{"id":47595,"date":"2013-10-25T17:27:17","date_gmt":"2013-10-25T09:27:17","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=47595"},"modified":"2021-10-06T16:19:44","modified_gmt":"2021-10-06T08:19:44","slug":"%e4%bc%bd%e5%88%a9%e7%95%a5%e7%9a%84%e7%9b%b8%e5%b0%8d%e6%80%a7%e5%8e%9f%e7%90%86","status":"publish","type":"post","link":"http:\/\/localhost\/%e4%bc%bd%e5%88%a9%e7%95%a5%e7%9a%84%e7%9b%b8%e5%b0%8d%e6%80%a7%e5%8e%9f%e7%90%86\/","title":{"rendered":"\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406"},"content":{"rendered":"

\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406<\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u61c9\u7528\u7269\u7406\u535a\u58eb\u73ed\u5f35\u667a\u8c6a<\/span><\/strong><\/strong><\/p>\n

\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406\u662f\u8aaa\u660e\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u8207\u7269\u7406\u5b9a\u5f8b\u7684\u539f\u7406\u3002\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406\u8aaa\u6240\u6709\u7269\u7406\u5b9a\u5f8b\u4e0d\u6703\u56e0\u70ba\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u6539\u8b8a\u800c\u6539\u8b8a\u3002\u6240\u8b02\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u662f\u6307\u67d0\u4e00\u500b\u4eba\u5728\u7a7a\u9593\u4e0a\u7684\u67d0\u4e00\u9ede\uff0c\u800c\u9019\u500b\u4eba\u4ee5\u67d0\u500b\u7b49\u901f\u5ea6 $$V$$ \u5728\u904b\u52d5\uff0c\u7136\u5f8c\u6211\u5011\u4ee5\u9019\u500b\u4eba\u7684\u89d2\u5ea6\u53bb\u89c0\u5bdf\u9019\u500b\u4e16\u754c\uff0c\u90a3\u6211\u5011\u5c31\u662f\u4ee5\u9019\u500b\u4eba\u505a\u70ba\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u53bb\u89c0\u5bdf\u9019\u500b\u4e16\u754c\u3002<\/p>\n

\u7269\u7406\u5b9a\u5f8b\u662f\u6307\u6240\u6709\u7269\u9ad4\u5fc5\u9808\u9075\u5b88\u7684\u5b9a\u5f8b\uff0c\u4f8b\u5982 $$F=ma, (GMm)\/r^2=F$$, \u4f5c\u7528\u529b=\u53cd\u4f5c\u7528\u529b \u7b49\u7b49\u90fd\u662f\u7269\u9ad4\u6240\u5fc5\u9808\u9075\u5b88\u7684\u7269\u7406\u5b9a\u5f8b\uff0c\u800c\u6211\u5011\u4ee5\u67d0\u500b\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u53bb\u89c0\u5bdf\u9019\u500b\u4e16\u754c\u7684\u8a71\uff0c \u6211\u5011\u6703\u767c\u73fe\u4e0d\u7ba1\u6211\u5011\u7528\u54ea\u500b\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u53bb\u89c0\u5bdf\u9019\u4e16\u754c\uff0c\u9019\u4e9b\u5b9a\u5f8b\u7684\u5f62\u5f0f\u90fd\u9084\u662f\u6703\u4e00\u6a23\u7684\uff0c\u4e0d\u6703\u56e0\u70ba\u63db\u4e86\u500b\u6163\u6027\u53c3\u8003\u5ea7\u6a19\uff0c\u7269\u7406\u5b9a\u5f8b\u5c31\u6709\u6240\u6539\u8b8a\u3002(\u4ee5\u7b49\u901f\u904b\u52d5\u7684\u5ea7\u6a19\u624d\u53ef\u4ee5\u4f5c\u70ba\u6163\u6027\u53c3\u8003\u5ea7\u6a19 ,\u8b8a\u901f\u904b\u52d5\u5c31\u4e0d\u662f\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u3002)<\/p>\n

\u63a5\u4e0b\u4f86\u6211\u5011\u8209\u4e00\u4e9b\u6578\u5b78\u5f0f\u8a08\u7b97\u7684\u4f8b\u5b50\u4f86\u8aaa\u660e\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406\u3002<\/p>\n

