{"id":1632,"date":"2025-11-03T21:09:12","date_gmt":"2025-11-03T12:09:12","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=1632"},"modified":"2026-02-14T22:05:39","modified_gmt":"2026-02-14T13:05:39","slug":"post-1632","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=1632","title":{"rendered":"\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/daba-no-heya.com\/?p=1632\/#%E5%B0%8E%E5%85%A5\" >\u5c0e\u5165<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/daba-no-heya.com\/?p=1632\/#%E4%BD%8D%E7%BD%AE%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E3%81%AE%E5%AE%9A%E7%BE%A9\" >\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5b9a\u7fa9<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/daba-no-heya.com\/?p=1632\/#%E5%8A%9B%E5%AD%A6%E7%9A%84%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E4%BF%9D%E5%AD%98%E5%89%87\" >\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/daba-no-heya.com\/?p=1632\/#%E9%87%8D%E5%8A%9B%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%E3%81%AE%E5%AE%9A%E7%BE%A9\" >\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u5b9a\u7fa9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/daba-no-heya.com\/?p=1632\/#%E9%87%8D%E5%8A%9B%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%E3%81%A8%E3%83%9D%E3%82%A2%E3%82%BD%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F\" >\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/daba-no-heya.com\/?p=1632\/#%E7%A9%8D%E5%88%86%E5%BD%A2%E5%BC%8F\" >\u7a4d\u5206\u5f62\u5f0f<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%B0%8E%E5%85%A5\"><\/span>\u5c0e\u5165<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4ee5\u524d\u306b\u3001<a href=\"https:\/\/daba-no-heya.com\/?p=503\" data-type=\"link\" data-id=\"https:\/\/daba-no-heya.com\/?p=503\">\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u3092\u6c42\u3081\u308b\u8a18\u4e8b<\/a>\u3092\u4f5c\u6210\u3057\u305f\u306e\u3067\u3059\u304c\u3001\u305d\u306e\u8a18\u4e8b\u306e\u6700\u521d\u3067\u3001\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u304c$\\nabla^2\\phi=4\\pi G\\rho$\u306e\u5f62\u3067\u8868\u305b\u308b\u3068\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002<br>\u3053\u308c\u306f\u5c11\u3057\u5c0e\u5165\u304c\u96d1\u306a\u306e\u3068\u3001\u81ea\u5206\u81ea\u8eab\u3042\u307e\u308a\u3088\u304f\u7406\u89e3\u3057\u3066\u3044\u306a\u304b\u3063\u305f\u305f\u3081\u3001\u4eca\u56de\u6539\u3081\u3066\u8abf\u3079\u3066\u8a18\u4e8b\u306b\u307e\u3068\u3081\u308b\u3053\u3068\u306b\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%BD%8D%E7%BD%AE%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E3%81%AE%E5%AE%9A%E7%BE%A9\"><\/span>\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>$\\boldsymbol{F}$\u3092\u4fdd\u5b58\u529b\u3068\u3057\u305f\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u91cf\u3092\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>U(\\boldsymbol{r})=-\\int_{\\boldsymbol{r_0}}^{\\boldsymbol{r}}\\boldsymbol{F}\\cdot