{"id":47271,"date":"2026-07-15T16:55:07","date_gmt":"2026-07-15T08:55:07","guid":{"rendered":"https:\/\/www.qiusir.com\/?p=47271"},"modified":"2026-07-15T16:56:13","modified_gmt":"2026-07-15T08:56:13","slug":"%e7%a9%bf%e8%b6%8a%e5%9c%b0%e5%bf%83%e7%9a%84%e8%bf%90%e5%8a%a8","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=47271","title":{"rendered":"\u7a7f\u8d8a\u5730\u5fc3\u7684\u8fd0\u52a8"},"content":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c28\u671f\uff082026.04.23\uff09\u4e00\u9053\u9ad8\u8003\u6539\u7f16\u9898\u4e2d\u5bf9\u80fd\u91cf\u5206\u914d\u7684\u63a2\u7a76
\n\"\"
\n

\u7a7f\u8d8a\u5730\u5fc3\u7684\u5f15\u529b\u632f\u8361
\n\"\"
\nJQX|Xiao<\/center><\/p>\n

\u5047\u8bbe\u5730\u7403\u662f\u4e00\u4e2a\u5bc6\u5ea6\u5747\u5300\u7684\u7406\u60f3\u7403\u4f53\uff0c\u5728\u5176\u5185\u90e8\u6316\u51fa\u4e00\u6761\u7a7f\u8fc7\u5730\u5fc3\u7684\u96a7\u9053\u3002\u5f53\u6211\u4eec\u4ece\u5730\u7403\u8868\u9762\u4e0a\u65b9\u67d0\u4e00\u9ad8\u5ea6\u91ca\u653e\u4e00\u4e2a\u7269\u4f53\u65f6\uff0c\u5b83\u5c06\u7ecf\u5386\u4e00\u6bb5\u7279\u6b8a\u7684\u65c5\u7a0b\u3002\u5728\u5730\u7403\u5916\u90e8\uff0c\u7269\u4f53\u7684\u4e0b\u843d\u662f\u4e00\u6bb5\u9000\u5316\u6210\u76f4\u7ebf\u7684\u692d\u5706\u8f68\u9053\u8fd0\u52a8\uff1b\u5728\u5730\u7403\u5185\u90e8\uff0c\u7269\u4f53\u7684\u8fd0\u52a8\u8f6c\u5316\u4e3a\u7b80\u8c10\u632f\u52a8\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u5bf9\u7269\u4f53\u8fd0\u52a8\u7684\u5468\u671f\u8fdb\u884c\u5206\u6790\u3002<\/p>\n

\u4e00\u3001 \u9898\u76ee
\n\u5047\u8bbe\u5730\u7403\u7684\u8d28\u91cf\u4e3a $M$\uff0c\u534a\u5f84\u4e3a $R$\uff0c\u4e07\u6709\u5f15\u529b\u5e38\u6570\u4e3a $G$\u3002\u7269\u4f53\u4ece\u8ddd\u79bb\u5730\u9762\u9ad8\u5ea6\u4e3a $h$ \u7684\u4f4d\u7f6e\u7531\u9759\u6b62\u91ca\u653e\u3002\u4e3a\u4e86\u4fbf\u4e8e\u8ba1\u7b97\uff0c\u6211\u4eec\u5b9a\u4e49\u91ca\u653e\u70b9\u5230\u5730\u5fc3\u7684\u521d\u59cb\u8ddd\u79bb\u4e3a $r_0 = R + h$\u3002\u5728\u6574\u4e2a\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u5ffd\u7565\u7a7a\u6c14\u963b\u529b\u3001\u5730\u7403\u81ea\u8f6c\u7b49\u4e00\u5207\u975e\u4fdd\u5b88\u529b\u56e0\u7d20\uff0c\u8ba4\u4e3a\u7269\u4f53\u7684\u673a\u68b0\u80fd\u4e25\u683c\u5b88\u6052\u3002\u7269\u4f53\u7684\u8fd0\u52a8\u8f68\u8ff9\u662f\u4e00\u6761\u7a7f\u8fc7\u5730\u5fc3\u7684\u76f4\u7ebf\uff0c\u4e00\u6b21\u5b8c\u6574\u7684\u5468\u671f\u6027\u8fd0\u52a8\u5305\u542b\uff1a\u4ece\u4e0a\u65b9 $r_0$ \u4e0b\u843d\u81f3\u5730\u7403\u8868\u9762\u3001\u7a7f\u8d8a\u5730\u7403\u5185\u90e8\u5230\u8fbe\u53e6\u4e00\u4fa7\u8868\u9762\u3001\u98de\u51fa\u8868\u9762\u5230\u8fbe\u53e6\u4e00\u4fa7\u5bf9\u79f0\u9ad8\u5ea6 $r_0$\u3001\u7136\u540e\u539f\u8def\u8fd4\u56de\u81f3\u521d\u59cb\u91ca\u653e\u70b9\u3002<\/p>\n

