{"id":3520,"date":"2022-08-24T17:12:36","date_gmt":"2022-08-24T08:12:36","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3520"},"modified":"2023-03-14T16:52:21","modified_gmt":"2023-03-14T07:52:21","slug":"%e6%a8%aa%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c%e3%82%92%e5%88%a5%e3%81%ae%e7%ab%8b%e5%a0%b4%e3%81%8b%e3%82%89%e3%81%bf%e3%82%8b%e3%81%a8%e3%80%8c%e7%9c%9f%e6%a8%aa%e3%80%8d","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3520\/","title":{"rendered":"\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u3092\u5225\u306e\u7acb\u5834\u304b\u3089\u307f\u308b\u3068\u300c\u771f\u6a2a\u300d\u3067\u306f\u306a\u3044\u3068\u3044\u3046\u8a71"},"content":{"rendered":"<p>\u7279\u6b8a\u76f8\u5bfe\u8ad6\u306b\u304a\u3044\u3066\u306f\uff0c\u5149\u6e90\u30fb\u89b3\u6e2c\u8005\u9593\u306e\u76f8\u5bfe\u901f\u5ea6\u304c\u30bc\u30ed\u306e\u77ac\u9593\u3067\u3042\u3063\u3066\u3082\uff0c\u89b3\u6e2c\u3055\u308c\u308b\u5149\u306e\u632f\u52d5\u6570\u306e\u5909\u5316\u304c\u8d77\u3053\u308b\u3002\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7279\u6709\u306e\u3053\u306e\u52b9\u679c\u306f\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u300d\u3068\u547c\u3070\u308c\u308b\u3002\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u539f\u56e0\u3068\u3057\u3066\u306f\uff0c\u5149\u6e90\u306e\u6642\u9593\u306e\u9032\u307f\u65b9\u304c\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7684\u52b9\u679c\u306b\u3088\u3063\u3066\u9045\u308c\u308b\u304b\u3089\u3060\uff0c\u306a\u3069\u3068\u3044\u3046\u8aac\u660e\u304c\u3042\u308b\u304c&#8230;<\/p>\n<p><!--more--><\/p>\n<h3>\u89b3\u6e2c\u8005\u304c\u52d5\u304f\u5834\u5408<\/h3>\n<p>\u5149\u6e90\u304c\u9759\u6b62\u3057\uff0c\u89b3\u6e2c\u8005\u304c\u904b\u52d5\u3059\u308b\u5834\u5408\u3092\u4f8b\u306b\uff0c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c\/\" target=\"_blank\" rel=\"noopener\">\u5225\u30da\u30fc\u30b8<\/a>\u306b\u66f8\u3044\u305f\u5185\u5bb9\u3092\u304a\u3055\u3089\u3044\u3059\u308b\u3068\uff0c\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u306e\u632f\u52d5\u6570\u3092 \\(\\omega_0\\) \uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570\u3092 \\(\\omega_{\\rm obs}\\) \u3068\u8868\u8a18\u3059\u308b\u3068<br id=\"yui_3_17_2_1_1641360729261_1410\" \/>$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1+V \\cos\\bar{\\theta}}$$<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u3068\u306f\uff0c\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u771f\u6a2a<\/strong><\/span> $\\displaystyle \\bar{\\theta} = \\frac{\\pi}{2}$ \u304b\u3089\u304f\u308b\u5149\u306b\u5bfe\u3057\u3066<\/p>\n<p>$$ \\omega_{\\rm obs} = \\omega_0 {\\sqrt{1-V^2}}\u00a0 &lt; \\omega_0$$<\/p>\n<p>\u3068\u306a\u308a\uff0c\u5149\u6e90\u30fb\u89b3\u6e2c\u8005\u9593\u306e\u76f8\u5bfe\u901f\u5ea6\u306f\u3053\u306e\u77ac\u9593\u30bc\u30ed\uff08\u5149\u6e90\u306b\u5411\u304b\u3046\u3042\u308b\u3044\u306f\u96e2\u308c\u308b\u901f\u5ea6\u6210\u5206\u304c\u30bc\u30ed\uff09\u3067\u3042\u308b\u304c\uff0c\u632f\u52d5\u6570\u306e\u5909\u5316\u304c\u8d77\u3053\u308b\u73fe\u8c61\u3067\u3042\u308b\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3545 size-medium\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop1-300x194.png\" alt=\"\" width=\"300\" height=\"194\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop1-300x194.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop1-640x414.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop1-1536x992.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop1-2048x1323.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop1-750x485.png 750w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u3053\u306e\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u304c\u8d77\u3053\u3063\u305f\u72b6\u6cc1\u3092\uff0c\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u307f\u308b\u3068\uff0c\u3069\u3046\u306a\u308b\u304b\u3002<\/p>\n<p>\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e5%85%89%e8%a1%8c%e5%b7%ae\/\" target=\"_blank\" rel=\"noopener\">\u5149\u884c\u5dee<\/a>\u300d\u306e\u30da\u30fc\u30b8\u3067\u5c0e\u3044\u305f\u3088\u3046\u306b\uff0c\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u307f\u305f\u6642\u306e\u5149\u306e\u89d2\u5ea6 $\\theta$ \u306f $\\bar{\\theta}$ \u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u3042\u308b\u3002<\/p>\n<p>$$\\cos \\bar{\\theta} = \\frac{\\cos\\theta -V}{1 &#8211; V\\cos\\theta} \\tag{1}$$<\/p>\n<p>\u5f93\u3063\u3066 $\\displaystyle \\cos\\bar{\\theta} = \\cos\\frac{\\pi}{2} = 0$ \u306e\u6642\u306e $\\theta$\u00a0 \u306f<\/p>\n<p>$$\\cos\\theta = V, \\quad \\therefore\\ \\ 0 &lt; \\theta &lt; \\frac{\\pi}{2} $$<\/p>\n<p>\u3068\u306a\u308b\u3002<\/p>\n<p>\u5149\u306e\u5165\u5c04\u89d2 $\\varTheta = \\pi &#8211; \\theta$ \u3067\u8868\u3059\u3068<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-3551\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku-300x171.png\" alt=\"\" width=\"300\" height=\"171\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku-300x171.