\u6163\u6027\u5ea7\u6a19\u8f49\u63db\u516c\u5f0f\uff1a<\/p>\n

\u9996\u5148\u662f\u4f4d\u79fb\u7684\u8f49\u63db \u00a0$$r =r’+ d$$ , \u5176\u4e2d $$d$$ \u662f\u65b0\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u539f\u9ede\u8207\u539f\u672c\u6163\u6027\u5ea7\u6a19\u539f\u9ede\u7684\u76f8\u5c0d\u4f4d\u7f6e\uff0c$$r$$ \u662f\u88ab\u89c0\u5bdf\u7684\u7269\u9ad4\u5728\u539f\u6163\u6027\u5ea7\u6a19\u7684\u4f4d\u7f6e\uff0c $$r’$$ \u662f\u5728\u65b0\u6163\u6027\u5ea7\u6a19\u6240\u89c0\u5bdf\u5230\u7684\u7269\u9ad4\u7684\u4f4d\u7f6e\u3002<\/p>\n

\u63a5\u8457\u662f\u901f\u5ea6\u7684\u8f49\u63db $$u = u’+v$$, $$ v$$ \u662f\u65b0\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u8207\u539f\u672c\u6163\u6027\u5ea7\u6a19\u7684\u76f8\u5c0d\u901f\u5ea6\uff0c$$u$$ \u662f\u88ab\u89c0\u5bdf\u7684\u7269\u9ad4\u5728\u539f\u6163\u6027\u5ea7\u6a19\u7684\u79fb\u52d5\u901f\u5ea6\uff0c$$u’$$ \u662f\u5728\u65b0\u6163\u6027\u5ea7\u6a19\u6240\u89c0\u5bdf\u5230\u7684\u7269\u9ad4\u7684\u901f\u5ea6\u3002<\/p>\n

\u4ee5\u4e0a\u7684 $$v , u , u’ , r , d , r’$$ \u7686\u70ba\u5411\u91cf\u3002<\/p>\n

\u8209\u4f8b\u8aaa : \u4e00\u500b\u8cea\u91cf\u70ba $$m$$ \u7684\u7269\u9ad4\u5728\u4e00\u500b\u8cea\u91cf\u5f88\u5927(\u70ba $$M$$)\u7684\u7269\u9ad4\u4e4b\u842c\u6709\u5f15\u529b\u4f5c\u7528\u4e0b\u904b\u52d5\uff0c\u5247\u63cf\u8ff0\u5176\u904b\u52d5\u7684\u7269\u7406\u5b9a\u5f8b\u516c\u5f0f\u70ba \uff1a<\/p>\n

\u5728\u6163\u6027\u539f\u5ea7\u6a19\u5beb\u4e0b\u9019\u516c\u5f0f :<\/p>\n

$$\\displaystyle \\frac{GMm}{\\left|r_m-r_M \\right|^2}=F=m\\frac{\\mathrm{d}u}{\\mathrm{t}}$$<\/p>\n

\u900f\u904e\u6163\u6027\u5ea7\u6a19\u8f49\u63db\u516c\u5f0f\u5f8c\u5728\u65b0\u6163\u6027\u5ea7\u6a19\u4e4b\u4e0b\u5beb\u51fa\u9019\u516c\u5f0f\uff0c\u7d50\u679c\u662f<\/p>\n

$$\\displaystyle \\frac{GMm}{\\left|(r_m+d)-(r_M+d) \\right|^2}=F=m\\frac{\\mathrm{d}(u’+v)}{\\mathrm{t}}$$<\/p>\n

$$\\displaystyle \\Rightarrow\\frac{GMm}{\\left|r_m-r_M \\right|^2}=F=m\\frac{\\mathrm{d}u’}{\\mathrm{t}}+m\\frac{\\mathrm{d}v}{\\mathrm{t}}$$<\/p>\n

