{"id":1025,"date":"2024-04-04T13:00:41","date_gmt":"2024-04-04T04:00:41","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1025"},"modified":"2025-06-21T10:56:02","modified_gmt":"2025-06-21T01:56:02","slug":"%e5%bc%b1%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e7%b2%92%e5%ad%90%e3%81%ae%e8%bb%8c%e9%81%93%e3%81%ae%e8%bf%91%e4%bc%bc%e8%a7%a3","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%e3%83%86%e3%82%b9%e3%83%88%e7%b2%92%e5%ad%90%e3%81%ae%e9%81%8b%e5%8b%95\/%e5%bc%b1%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e7%b2%92%e5%ad%90%e3%81%ae%e8%bb%8c%e9%81%93%e3%81%ae%e8%bf%91%e4%bc%bc%e8%a7%a3\/","title":{"rendered":"\u5f31\u91cd\u529b\u5834\u4e2d\u306e\u7c92\u5b50\u306e\u8ecc\u9053\u306e\u8fd1\u4f3c\u89e3\uff1a\u8fd1\u70b9\u79fb\u52d5"},"content":{"rendered":"

\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u8ecc\u9053\u3092\u6c7a\u3081\u308b\u5f0f\u306f\uff0c\u4e00\u822c\u306b\u306f\u89e3\u6790\u7684\u306a\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3002\u3053\u3053\u3067\u306f\uff0c\u7c92\u5b50\u306e\u8ecc\u9053\u306e\u3044\u305f\u308b\u3068\u3053\u308d\u3067\u91cd\u529b\u5834\u304c\u5f31\u3044\u3068\u3044\u3046\u8fd1\u4f3c\u306e\u3082\u3068\uff0c\u7c92\u5b50\uff08\u5929\u4f53\uff0c\u4eba\u5de5\u885b\u661f\u7b49\uff09\u306e\u8ecc\u9053\u3092\u8fd1\u4f3c\u7684\u306b\u89e3\u304f\u3002<\/p>\n

\u5ff5\u306e\u305f\u3081\uff0c\u300c\u8ecc\u9053\u306e\u3044\u305f\u308b\u3068\u3053\u308d\u3067\u91cd\u529b\u5834\u304c\u5f31\u3044<\/strong><\/span>\u300d\u3068\u306f\uff0c\u4e2d\u5fc3\u5929\u4f53\u304b\u3089\u306e\u8ddd\u96e2 $r$ \u304c\uff0c\u4e2d\u5fc3\u5929\u4f53\u306e\u8cea\u91cf $M$ \u3067\u6c7a\u307e\u308b\u91cd\u529b\u534a\u5f84 $r_g \\equiv \\dfrac{2GM}{c^2}$ \u306e\u5341\u5206\u5916\u5074\uff0c\u3064\u307e\u308a $ r_g \\ll r$ \u3067\u3042\u308b\u3088\u3046\u306a\u9818\u57df\u3092\u904b\u52d5\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3002\u8a00\u3044\u63db\u3048\u308b\u3068<\/p>\n

$$\\frac{r_g}{r} \\ll 1, \\ \\ \\frac{r_g}{a} \\ll 1, \\quad a \\equiv \\frac{r_{\\rm min} + r_{\\rm max}}{2}$$ \u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3088\u3002<\/p>\n