\u4e8c\u3001 \u5730\u7403\u5916\u90e8\u7684\u8fd0\u52a8\uff1a\u9000\u5316\u692d\u5706\u4e0e\u5f00\u666e\u52d2\u65b9\u7a0b
\n\u5f53\u7269\u4f53\u5728\u5730\u7403\u5916\u90e8\uff08\u5373\u8ddd\u79bb\u5730\u5fc3 $r \\ge R$\uff09\u8fd0\u52a8\u65f6\uff0c\u53d7\u5230\u7684\u4e07\u6709\u5f15\u529b\u9075\u5faa\u5e73\u65b9\u53cd\u6bd4\u5b9a\u5f8b $F = -GmM\/r^2$\u3002\u7269\u4f53\u5728\u5730\u7403\u5916\u90e8\u7684\u8fd0\u52a8\u53ef\u4ee5\u770b\u6210\u79bb\u5fc3\u7387 $e = 1$ \u7684\u201c\u9000\u5316\u692d\u5706\u201d\uff08\u5373\u4e00\u6761\u76f4\u7ebf\uff09\u3002<\/p>\n

\u5bf9\u4e8e\u8fd9\u4e2a\u9000\u5316\u7684\u76f4\u7ebf\u692d\u5706\uff0c\u5176\u8fdc\u5730\u70b9\u8ddd\u79bb\u5c31\u662f\u521d\u59cb\u91ca\u653e\u4f4d\u7f6e $r_0$\uff0c\u800c\u8fd1\u5730\u70b9\u8ddd\u79bb\u4e3a $0$\uff08\u5373\u5730\u5fc3\uff09\u3002\u56e0\u6b64\uff0c\u8be5\u692d\u5706\u7684\u534a\u957f\u8f74\u4e3a $a = r_0 \/ 2$\u3002\u7531\u4e8e\u7269\u4f53\u4ece\u91ca\u653e\u70b9 $r_0$ \u5230\u4e0b\u843d\u5230\u5730\u7403\u8868\u9762 $R$\u662f\u53d8\u901f\u8fd0\u52a8\uff0c \u6240\u9700\u7684\u65f6\u95f4\u5728\u9ad8\u4e2d\u8303\u56f4\u5185\u5f88\u96be\u89e3\u51b3\uff0c\u5f00\u666e\u52d2\u5229\u7528\u5f00\u666e\u52d2\u7b2c\u4e8c\u5b9a\u5f8b\u7ed9\u51fa\u4e86\u4e00\u4e2a\u975e\u5e38\u7f8e\u5999\u7684\u65b9\u6cd5\uff0c\u8fd9\u91cc\u6211\u4eec\u7528\u5f00\u666e\u52d2\u65b9\u7a0b $M_e = E – e \\sin E$\u6765\u89e3\u51b3\u5730\u7403\u5916\u90e8\u7269\u4f53\u8fd0\u52a8\u7684\u65f6\u95f4\u3002\u5176\u4e2d $M_e$ \u4e3a\u5e73\u8fd1\u70b9\u89d2\uff0c $E$ \u4e3a\u504f\u8fd1\u70b9\u89d2\u3002\u5bf9\u4e8e\u9000\u5316\u692d\u5706\uff0c\u79bb\u5fc3\u7387 $e = 1$\uff0c\u5f00\u666e\u52d2\u65b9\u7a0b\u7b80\u5316\u4e3a $M_e = E – \\sin E$\u3002<\/p>\n