d\\boldsymbol{r&#8217;}<br>$$<\/p>\n\n\n\n<p>\u4f4d\u7f6e$\\boldsymbol{r_0}$\u304b\u3089$\\boldsymbol{r}$\u307e\u3067\u79fb\u52d5\u3059\u308b\u969b\u306b\u3001\u4fdd\u5b58\u529b\u306b\u9006\u3089\u3046\u529b$-\\boldsymbol{F}$\u306b\u3088\u3063\u3066\u306a\u3055\u308c\u308b\u4ed5\u4e8b\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%8A%9B%E5%AD%A6%E7%9A%84%E3%82%A8%E3%83%8D%E3%83%AB%E3%82%AE%E3%83%BC%E4%BF%9D%E5%AD%98%E5%89%87\"><\/span>\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u7269\u4f53\u304c\u4f4d\u7f6e$\\boldsymbol{r_A}$\u304b\u3089$\\boldsymbol{r_B}$\u307e\u3067\u4fdd\u5b58\u529b$\\boldsymbol{F}$\u306b\u3088\u3063\u3066\u79fb\u52d5\u3057\u305f\u5834\u5408\u306b\u53d7\u3051\u53d6\u308b\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u3001\u4fdd\u5b58\u529b$\\boldsymbol{F}$\u306b\u3088\u3063\u3066\u306a\u3055\u308c\u305f\u4ed5\u4e8b\u306b\u7b49\u3057\u3044\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$ <br>\\begin{align} \\left.\\frac{1}{2}mv^2\\right|_{\\boldsymbol{r_B}}-\\left.\\frac{1}{2}mv^2\\right|_{\\boldsymbol{r_A}}&amp;=\\int_{\\boldsymbol{r_A}}^{\\boldsymbol{r_B}}\\boldsymbol{F}\\cdot d\\boldsymbol{r} \\\\ &amp;=\\int_{\\boldsymbol{r_A}}^{\\boldsymbol{r_0}}\\boldsymbol{F}\\cdot d\\boldsymbol{r}+\\int_{\\boldsymbol{r_0}}^{\\boldsymbol{r_B}}\\boldsymbol{F}\\cdot d\\boldsymbol{r} \\\\ &amp;=-\\int_{\\boldsymbol{r_0}}^{\\boldsymbol{r_A}}\\boldsymbol{F}\\cdot d\\boldsymbol{r}+\\int_{\\boldsymbol{r_0}}^{\\boldsymbol{r_B}}\\boldsymbol{F}\\cdot d\\boldsymbol{r} \\\\ &amp;=U(\\boldsymbol{r_A})-U(\\boldsymbol{r_B}) \\end{align} <br>$$<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n<p>\n$$\n\\left.\\frac{1}{2}mv^2\\right|_{\\boldsymbol{r_A}}+U(\\boldsymbol{r_A})=\\left.\\frac{1}{2}mv^2\\right|_{\\boldsymbol{r_B}}+U(\\boldsymbol{r_B})=\\text{const.}\n$$\n<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8D%E5%8A%9B%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%E3%81%AE%E5%AE%9A%E7%BE%A9\"><\/span>\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5358\u4f4d\u8cea\u91cf\u3042\u305f\u308a\u306e\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc$\\Phi(\\boldsymbol{r})$\u3092\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\Phi(\\boldsymbol{r})=\\frac{1}{m}U(\\boldsymbol{r})<br>$$<\/p>\n\n\n\n<p>\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5b9a\u7fa9\u304b\u3089\u3001<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{F}(\\boldsymbol{r})=-\\nabla U(\\boldsymbol{r})=-m\\nabla\\Phi(\\boldsymbol{r})<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u3053\u3053\u3067\u767b\u5834\u3057\u305f$\\nabla$ (nabla)\u306b\u3064\u3044\u3066\u5c11\u3057\u8aac\u660e\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30ab\u30e9\u30fc\u5834$f$\u306b\u5bfe\u3057\u3066$\\nabla f$\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<br>\u3053\u308c\u3092\u52fe\u914d(gradient)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\nabla f=\\frac{\\partial f}{\\partial x}\\boldsymbol{\\hat{x}}+\\frac{\\partial f}{\\partial y}\\boldsymbol{\\hat{y}}+\\frac{\\partial f}{\\partial z}\\boldsymbol{\\hat{z}}<br>$$<\/p>\n\n\n\n<p>\u4e00\u65b9\u3001\u30d9\u30af\u30c8\u30eb\u5834$\\boldsymbol{v}$\u306b\u5bfe\u3057\u3066\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<br>\u3053\u308c\u3092\u767a\u6563(divergence)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\nabla\\cdot\\boldsymbol{v}=\\frac{\\partial