\u4e16\u306b\u3042\u307e\u305f\u3042\u308b\u76f8\u5bfe\u8ad6\u306e\u6559\u79d1\u66f8\u3067\u306f\uff0c\u305d\u308c\u305e\u308c\u306e\u8457\u8005\u304c\u8da3\u5411\u3092\u3053\u3089\u3057\u3066\u8fd1\u70b9\u79fb\u52d5<\/strong><\/span>\uff08\u592a\u967d\u306e\u307e\u308f\u308a\u306e\u8ecc\u9053\u306b\u3064\u3044\u3066\u306f\u8fd1\u65e5<\/span>\u70b9\u79fb\u52d5<\/strong><\/span>\uff09\u3092\u5c0e\u51fa\u3057\u3066\u3044\u308b\u304c\uff0c\u3068\u3082\u3059\u308c\u3070\u521d\u3081\u304b\u3089\u8fd1\u70b9\u79fb\u52d5\u3042\u308a\u304d\u3068\u3057\u3066\uff0c$\\cos \\gamma \\phi$ \u306b\u6bd4\u4f8b\u3059\u308b\u89e3\u3092\u982d\u304b\u3089\u4eee\u5b9a\u3057\u3066\u5c0e\u51fa\u3059\u308b\u4f8b\u3082\u3042\u308b\u3002\u3053\u3053\u3067\u306f\uff0c\u306a\u308b\u3079\u304f\u30b7\u30b9\u30c6\u30de\u30c6\u30a3\u30c3\u30af\u306b\uff0c\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u306e\u7a4d\u5206\u304b\u3089\u5f97\u3089\u308c\u305f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u3046\u307e\u304f\u5909\u5f62\u3057\u3066\u3084\u308b\u3068\uff0c\u81ea\u7136\u3068\u8fd1\u70b9\u79fb\u52d5\u3059\u308b\u8ecc\u9053\u304c\u89e3\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3088\u3046\u306a\u5c0e\u51fa\u6cd5\u3092\u307e\u3068\u3081\u3066\u304a\u304f\u3002<\/p>\n

\u5148\u306b\u7b54\u3048\u3092\u66f8\u3044\u3066\u304a\u304f\u3002<\/p>\n

\u307b\u307c \\(r_g\\) \uff08\u53b3\u5bc6\u306b\u8a00\u3048\u3070 $\\frac{r_g}{a}$\uff09\u306e1\u6b21\u307e\u3067\u306e\u7bc4\u56f2\u3067\uff08\u3082\u3046\u5c11\u3057\u7d30\u304b\u304f\u8a00\u3048\u3070\uff0c\\(O(r_g^2)\\) \u4ee5\u4e0a\u306e\u9805\u304a\u3088\u3073 \\(O(r_g e^2)\\) \u306e\u9805\u306f\u7121\u8996\u3059\u308b\u3068\u3044\u3046\u8fd1\u4f3c\u3067\uff09\u6c42\u3081\u305f\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u8ecc\u9053\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n

$$ r =\u00a0 \\frac{a(1-e^2)}{1 + e \\cos(\\gamma\\phi) } $$<\/p>\n

\u3053\u3053\u3067\uff0c<\/p>\n

$$ \\gamma = \\sqrt{ 1 -\\frac{3 r_g}{a(1-e^2)}} \\simeq 1 -\\frac{3 r_g}{2a(1-e^2)}$$<\/p>\n

\u307b\u307c\u6955\u5186\u8ecc\u9053\u3060\u304c\u91cd\u8981\u306a\u9055\u3044\u306f $\\gamma$ \u304c $1$ \u3067\u306f\u306a\u3044\u3053\u3068\u3067\uff0c\u3053\u308c\u304c\u8fd1\u70b9\u79fb\u52d5<\/strong><\/span>\u3092\u8868\u3059\u3002<\/p>\n

\u307e\u305f\uff0c$a$ \u304a\u3088\u3073 $e$ \u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u7406\u8ad6\u3067\u306f\u6955\u5186\u306e\u300c\u8ecc\u9053\u9577\u534a\u5f84<\/strong><\/span>\u300d\u304a\u3088\u3073\u300c\u96e2\u5fc3\u7387<\/strong><\/span>\u300d\u306b\u5bfe\u5fdc\u3059\u308b\u304c\uff0c\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u306a\u8fd1\u4f3c\u89e3\u3067\u306f\uff0c\u9589\u3058\u305f\u6955\u5186\u306b\u306a\u3089\u306a\u3044\u306e\u3067\uff0c\u53b3\u5bc6\u306b\u306f\u300c\u8ecc\u9053\u9577\u534a\u5f84<\/strong><\/span>\u300d\u3068\u304b\u300c\u96e2\u5fc3\u7387<\/strong><\/span>\u300d\u3068\u304b\u306a\u3069\u3068\u547c\u3076\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n