\u5e73\u8fd1\u70b9\u89d2\u4e0e\u65f6\u95f4 $t$ \u7684\u5173\u7cfb\u4e3a $M_e = \\sqrt{GM\/a^3} \\cdot t$\u3002\u5728\u692d\u5706\u8f68\u9053\u4e2d\uff0c\u4e2d\u5fc3\u8ddd\u79bb $r$ \u4e0e\u504f\u8fd1\u70b9\u89d2 $E$ \u7684\u51e0\u4f55\u5173\u7cfb\u4e3a $r = a(1 – e \\cos E)$\uff0c\u4ee3\u5165 $e = 1$ \u5f97\u5230 $r = a(1 – \\cos E)$\u3002\u5f53\u7269\u4f53\u5728\u8fdc\u5730\u70b9\uff08\u5373\u521d\u59cb\u91ca\u653e\u70b9 $r_0$\uff09\u65f6\uff0c$r = r_0 = 2a$\uff0c\u6b64\u65f6\u5bf9\u5e94\u7684\u504f\u8fd1\u70b9\u89d2 $E_{start} = \\pi$\u3002\u5f53\u7269\u4f53\u4e0b\u843d\u5230\u5730\u7403\u8868\u9762\u5373 $r = R$ \u65f6\uff0c\u8bbe\u6b64\u65f6\u7684\u504f\u8fd1\u70b9\u89d2\u4e3a $\\theta$\uff0c\u5219\u6709 $R = a(1 – \\cos \\theta) = (r_0 \/ 2)(1 – \\cos \\theta)$\u3002\u901a\u8fc7\u6574\u7406\u53ef\u5f97 $\\cos \\theta = 1 – 2R\/r_0$\uff0c\u5373\u5230\u8fbe\u5730\u8868\u65f6\u7684\u504f\u8fd1\u70b9\u89d2\u4e3a $\\theta = \\arccos(1 – 2R\/r_0)$\u3002<\/p>\n

\u7531\u4e8e\u7269\u4f53\u662f\u4ece $E = \\pi$ \u8fd0\u52a8\u5230 $E = \\theta$\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5f00\u666e\u52d2\u65b9\u7a0b\u8ba1\u7b97\u51fa\u8fd9\u6bb5\u65f6\u95f4\u5dee\u3002\u5355\u6b21\u4ece\u9ad8\u7a7a\u843d\u81f3\u5730\u8868\u7684\u65f6\u95f4 $t_{out}$ \u53ef\u4ee5\u8868\u793a\u4e3a $t_{out} = \\sqrt{a^3 \/ GM} \\cdot [(\\pi – \\sin \\pi) – (\\theta – \\sin \\theta)]$\u3002\u4ee3\u5165\u534a\u957f\u8f74 $a = r_0 \/ 2$\uff0c\u65f6\u95f4\u8868\u8fbe\u5f0f\u5316\u7b80\u4e3a $t_{out} = \\sqrt{r_0^3 \/ (8GM)} \\cdot (\\pi – \\theta + \\sin \\theta)$\u3002\u8fd9\u4e00\u516c\u5f0f\u4f18\u96c5\u5730\u7ed9\u51fa\u4e86\u7269\u4f53\u5728\u5730\u7403\u5916\u90e8\u5355\u6b21\u5355\u5411\u98de\u884c\u7684\u65f6\u95f4\u3002<\/p>\n