v_x}{\\partial x}+\\frac{\\partial v_y}{\\partial y}+\\frac{\\partial v_z}{\\partial z}<br>$$<\/p>\n\n\n\n<p>\u3055\u3089\u306b\u3001$\\nabla$\u30922\u56de\u9069\u7528\u3057\u305f\u3082\u306e\u3092\u30e9\u30d7\u30e9\u30b9\u4f5c\u7528\u7d20\u3068\u547c\u3073\u3001\u8a18\u53f7$\\Delta$\u3067\u8868\u3059\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\Delta=\\nabla\\cdot\\nabla=\\frac{\\partial^2}{\\partial x^2}+\\frac{\\partial^2}{\\partial y^2}+\\frac{\\partial^2}{\\partial z^2}<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u91cd\u529b\u5834$\\boldsymbol{g}(\\boldsymbol{r})$\u3092\u4f7f\u3048\u3070\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{F}(\\boldsymbol{r})=m\\boldsymbol{g}(\\boldsymbol{r})<br>$$<\/p>\n\n\n\n<p>\u5148\u7a0b\u306e\u5f0f\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3001$-m\\nabla\\Phi(\\boldsymbol{r})=m\\boldsymbol{g}(\\boldsymbol{r})$\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{g}(\\boldsymbol{r})=-\\nabla\\Phi(\\boldsymbol{r})<br>$$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8D%E5%8A%9B%E3%83%9D%E3%83%86%E3%83%B3%E3%82%B7%E3%83%A3%E3%83%AB%E3%81%A8%E3%83%9D%E3%82%A2%E3%82%BD%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F\"><\/span>\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4f4d\u7f6e$\\boldsymbol{r&#8217;}$\u306b\u3042\u308b\u8cea\u91cf$m$\u306e\u8cea\u70b9\u304c\u4f5c\u308b\u91cd\u529b\u5834\u306f\u3001\u91cd\u529b\u5b9a\u6570\u3092$G$\u3068\u3057\u3066\u3001<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{g}(\\boldsymbol{r})=-G\\frac{m(\\boldsymbol{r}-\\boldsymbol{r&#8217;})}{|\\boldsymbol{r}-\\boldsymbol{r&#8217;}|^3}<br>$$<\/p>\n\n\n\n<p>\u9023\u7d9a\u7684\u306a\u8cea\u91cf\u5206\u5e03\u3092\u3082\u3064\u5834\u5408\u306f\u3001\u8cea\u91cf\u5bc6\u5ea6$\\rho(\\boldsymbol{r&#8217;})$\u3068\u3057\u3066\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u306b\u3064\u3044\u3066\u8db3\u3057\u5408\u308f\u305b\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{g}(\\boldsymbol{r})=-G\\int\\frac{\\rho(\\boldsymbol{r&#8217;})(\\boldsymbol{r}-\\boldsymbol{r&#8217;})}{|\\boldsymbol{r}-\\boldsymbol{r&#8217;}|^3}d^3r&#8217;<br>$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001<\/p>\n\n\n\n<p>$$<br>\\nabla\\cdot\\left(\\frac{\\boldsymbol{r}-\\boldsymbol{r&#8217;}}{|\\boldsymbol{r}-\\boldsymbol{r&#8217;}|^3}\\right)=4\\pi\\delta^3(\\boldsymbol{r}-\\boldsymbol{r&#8217;})<br>$$<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u95a2\u4fc2\u5f0f\u3092\u4f7f\u3048\u3070\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>\\nabla\\cdot\\boldsymbol{g}(\\boldsymbol{r})&amp;=-G\\int\\rho(\\boldsymbol{r&#8217;})\\nabla\\cdot\\left(\\frac{\\boldsymbol{r}-\\boldsymbol{r&#8217;}}{|\\boldsymbol{r}-\\boldsymbol{r&#8217;}|^3}\\right)d^3r&#8217; \\\\<br>&amp;=-G\\int\\rho(\\boldsymbol{r&#8217;})4\\pi\\delta^3(\\boldsymbol{r}-\\boldsymbol{r&#8217;})d^3r&#8217; \\\\<br>&amp;=4\\pi G\\rho(\\boldsymbol{r})<br>\\end{align}<br>$$<\/p>\n\n\n\n<p>$\\nabla\\cdot\\boldsymbol{g}=-\\nabla^2\\Phi=-4\\pi