\u3057\u304b\u3057\uff0c\u8ecc\u9053\u304c\u53b3\u5bc6\u306b\u306f\u89e3\u3051\u306a\u3044\u3068\u3057\u3066\u3082\uff0c\u904b\u52d5\u304c\u6709\u754c\u3067\u3042\u308c\u3070 $r$ \u304c\u7121\u9650\u5927\u306b\u306a\u3063\u305f\u308a\u30bc\u30ed\u306b\u306a\u3063\u305f\u308a\u3059\u308b\u3053\u3068\u306a\u304f\uff0c\u539f\u70b9\u306e\u307e\u308f\u308a\u3092\u6709\u9650\u306e\u7bc4\u56f2<\/p>\n

$$ r_g < r_{\\rm min} \\le r \\le r_{\\rm max}$$<\/p>\n

\u3067\uff0c\u6709\u754c\u306a\u675f\u7e1b\u904b\u52d5\u3092\u3059\u308b\u30cf\u30ba\u3067\u3042\u308b\u3002\u305d\u3053\u3067\uff0c<\/p>\n

\\begin{eqnarray}
\nr_{\\rm max} &\\equiv& a\\,(1+e) \\\\
\nr_{\\rm min} &\\equiv& a\\,(1-e)
\n\\end{eqnarray}<\/p>\n

\u3068\u3057\u3066\u5909\u6570 $a$ \u304a\u3088\u3073 $e$ \u3092\u5b9a\u7fa9\u3059\u308b\u3002\uff08\u7e70\u308a\u8fd4\u3059\u304c\uff0c\u9589\u3058\u305f\u6955\u5186\u8ecc\u9053\u306e\u5834\u5408\u306b\u9650\u308a\uff0c$a$ \u304a\u3088\u3073 $e$ \u306f\u307e\u3055\u306b\u300c\u8ecc\u9053\u9577\u534a\u5f84<\/strong><\/span>\u300d\u304a\u3088\u3073\u300c\u96e2\u5fc3\u7387<\/strong><\/span>\u300d\u3067\u3042\u308b\u3002\uff09<\/p>\n

\u307e\u305f\uff0c\\(O(r_g e^2)\\) \u306e\u9805\u3092\u7121\u8996\u305b\u305a\u306b\uff0c$r_g$ \u306e1\u6b21\u306e\u9805\u3092\u5168\u3066\u542b\u3093\u3060\u5834\u5408\u306e\u89e3\u306b\u3064\u3044\u3066\u3082\u8ffd\u8a18\u3057\u3066\u3044\u308b\u3002<\/p>\n

\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u306e<\/span>\u30c6\u30b9\u30c8\u7c92\u5b50\u306e\u8ecc\u9053\u3092\u6c7a\u3081\u308b\u5f0f<\/span><\/h3>\n

$\\displaystyle s \\equiv \\frac{1}{r}$ \u3068\u3059\u308b\u3068\uff0c\u300c\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u306e\u7c92\u5b50\uff08\u89b3\u6e2c\u8005\uff09\u306e\u904b\u52d5<\/a>\u300d\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u305f\u3088\u3046\u306b\uff08\u9069\u5b9c\u79fb\u9805\u3057\u3066\uff09<\/p>\n

\\begin{eqnarray}
\n\\left( \\frac{ds}{d\\phi} \\right)^2\u00a0 +s^2 -\\frac{2GM}{\\ell^2} s\u00a0 &=& \\frac{\\epsilon^2 c^2 -c^2}{\\ell^2} +r_g\\, s^3 \\tag{1}
\n\\end{eqnarray}<\/p>\n

\u3053\u308c\u304c\u7c92\u5b50\u306e\u8ecc\u9053\u3092\u6c7a\u3081\u308b\u5f0f\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u3053\u3053\u3067\uff0c$\\epsilon$ \u304a\u3088\u3073 $\\ell$ \u306f\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u969b\u306b\u5f97\u3089\u308c\u305f\u904b\u52d5\u306e\u5b9a\u6570\u3067\u3042\u308a\uff0c<\/p>\n

$$ \\frac{d x^0}{d\\tau} = \\frac{c\\, dt}{d\\tau} = \\frac{\\epsilon\\, c}{1 -\\frac{r_g}{r}}, \\quad \\frac{d x^3}{d\\tau} = \\frac{d\\phi}{d\\tau} = \\frac{\\ell}{r^2}$$<\/p>\n