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku-640x365.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku-1536x875.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku-2048x1167.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku-750x427.png 750w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>$$ \\frac{\\pi}{2} &lt; \\varTheta &lt; \\pi$$<\/p>\n<p>\u3068\u306a\u308a\uff0c\u5149\u6e90\u9759\u6b62\u7cfb\u304b\u3089\u307f\u308b\u3068\u300c\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u300d\u3092\u8d77\u3053\u3057\u3066\u3044\u308b\u5149\u306f\u904b\u52d5\u89b3\u6e2c\u8005\u306e\u5f8c\u65b9\u304b\u3089\u5165\u5c04\u3057\u3066\u3044\u308b\u3068\u898b\u3048\u308b\u3002<\/p>\n<p>\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u771f\u6a2a<\/strong><\/span>\u300d\u304b\u3089\u306e\u5149\u3067\u306f\u306a\u304f\u3066\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5f8c\u65b9\u304b\u3089\u306e\u5149\u3092\u9060\u3056\u304b\u308a\u306a\u304c\u3089\u898b\u3066\u3044\u308b\u306e\u3060\u304b\u3089\uff0c\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u3067\u632f\u52d5\u6570\u304c\u5c0f\u3055\u304f\u306a\u308b\u306e\u306f\u5f53\u7136\u3060\u3088\u306d<\/strong><\/span>\uff0c\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<h3>\u5149\u6e90\u304c\u52d5\u304f\u5834\u5408<\/h3>\n<p>$$\\omega_{\\rm obs} = \\omega_0 \\frac{\\sqrt{1-V^2}}{1-V \\cos{\\theta}}$$<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3546 size-medium\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop2-300x202.png\" alt=\"\" width=\"300\" height=\"202\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop2-300x202.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop2-640x432.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop2-1536x1036.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop2-2048x1381.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/yoko-dop2-750x506.png 750w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u771f\u6a2a<\/strong><\/span> $\\displaystyle {\\theta} = \\frac{\\pi}{2}$ \u304b\u3089\u304f\u308b\u5149\u306b\u5bfe\u3057\u3066<\/p>\n<p>$$ \\omega_{\\rm obs} = \\omega_0 {\\sqrt{1-V^2}}\u00a0 &lt; \\omega_0$$<\/p>\n<p>\u3068\u306a\u308a\uff0c\u5149\u6e90\u30fb\u89b3\u6e2c\u8005\u9593\u306e\u76f8\u5bfe\u901f\u5ea6\u306f\u3053\u306e\u77ac\u9593\u30bc\u30ed\u3067\u3042\u308b\u304c\uff0c\u632f\u52d5\u6570\u306e\u5909\u5316\u304c\u8d77\u3053\u308b\u3002<\/p>\n<p>\u3053\u308c\u3092\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u307f\u308b\u3068\uff0c$\\displaystyle \\cos{\\theta} = \\cos\\frac{\\pi}{2} = 0$ \u306e\u6642\u306e $\\bar{\\theta}$\u00a0 \u306f $(1)$ \u5f0f\u304b\u3089<\/p>\n<p>$$\\cos\\bar{\\theta} = -V, \\quad \\therefore\\ \\ \\bar{\\theta} &gt; \\frac{\\pi}{2} $$<\/p>\n<p>\u3068\u306a\u308b\u3002<\/p>\n<p>\u5149\u306e\u5165\u5c04\u89d2 $\\bar{\\varTheta} = \\pi &#8211; \\bar{\\theta}$ \u3067\u8868\u3059\u3068<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-3555\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku2-300x211.png\" alt=\"\" width=\"300\" height=\"211\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku2-300x211.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku2-640x449.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku2-1536x1078.png 1536w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku2-2048x1437.png 2048w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/nyushakaku2-750x526.png 750w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>$$ 0&lt; \\bar{\\varTheta} &lt; \\frac{\\pi}{2}$$<\/p>\n<p>\u3068\u306a\u308a\uff0c\u5149\u6e90\u9759\u6b62\u7cfb\u304b\u3089\u307f\u308b\u3068\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6a2a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/strong><\/span>\u300d\u3092\u8d77\u3053\u3057\u3066\u3044\u308b\u5149\u306f\uff0c\u904b\u52d5\u5149\u6e90\u304c\u89b3\u6e2c\u8005\u304b\u3089\u9060\u3056\u304b\u308a\u306a\u304c\u3089\u653e\u51fa\u3057\u305f\u5149\u304c\u89b3\u6e2c\u8005\u306b\u5c4a\u3044\u3066\u3044\u308b\u3068\u898b\u3048\u308b\u3002<\/p>\n<p>\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u771f\u6a2a<\/strong><\/span>\u300d\u304b\u3089\u306e\u5149\u3067\u306f\u306a\u304f\u3066\uff0c<span style=\"font-family: helvetica, arial, 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