308b<\/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