\u904b\u52d5\u304c\u6709\u754c\u3067\u3042\u308b\u5834\u5408<\/h4>\n

\u904b\u52d5\u304c\u6709\u754c\u3067\u3042\u308c\u3070\uff0c\u52d5\u5f84\u5ea7\u6a19 $r$ \u306e\u5024\u306f\uff0c\u3042\u308b\u6709\u9650\u306e\u7bc4\u56f2\u5185\u306b\u3068\u3069\u307e\u308b\uff0c\u3064\u307e\u308a $r_{\\rm min} \\leq r \\leq r_{\\rm max}$\u3002<\/p>\n

\\begin{eqnarray}
\nr_{\\rm min} &\\equiv& a(1 -e) \\\\
\nr_{\\rm max} &\\equiv& a(1 +e)
\n\\end{eqnarray}<\/p>\n

\u3068\u3059\u308b\u3068\uff0c$s = \\frac{1}{r}$ \u306b\u5bfe\u3057\u3066\u306f<\/p>\n

$$ \\frac{1}{a(1+e)} \\equiv \\frac{1}{r_{\\rm max}} \\leq s \\leq \\frac{1}{r_{\\rm min}} \\equiv \\frac{1}{a(1 -e)}$$<\/p>\n

\u6975\u5024\u3092\u3068\u308b\u70b9\u3067 $\\displaystyle \\frac{ds}{d\\phi} =0$ \u3067\u3042\u308b\u304b\u3089<\/p>\n

\\begin{eqnarray}
\n\\left( \\frac{1}{a (1+e)}\\right)^2 -2 \\frac{GM}{\\ell^2} \\left( \\frac{1}{a (1+e)}\\right) &=& \\frac{\\epsilon^2 c^2 -c^2}{\\ell^2} +r_g\\, \\left( \\frac{1}{a (1+e)}\\right)^3 \\\\
\n\\left( \\frac{1}{a (1-e)}\\right)^2 -2 \\frac{GM}{\\ell^2} \\left( \\frac{1}{a (1-e)}\\right)\u00a0 &=& \\frac{\\epsilon^2 c^2 -c^2}{\\ell^2} +r_g\\, \\left( \\frac{1}{a (1-e)}\\right)^3
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\uff08\u7dda\u5f62\u8fd1\u4f3c\u3067\u306f\u306a\u304f\uff0c\u53b3\u5bc6\u306b\u89e3\u3044\u3066\u3044\u308b\u306e\u3067\u3042\u308b\u304c\uff0c\u7d50\u679c\u306f $r_g$ \u306e1\u6b21\u307e\u3067\u306e\u5f62\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3082\u8208\u5473\u6df1\u3044\u3002\uff09<\/p>\n

\\begin{eqnarray}
\n\\frac{GM}{\\ell^2} &=& \\frac{1}{a (1 -e^2)} -\\frac{(3 + e^2) r_g}{2 a^2 (1 -e^2)^2} \\tag{2}\\\\
\n\\frac{\\epsilon^2 c^2 -c^2}{\\ell^2} &=& -\\frac{1}{a^2 (1 -e^2)} + \\frac{2 r_g}{a^3 (1 -e^2)^2} \\\\
\n&=& \\left(\\frac{e}{a (1-e^2)}\\right)^2 -\\left(\\frac{1}{a (1 -e^2)} \\right)^2+ \\frac{2 r_g}{a^3 (1 -e^2)^2} \\tag{3}
\n\\end{eqnarray}<\/p>\n

$a, \\, e$ \u306f\u6955\u5186\u8ecc\u9053\u306e\u5834\u5408\u306b\u306f\u8ecc\u9053\u9577\u534a\u5f84\uff0c\u96e2\u5fc3\u7387\u3068\u547c\u3070\u308c\u308b\u304c\uff0c\u3053\u3053\u3067\u306f $r_{\\rm max}, \\, r_{\\rm min}$ \u304b\u3089\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u6c7a\u3081\u3089\u308c\u308b\u5b9a\u6570\u3067\u3042\u308b\u3053\u3068\u3060\u3051\u3092\u899a\u3048\u3066\u304a\u304f\u3002<\/p>\n

\\begin{eqnarray}
\na &\\equiv& \\frac{1}{2} (r_{\\rm max} + r_{\\rm min}) \\\\
\ne &\\equiv& \\frac{r_{\\rm max} -r_{\\rm min}}{r_{\\rm max} + r_{\\rm min}}
\n\\end{eqnarray}<\/p>\n