\u4e09\u3001 \u5730\u7403\u5185\u90e8\u7684\u8fd0\u52a8\uff1a\u7b80\u8c10\u632f\u52a8\u4e0e\u53c2\u8003\u5706\u6cd5
\n\u5f53\u7269\u4f53\u8fdb\u5165\u5730\u7403\u5185\u90e8\u96a7\u9053\uff08\u5373 $r < R$\uff09\u65f6\uff0c\u7269\u4f53\u53d7\u5230\u7684\u5f15\u529b\u4e0e\u8ddd\u79bb\u5730\u5fc3\u7684\u8ddd\u79bb\u6210\u6b63\u6bd4\uff0c\u8868\u8fbe\u5f0f\u4e3a $F = -GmM r \/ R^3$\u3002\u56e0\u6b64\u7269\u4f53\u5728\u5730\u7403\u5185\u90e8\u7684\u8fd0\u52a8\u662f\u7b80\u8c10\u632f\u52a8\uff0c\u8fd0\u52a8\u65b9\u7a0b\u6ee1\u8db3 $a = -\\omega^2 r$\uff0c\u5176\u4e2d\u5706\u9891\u7387 $\\omega = \\sqrt{GM\/R^3}$\u3002<\/p>\n

\u7531\u4e8e\u7269\u4f53\u521a\u843d\u5230\u5730\u9762\u4e0a\u65f6\u6709\u901f\u5ea6\uff0c\u6240\u4ee5\u5e76\u4e0d\u662f\u4e00\u6b21\u5b8c\u6574\u7684\u7b80\u8c10\u632f\u52a8\uff0c\u56e0\u6b64\u6211\u4eec\u4f7f\u7528\u53c2\u8003\u5706\u6cd5\u6765\u6c42\u89e3\u5728\u5730\u7403\u5185\u90e8\u7684\u65f6\u95f4\u3002\u9996\u5148\u8981\u786e\u5b9a\u7b80\u8c10\u632f\u52a8\u7684\u632f\u5e45 $A$\u3002\u6839\u636e\u5730\u8868\u5904\u7684\u80fd\u91cf\u5b88\u6052\uff0c\u7269\u4f53\u5728\u5730\u8868\u65f6\u7684\u52a8\u80fd\u52a0\u4e0a\u52bf\u80fd\u7b49\u4e8e\u521d\u59cb\u91ca\u653e\u65f6\u7684\u603b\u80fd\u91cf\uff0c\u5373 $v_R^2 \/ 2 – GM\/R = -GM\/r_0$\u3002\u7531\u6b64\u53ef\u4ee5\u6c42\u51fa\u7269\u4f53\u8fdb\u5165\u5730\u8868\u65f6\u7684\u901f\u5ea6\u5927\u5c0f $v_R = \\sqrt{2GM(1\/R – 1\/r_0)}$\u3002<\/p>\n

\u7b80\u8c10\u632f\u52a8\u7684\u632f\u5e45 $A$ \u53ef\u4ee5\u901a\u8fc7\u516c\u5f0f $A = \\sqrt{R^2 + (v_R \/ \\omega)^2}$ \u5f97\u5230\u3002\u5c06\u901f\u5ea6 $v_R$ \u548c\u5706\u9891\u7387 $\\omega$ \u7684\u5e73\u65b9\u4ee3\u5165\uff0c\u5f97\u5230 $(v_R \/ \\omega)^2 = [2GM(r_0 – R)\/(R r_0)] \/ (GM\/R^3) = 2R^2(1 – R\/r_0)$\u3002\u56e0\u6b64\uff0c\u632f\u5e45\u7684\u5e73\u65b9\u4e3a $A^2 = R^2 + 2R^2 – 2R^3\/r_0 = R^2(3 – 2R\/r_0)$\u3002\u6240\u4ee5\uff0c\u8be5\u7b80\u8c10\u632f\u52a8\u7684\u7b49\u6548\u632f\u5e45\u4e3a $A = R\\sqrt{3 – 2R\/r_0}$\u3002\u663e\u7136\uff0c\u7531\u4e8e\u7269\u4f53\u662f\u4ece\u9ad8\u7a7a\u843d\u4e0b\u7684\uff0c$A$ \u5927\u4e8e\u5730\u7403\u534a\u5f84 $R$\u3002<\/p>\n