\u53ef\u662f \u00a0$$v$$ \u662f\u4e00\u500b\u5e38\u6578\u5411\u91cf\uff0c\u56e0\u70ba\u5169\u500b\u5ea7\u6a19\u7cfb\u4e4b\u9593\u7684\u76f8\u5c0d\u901f\u5ea6\u4e0d\u96a8\u6642\u9593\u6539\u8b8a\uff0c\u6240\u4ee5<\/p>\n

$$\\displaystyle \\Rightarrow\\frac{GMm}{\\left|r’_m-r’_M \\right|^2}=F=m\\frac{\\mathrm{d}u’}{\\mathrm{t}}$$<\/p>\n

\u7d50\u679c\u5f97\u51fa\u540c\u6a23\u5f62\u5f0f\u7684\u904b\u52d5\u516c\u5f0f\u3002\u6240\u4ee5\u5728\u9019\u4f8b\u5b50\u4e2d\uff0c\u65bc\u842c\u6709\u5f15\u529b\u7684\u4f5c\u7528\u4e0b\u4e4b\u7269\u9ad4\u904b\u52d5\u6240\u6eff\u8db3\u7684\u7269\u7406\u5b9a\u5f8b\uff0c\u5176\u5f62\u5f0f\u4e0d\u8b8a\uff0c\u9019\u6b63\u7b26\u5408\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406\u3002<\/p>\n

\u53e6\u5916 \u7531\u65bc\u6240\u6709\u7269\u7406\u5b9a\u5f8b\u5728\u6240\u6709\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u7684\u5f62\u5f0f\u90fd\u662f\u4e00\u6a23\u7684\uff0c\u6240\u4ee5\u6211\u5011\u7121\u6cd5\u8aaa\u54ea\u500b\u6163\u6027\u5ea7\u6a19\u6bd4\u8f03\u7279\u5225 \uff0c\u800c\u53ef\u4ee5\u62ff\u4f86\u7576\u4f5c\u7d55\u5c0d\u53c3\u8003\u5ea7\u6a19\uff0c\u9019\u662f\u4f3d\u5229\u7565\u76f8\u5c0d\u6027\u539f\u7406\u6240\u5bd3\u610f\u7684\u3002\u4f46\u56e0\u70ba\u52a0\u901f\u5ea6\u6703\u6539\u8b8a\u7269\u7406\u5b9a\u5f8b\u516c\u5f0f\u7684\u5f62\u5f0f (\u4f8b\u5982\u975e\u6163\u6027\u5ea7\u6a19\u9700\u8981\u5c0d\u6240\u89c0\u5bdf\u5230\u7684\u7269\u9ad4\u7684\u52a0\u901f\u5ea6\u52a0\u4e0a\u4e00\u9805\u865b\u64ec\u52a0\u901f\u5ea6)\uff0c\u6240\u4ee5\u6211\u5011\u53ef\u4ee5\u8aaa\u975e\u6163\u6027\u5ea7\u6a19\u6709\u5225\u65bc\u6163\u6027\u5ea7\u6a19\uff0c\u56e0\u6b64\u6163\u6027\u5ea7\u6a19\u53ef\u4ee5\u4f5c\u70ba\u975e\u6163\u6027\u5ea7\u6a19\u7684\u7d55\u5c0d\u53c3\u8003\u5ea7\u6a19\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406 \u570b\u7acb\u81fa\u7063\u5927\u5b78\u61c9\u7528\u7269\u7406\u535a\u58eb\u73ed\u5f35\u667a\u8c6a \u4f3d\u5229\u7565\u7684\u76f8\u5c0d\u6027\u539f\u7406\u662f\u8aaa\u660e\u6163\u6027\u53c3\u8003\u5ea7\u6a19\u8207\u7269\u7406\u5b9a\u5f8b\u7684\u539f\u7406\u3002\u4f3d…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107,4,3],"tags":[5706,5705,5704,2004],"class_list":["post-47595","post","type-post","status-publish","format-standard","hentry","category-physics00","category-physics01-01","category-physics01","tag-5706","tag-5705","tag-5704","tag-2004","loop-entry","cat-107","cat-4","cat-3","no-thumbnail"],"views":5313,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/47595","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=47595"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/47595\/revisions"}],"predecessor-version":[{"id":87340,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/47595\/revisions\/87340"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=47595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=47595"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=47595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}