(2) \u5f0f\u3068 (3) \u5f0f\u3092 (1) \u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\uff0c(1) \u5f0f\u306e\u5de6\u8fba\u304a\u3088\u3073\u53f3\u8fba\u306f<\/p>\n

\\begin{eqnarray}
\n\\mbox{\u5de6\u8fba} &=& \\left(\\frac{ds}{d\\phi} \\right)^2 + s^2 -2\\left(\\frac{1}{a (1 -e^2)} -\\frac{(3 + e^2) r_g}{2 a^2 (1 -e^2)^2} \\right)\\, s \\\\
\n&=& \\left(\\frac{ds}{d\\phi} \\right)^2 + \\left(s -\\frac{1}{a (1 -e^2)} \\right)^2 -\\left(\\frac{1}{a (1 -e^2)} \\right)^2 \\\\
\n&& +\u00a0 \\frac{(3 + e^2) r_g}{a^3 (1 -e^2)^3} \\\\
\n&& + \\frac{(3 + e^2) r_g}{a^2 (1 -e^2)^2} \\left(s -\\frac{1}{a (1 -e^2)} \\right)\\\\ \\ \\\\
\n\\mbox{\u53f3\u8fba} &=&
\n\\left(\\frac{e}{a (1-e^2)}\\right)^2 -\\left(\\frac{1}{a (1 -e^2)} \\right)^2 \\\\
\n&& + \\frac{2 r_g}{a^3 (1 -e^2)^2} \\\\
\n&& + r_g \\left\\{\\frac{1}{a (1 -e^2)} + \\left(s -\\frac{1}{a (1 -e^2)} \\right) \\right\\}^3 \\\\
\n&=& \\left(\\frac{e}{a (1-e^2)}\\right)^2 -\\left(\\frac{1}{a (1 -e^2)} \\right)^2 \\\\
\n&& + \\frac{(3-2 e^2) r_g}{a^3 (1 -e^2)^3} \\\\
\n&& + \\frac{3 r_g}{a^2 (1 -e^2)^2} \\left(s -\\frac{1}{a (1 -e^2)} \\right) \\\\
\n&& + \\frac{3 r_g}{a (1 -e^2)} \\left(s -\\frac{1}{a (1 -e^2)} \\right)^2 \\\\
\n&& + r_g \\left(s -\\frac{1}{a (1 -e^2)} \\right)^3
\n\\end{eqnarray}<\/p>\n

\u3068\u3044\u3046\u3053\u3068\u3067\uff0c$\\mbox{\u5de6\u8fba} = \\mbox{\u53f3\u8fba}$ \u3068\u3057\u3066\uff0c\u9069\u5b9c\u79fb\u9805\u3057\u3066\u307e\u3068\u3081\u308b\u3068<\/p>\n

\\begin{eqnarray}
\n\\left(\\frac{ds}{d\\phi} \\right)^2 +\\gamma^2 \\left(s -\\frac{1}{a (1 -e^2)} \\right)^2 &=&
\n\\gamma^2 \\left(\\frac{e}{a (1 -e^2)} \\right)^2 \\\\
\n&& -\\frac{e^2\\, r_g}{a^2 (1 -e^2)^2} \\left(s -\\frac{1}{a (1 -e^2)} \\right) \\\\
\n&& + r_g \\left(s -\\frac{1}{a (1 -e^2)} \\right)^3 \\\\ \\ \\\\
\n\\gamma^2 &\\equiv& \\left(1 -\\frac{3r_g}{a(1 -e^2)} \\right)
\n\\end{eqnarray}<\/p>\n

\u3053\u3053\u307e\u3067\u306f\u53b3\u5bc6\u306a\u5f0f\u3067\u3042\u308b\u3002\u3053\u306e\u307e\u307e\u3067\u306f\u89e3\u6790\u306b\u89e3\u3051\u306a\u3044\u3002\u7279\u306b\u53f3\u8fba\u306e\u7b2c3\u9805\uff083\u4e57\u306e\u9805\uff09\u304c\u66f2\u8005\u3067\u3042\u308b\u3002\u305d\u3053\u3067\uff0c\u4ee5\u4e0b\u3067\u306f\u4f55\u3089\u304b\u306e\u65b9\u6cd5\u3067\u8fd1\u4f3c\u7684\u306b\u89e3\u304f\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n