\u73b0\u5728\u5f15\u5165\u53c2\u8003\u5706\uff1a\u60f3\u8c61\u4e00\u4e2a\u534a\u5f84\u4e3a $A$ \u7684\u5300\u901f\u5706\u5468\u8fd0\u52a8\uff0c\u5176\u5728\u7a7f\u8fc7\u5730\u5fc3\u7684\u76f4\u7ebf\u4e0a\u7684\u6295\u5f71\u5c31\u662f\u8be5\u7269\u4f53\u7684\u7b80\u8c10\u632f\u52a8\u3002\u7269\u4f53\u4ece\u4e00\u4fa7\u5730\u8868 $r = R$ \u8fdb\u5165\uff0c\u7a7f\u8fc7\u5730\u5fc3\u5230\u8fbe\u53e6\u4e00\u4fa7\u5730\u8868 $r = -R$\u3002\u5728\u53c2\u8003\u5706\u4e0a\uff0c\u8fdb\u5165\u70b9\u7684\u76f8\u4f4d\u89d2 $\\phi$ \u6ee1\u8db3 $\\cos \\phi = R\/A$\uff08\u56e0\u4e3a\u7269\u4f53\u5411\u5730\u5fc3\u8fd0\u52a8\uff0c\u53d6\u7b2c\u4e00\u8c61\u9650\u89d2\u5ea6\uff09\u3002\u5f53\u7269\u4f53\u5230\u8fbe\u5bf9\u79f0\u8868\u9762 $-R$ \u65f6\uff0c\u76f8\u4f4d\u89d2\u53d8\u4e3a $\\pi – \\phi$\u3002<\/p>\n

\u56e0\u6b64\uff0c\u7269\u4f53\u5728\u5730\u7403\u5185\u90e8\u5355\u6b21\u7a7f\u8d8a\u626b\u8fc7\u7684\u53c2\u8003\u5706\u5706\u5fc3\u89d2\u4e3a $\\Delta \\phi = (\\pi – \\phi) – \\phi = \\pi – 2\\phi = \\pi – 2\\arccos(R\/A)$\u3002\u5229\u7528\u89d2\u901f\u5ea6\u516c\u5f0f\uff0c\u7269\u4f53\u5355\u6b21\u7a7f\u8d8a\u5730\u7403\u5185\u90e8\u6240\u9700\u7684\u65f6\u95f4 $t_{in}$ \u5c31\u662f $\\Delta \\phi \/ \\omega$\u3002\u4ee3\u5165\u5706\u9891\u7387\u540e\uff0c\u5730\u7403\u5185\u90e8\u8fd0\u52a8\u65f6\u95f4\u4e3a $t_{in} = \\sqrt{R^3\/GM} \\cdot [\\pi – 2\\arccos(R\/A)]$\u3002<\/p>\n

\u56db\u3001 \u5b8c\u6574\u5468\u671f\u8fd0\u52a8
\n\u4e00\u6b21\u5b8c\u6574\u7684\u5468\u671f\u6027\u8fd0\u52a8\u5305\u542b\u4e86\u56db\u6b21\u5730\u7403\u5916\u90e8\u7684\u98de\u884c\u548c\u4e24\u6b21\u5730\u7403\u5185\u90e8\u7684\u7a7f\u8d8a\u3002\u56e0\u6b64\uff0c\u603b\u5468\u671f\u65f6\u95f4 $T = 4t_{out} + 2t_{in}$\u3002<\/p>\n