G\\rho$\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$<br>\\nabla^2\\Phi=4\\pi G\\rho<br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u4f55\u3082\u8aac\u660e\u3057\u3066\u3044\u307e\u305b\u3093\u3067\u3057\u305f\u304c\u3001$f$\u3092\u65e2\u77e5\u306e\u95a2\u6570\u3001$u$\u3092\u672a\u77e5\u306e\u95a2\u6570\u3068\u3057\u305f\u3068\u304d\u3001$\\nabla^2 u=f$\u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b2\u968e\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f\u3068\u547c\u3073\u307e\u3059\u3002<br>\u53c2\u8003: <a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%9D%E3%82%A2%E3%82%BD%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F\" data-type=\"link\" data-id=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%9D%E3%82%A2%E3%82%BD%E3%83%B3%E6%96%B9%E7%A8%8B%E5%BC%8F\">Wikipedia<\/a><\/p>\n\n\n\n<p>$\\nabla^2\\Phi=4\\pi G\\rho$\u306e\u95a2\u4fc2\u5f0f\u3092\u898b\u308b\u3068\u3001\u3061\u3087\u3046\u3069\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%A9%8D%E5%88%86%E5%BD%A2%E5%BC%8F\"><\/span>\u7a4d\u5206\u5f62\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>ChatGPT\u306b\u8cea\u554f\u3057\u305f\u3089\u3001\u7a4d\u5206\u5f62\u5f0f\u306b\u3064\u3044\u3066\u3082\u6559\u3048\u3066\u304f\u308c\u305f\u306e\u3067\u3001\u3064\u3044\u3067\u306b\u7d39\u4ecb\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u767a\u6563\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$<br>\\int_V\\left(\\nabla\\cdot\\boldsymbol{g}\\right)dV=\\oint_S\\boldsymbol{g}\\cdot d\\boldsymbol{A}<br>$$<\/p>\n\n\n\n<p>$\\nabla\\cdot\\boldsymbol{g}=-4\\pi G\\rho$\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$<br>\\oint_S\\boldsymbol{g}\\cdot d\\boldsymbol{A}=\\int_V(-4\\pi G\\rho)dV=-4\\pi GM_{\\text{enc}}<br>$$<\/p>\n\n\n\n<p>\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$<br>\\oint_S\\boldsymbol{g}\\cdot d\\boldsymbol{A}=-4\\pi GM_{\\text{enc}}<br>$$<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u95a2\u4fc2\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002<br>\u306a\u304a\u3001$M_{\\text{enc}}=\\int_V\\rho dV$\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u4ee5\u524d\u306b\u3001\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u3092\u6c42\u3081\u308b\u8a18\u4e8b\u3092\u4f5c\u6210\u3057\u305f\u306e\u3067\u3059\u304c\u3001\u305d\u306e\u8a18\u4e8b\u306e\u6700\u521d\u3067\u3001\u91cd\u529b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u304c$\\nabla^2\\phi=4\\pi G\\rho$\u306e\u5f62\u3067\u8868\u305b\u308b\u3068\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u5c11\u3057\u5c0e\u5165\u304c\u96d1\u306a\u306e\u3068\u3001\u81ea\u5206 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-1632","post","type-post","status-publish","format-standard","hentry","category-9"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1632"}],"version-history":[{"count":11,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1632\/revisions"}],"predecessor-version":[{"id":1673,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1632\/revisions\/1673"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}