\u8ecc\u9053\u3092\u6c7a\u3081\u308b\u5f0f\u30922\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u3057\u3066\u89e3\u304f<\/span><\/h3>\n

\u3053\u306e\u307e\u307e\u3067\u3082\u8fd1\u4f3c\u7684\u306b\u89e3\u304f\u3053\u3068\u306f\u53ef\u80fd\u3067\u3042\u308b\u304c\uff08\u5225\u30da\u30fc\u30b8\u53c2\u7167\uff09<\/a>\uff0c\u4e21\u8fba\u3092 \\(\\phi\\) \u3067\u5fae\u5206\u3057\u3066<\/p>\n

\\begin{eqnarray}
\n2\\frac{ds}{d\\phi} \\frac{d^2s}{d\\phi^2}\u00a0 + 2\\gamma^2 \\left( s – \\frac{1}{a (1 -e^2)} \\right) \\frac{ds}{d\\phi}
\n&=& -\\frac{e^2\\, r_g}{a^2 (1 -e^2)^2} \\frac{ds}{d\\phi} + 3 r_g \\left( s – \\frac{1}{a (1 -e^2)} \\right)^2 \\frac{ds}{d\\phi}\\\\
\n\\therefore\\ \\\u00a0 \\frac{d^2s}{d\\phi^2} +\\gamma^2 \\left( s – \\frac{1}{a (1 -e^2)} \\right)
\n&=& -\\frac{{\\color{red}{e^2\\, r_g}}}{2 a^2 (1 -e^2)^2} + \\frac{3}{2}r_g \\left( s – \\frac{1}{a (1 -e^2)} \\right)^2 \\tag{4}
\n\\end{eqnarray}<\/p>\n

\u3068\u3057\u3066\uff0c\u3053\u3061\u3089\u3092\u8fd1\u4f3c\u7684\u306b\u89e3\u304f\u65b9\u6cd5\u3092\u7d39\u4ecb\u3059\u308b\u3002\u306a\u3093\u3067\u3082\u30461\u968e\u5fae\u5206\u3057\u3066\uff0c\u3053\u306e2\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u3057\u305f\u304b\u3068\u3044\u3046\u3068\uff0c\u307f\u3066\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u5168\u4f53\u3092\u898b\u308f\u305f\u3059\u3068\u61d0\u304b\u3057\u3044\u5358\u632f\u52d5\u306e\u65b9\u7a0b\u5f0f\u306b\u88dc\u6b63\u9805\u304c\u3064\u3044\u305f\u5f62\u306b\u306a\u3063\u3066\u3044\u3066\uff0c\u3072\u3087\u3063\u3068\u3057\u305f\u3089\u89e3\u304d\u3084\u3059\u3044\u304b\u3082\u2026 \u3068\u601d\u308f\u308c\u308b\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n

\u7a4d\u5206\u5b9a\u6570\u3092\u6c7a\u3081\u308b\u521d\u671f\u6761\u4ef6<\/span><\/h4>\n

\u305f\u3060\u3057\uff0c\u3053\u306e\u307e\u307e\u3060\u3068\u672c\u67651\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3060\u304b\u3089\u89e3\u306f\u7a4d\u5206\u5b9a\u6570\u30921\u500b\u6301\u3064\u306f\u305a\u304c\uff0c\u3082\u30461\u968e\u5fae\u5206\u3057\u30662\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u306a\u3063\u305f\u306e\u3067\u89e3\u306f\u7a4d\u5206\u5b9a\u6570\u30922\u500b\u6301\u3064\u3053\u3068\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3002<\/p>\n

\u5fae\u5206\u306e\u968e\u6570\u3092\u4eba\u70ba\u7684\u306b\u4e0a\u3052\u305f\u3053\u3068\u3067\u73fe\u308c\u308b\u3053\u3068\u306b\u306a\u3063\u3066\u3057\u307e\u3063\u305f\u4f59\u5206\u306e\u7a4d\u5206\u5b9a\u6570\u3082\u6c7a\u3081\u308b\u305f\u3081\u306e\u521d\u671f\u6761\u4ef6\u3068\u3057\u3066\uff0c\u4ee5\u4e0b\u3092\u63a1\u7528\u3059\u308b\u3002<\/p>\n