\u5c06\u524d\u6587\u63a8\u5bfc\u7684\u5177\u4f53\u8868\u8fbe\u5f0f\u4ee3\u5165\uff0c\u5e76\u63d0\u53d6\u51fa\u5408\u7406\u7684\u5e38\u6570\u9879\uff0c\u6700\u7ec8\u7684\u5468\u671f\u603b\u516c\u5f0f\u53ef\u4ee5\u5199\u4f5c $T = 4\\sqrt{r_0^3\/(8GM)} \\cdot (\\pi – \\theta + \\sin \\theta) + 2\\sqrt{R^3\/GM} \\cdot (\\pi – 2\\arccos(R\/A))$\u3002\u4e3a\u4e86\u4f7f\u516c\u5f0f\u770b\u8d77\u6765\u66f4\u52a0\u7b80\u6d01\uff0c\u7b2c\u4e00\u9879\u4e2d\u7684\u5e38\u6570\u53ef\u4ee5\u5316\u7b80\u4e3a $4\/\\sqrt{8} = \\sqrt{2}$\u3002<\/p>\n

\u6240\u4ee5\uff0c\u6700\u7ec8\u5b8c\u6574\u5468\u671f\u7684\u65f6\u95f4\u8868\u8fbe\u5f0f\u4e3a $T = \\sqrt{2r_0^3\/GM} \\cdot (\\pi – \\theta + \\sin \\theta) + 2\\sqrt{R^3\/GM} \\cdot (\\pi – 2\\arccos(R\/A))$\u3002\u5728\u5e94\u7528\u8be5\u516c\u5f0f\u65f6\uff0c\u6211\u4eec\u9700\u8981\u914d\u5957\u4f7f\u7528\u524d\u6587\u5b9a\u4e49\u7684\u4e24\u4e2a\u5173\u952e\u8f85\u52a9\u53c2\u91cf\uff1a\u504f\u8fd1\u70b9\u89d2\u53c2\u6570 $\\theta = \\arccos(1 – 2R\/r_0)$\uff0c\u4ee5\u53ca\u7b80\u8c10\u632f\u52a8\u7b49\u6548\u632f\u5e45 $A = R\\sqrt{3 – 2R\/r_0}$\u3002<\/p>\n

\u4e94\u3001 \u62d3\u5c55
\n\u91d1\u8001\u5e08\u989d\u5916\u63d0\u4f9b\u4e86\u4e00\u4e2a\u9898\u76ee\uff1a\u5728\u8d64\u9053\u4e0a\u4ee5\u901f\u5ea6 $v = \\sqrt{\\dfrac{GM}{R}}$ \u5411\u4e0a\u53d1\u5c04\u4e00\u822a\u5929\u5668\uff08$M$ \u4e3a\u5730\u7403\u8d28\u91cf\uff0c$R$ \u4e3a\u5730\u7403\u534a\u5f84\uff09\uff0c\u7136\u540e\u822a\u5929\u5668\u53c8\u7ad6\u76f4\u6389\u4e0b\u6765\u4e86\uff08\u4e0d\u8003\u8651\u5730\u7403\u81ea\u8f6c\uff09\u3002\u8bd5\u6c42\u822a\u5929\u5668\u4ece\u53d1\u5c04\u5230\u843d\u5730\u7684\u65f6\u95f4 $t$\u3002\u963b\u529b\u4e0d\u8ba1\u3002
\n\u89e3\u6790\uff1a1. \u7528\u673a\u68b0\u80fd\u5b88\u6052\u6c42\u6700\u9ad8\u70b9
\n\u822a\u5929\u5668\u4ece\u5730\u9762\u4ee5 $v = \\sqrt{\\dfrac{GM}{R}}$ \u7ad6\u76f4\u4e0a\u629b\uff0c\u5230\u6700\u9ad8\u70b9\u65f6\u901f\u5ea6\u4e3a 0\uff0c\u8fc7\u7a0b\u4e2d\u53ea\u6709\u4e07\u6709\u5f15\u529b\u505a\u529f\uff0c\u673a\u68b0\u80fd\u5b88\u6052\uff1a
\n$\\frac{1}{2}mv^2 – \\frac{GMm}{R} = 0 – \\frac{GMm}{R+h}$
\n\u89e3\u5f97\u6700\u9ad8\u70b9\u79bb\u5730\u5fc3\u8ddd\u79bb $R+h = 2R$\uff0c\u5373 $h = R$\u3002
\n2. \u7b49\u6548\u4e3a\u6781\u6241\u692d\u5706\u8f68\u9053
\n\u7ad6\u76f4\u4e0a\u629b\u7684\u8fd0\u52a8\uff0c\u53ef\u4ee5\u7b49\u6548\u4e3a\u4e00\u4e2a\u534a\u77ed\u8f74 $b \\to 0$ \u7684\u6781\u6241\u692d\u5706\u8f68\u9053\uff1a\u5730\u5fc3 $O$ \u662f\u692d\u5706\u7684\u4e00\u4e2a\u7126\u70b9\uff0c\u4e5f\u662f\u8f68\u9053\u7684\u8fd1\u5730\u70b9\uff08\u8ddd\u5730\u5fc3 $R$\uff09\uff0c\u6700\u9ad8\u70b9\u662f\u692d\u5706\u7684\u8fdc\u5730\u70b9\uff08\u8ddd\u5730\u5fc3 $2R$\uff09\u692d\u5706\u534a\u957f\u8f74\uff1a$a = \\frac{R + 2R}{2} = R$
\n3. \u7528\u5f00\u666e\u52d2\u7b2c\u4e09\u5b9a\u5f8b\u6c42\u692d\u5706\u5468\u671f $\\dfrac{T^2}{a^3} = \\dfrac{4\\pi^2}{GM}$\uff0c\u4ee3\u5165 $a = R$\uff0c$T = 2\\pi\\sqrt{\\frac{R^3}{GM}}$
\n4. \u7528\u5f00\u666e\u52d2\u7b2c\u4e8c\u5b9a\u5f8b\u6c42\u8fd0\u52a8\u65f6\u95f4\uff0c\u5355\u4f4d\u65f6\u95f4\u5185\u77e2\u5f84\u626b\u8fc7\u7684\u9762\u79ef\u6052\u5b9a\uff0c\u5373 $\\dfrac{s}{t} = \\dfrac{S}{T}$\u3002
\n\u692d\u5706\u603b\u9762\u79ef $S = \\pi ab = \\pi Rb$
\n\u822a\u5929\u5668\u4ece\u53d1\u5c04\u5230\u843d\u5730\uff0c\u77e2\u5f84\u626b\u8fc7\u7684\u9762\u79ef $s = \\dfrac{1}{2}\\pi Rb + Rb$\uff08\u534a\u4e2a\u692d\u5706 + \u4e09\u89d2\u5f62\uff09
\n\u4ee3\u5165\u6bd4\u4f8b\u5f0f\uff1a
\n$t = \\frac{s}{S} \\cdot T = \\frac{\\frac{1}{2}\\pi Rb + Rb}{\\pi Rb} \\cdot 2\\pi\\sqrt{\\frac{R^3}{GM}}$
\n\u7ea6\u53bb $Rb$ \u540e\u5316\u7b80\uff1a
\n$t = (\\pi + 2)\\sqrt{\\frac{R^3}{GM}}$\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c28\u671f\uff082026.04.23\uff09\u4e00\u9053\u9ad8\u8003\u6539\u7f16\u9898\u4e2d\u5bf9\u80fd\u91cf\u5206\u914d\u7684\u63a2\u7a76 \u7a7f\u8d8a\u5730\u5fc3\u7684\u5f15\u529b\u632f\u8361 J … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[9],"tags":[460,247],"class_list":["post-47271","post","type-post","status-publish","format-standard","hentry","category-jqx","tag-jqx","tag-physics"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/47271","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=47271"}],"version-history":[{"count":12,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/47271\/revisions"}],"predecessor-version":[{"id":48468,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/47271\/revisions\/48468"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=47271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=47271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=47271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}