{"id":14620,"date":"2010-11-10T18:32:03","date_gmt":"2010-11-10T10:32:03","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=14620"},"modified":"2021-10-06T16:30:51","modified_gmt":"2021-10-06T08:30:51","slug":"%e5%9c%b0%e7%90%83%e7%9a%84%e5%bd%a2%e7%8b%80%ef%bc%88shape-of-the-earth%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%9c%b0%e7%90%83%e7%9a%84%e5%bd%a2%e7%8b%80%ef%bc%88shape-of-the-earth%ef%bc%89\/","title":{"rendered":"\u5730\u7403\u7684\u5f62\u72c0"},"content":{"rendered":"

\u5730<\/span>\u7403<\/span>\u7684\u5f62\u72c0 (Shape of the Earth)
\n<\/span>\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u66f9\u4eae\u5409\u6559\u6388\/\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u66f9\u4eae\u5409\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u5927\u5bb6\u90fd\u77e5\u9053\uff0c\u5982\u679c\u4e0d\u8981\u592a\u8a08\u8f03\uff0c\u5730\u7403\u7684\u5f62\u72c0\u662f\u500b\u7403\u3002\u4f46\u725b\u9813\u8aaa\uff0c\u8a8d\u771f\u8a08\u8f03\u7684\u8a71\uff0c\u5730\u7403\u662f\u500b\u6a62\u5713\u65cb\u8f49\u9ad4\uff0c\u4e00\u500b\u4ee5\u5730\u7403\u8d64\u9053\u5927\u5713\u4e00\u76f4\u5f91\u70ba\u9577\u8ef8\uff0c\u5730\u7403\u5357\u5317\u8ef8\u7dda\u70ba\u77ed\u8ef8\u7684\u6a62\u5713\uff0c\u4ee5\u5357\u5317\u8ef8\u7dda\u70ba\u65cb\u8f49\u8ef8\uff0c\u65cb\u8f49\u800c\u6210\u7684\u65cb\u8f49\u9ad4\u3002\u6709\u4eba\u6709\u4e0d\u540c\u7684\u610f\u898b\uff0c\u8a8d\u70ba\u8d64\u9053\u5927\u5713\u7684\u76f4\u5f91\u6bd4\u5357\u5317\u8ef8\u7dda\u8981\u77ed\uff0c\u56e0\u6b64\u5c0d\u5357\u5317\u8ef8\u7dda\u65cb\u8f49\u7684\u7d50\u679c\uff0c\u5730\u7403\u6bd4\u8f03\u50cf\u6ab8\u6aac\uff0c\u5357\u5317\u6975\u8f03\u7a81\u51fa\uff0c\u8d64\u9053\u8f03\u5167\u7e2e\uff0c\u800c\u4e0d\u50cf\u6a58\u5b50\u2500\u2500\u725b\u9813\u7684\u4e3b\u5f35\u3002<\/p>\n

\u5169\u8005\u4e3b\u5f35\u722d\u6301\u4e0d\u4e0b\uff0c\u65bc\u662f\u6709\u4eba\u5c31\u53bb\u6e2c\u91cf\u5730\u8868\u4e00\u5f27\u5ea6\u7684\u5f27\u9577\uff0c\u4f86\u78ba\u5b9a\u54ea\u4e00\u65b9\u7684\u4e3b\u5f35\u8f03\u70ba\u6b63\u78ba\u3002\u5982\u679c\u8d64\u9053\u9644\u8fd1\u4e00\u7def\u5ea6\u5f27\u9577\u8f03\u6975\u5340\u9644\u8fd1\u4e00\u7def\u5ea6\u5f27\u9577\u70ba\u77ed\uff0c\u5247\u725b\u9813\u7684\u4e3b\u5f35\u6b63\u78ba\uff1b\u53cd\u4e4b\u5247\u5426\u3002<\/p>\n

\u4e00\u822c\u4eba\u8981\u4e86\u89e3\u722d\u8b70\u7684\u8981\u9ede\uff0c\u5f80\u5f80\u5c31\u6703\u5728\u9019\u88e1\u6389\u5165\u9677\u9631\u88e1\u982d\u3002\u5982\u5716\u4e00\uff0c\u5047\u8a2d\u6a62\u5713\u7684\u9577\u8ef8\u70ba $${a}$$\uff0c\u77ed\u8ef8\u70ba $${b}$$\uff1b$$\\phi$$ \u8868\u4e00\u5ea6\u7684\u5927\u5c0f\u3002\u90a3\u9ebc\u5f27\u9577 $$AC$$ \u5927\u7d04\u7b49\u65bc $$a\\phi$$ ($$\\phi$$ \u4ee5\u5f27\u5ea6\u8a08\u7b97\uff09\uff0c\u5f27\u9577 $$BD$$ \u5927\u7d04\u7b49\u65bc $$b\\phi$$\uff0c\u4f46 $${a}$$ \u5927\u65bc $${b}$$\uff0c\u6240\u4ee5 $$AC$$ \u6bd4 $$BD$$ \u9577\uff0c\u800c\u4e0d\u662f\u8f03\u77ed\u3002<\/p>\n

\"\"<\/p>\n

\u5982\u5716\u4e8c\uff0c\u4e00\u500b\u4eba\u7ad9\u5728\u5730\u7403\u4e0a\u67d0\u4e00\u9ede $$C$$ \u6642\uff0c\u901a\u5e38\u7121\u6cd5\u77e5\u9053 $$AC$$ \u5f27\u6240\u5c0d $$\\phi$$ \u89d2\u7684\u5927\u5c0f\uff0c\u800c\u8f49\u800c\u7528 $$\\lambda$$ \u89d2\u7684\u5927\u5c0f\u8868\u793a\u8a72\u5730\u7684\u7def\u5ea6\uff1b$$\\lambda$$ \u89d2\u5c31\u662f\u7ad9\u5728 $$C$$ \u9ede\u6642\u6240\u5f97\u5317\u6975\u65b9\u5411\u7684\u4ef0\u89d2\u3002<\/p>\n

\u6211\u5011\u5e38\u628a\u6a62\u5713\u7684\u5750\u6a19\u53c3\u6578\u5316\uff1a$$x=a\\cos\\theta$$\uff0c$$y=b\\sin\\theta$$\uff0c\u4f46\u662f\u53c3\u6578 $$\\theta$$ \u65e2\u4e0d\u662f $$\\phi$$\uff0c\u4e5f\u4e0d\u662f $$\\lambda$$\uff0c\u5982\u5716\u4e09\u3002\u4e09\u8005\u7684\u95dc\u4fc2\u70ba $$\\phi < \\theta <\\lambda$$\uff0c\u4e14 $$\\displaystyle\\tan\\lambda = \\frac{a}{b}\\tan\\theta=\\frac{a^2}{b^2}\\tan\\phi$$\u3002<\/p>\n

\"\"<\/a><\/p>\n

\u6211\u5011\u8aaa $$AC$$ \u8207 $$BD$$ \u6709\u76f8\u540c\u7684\u7def\u5ea6\u5dee $$\\lambda$$\uff08\u8b6c\u5982\u4e00\u5ea6\uff09\uff0c\u610f\u601d\u662f\u5982\u5716\u56db\u6240\u793a\uff0c\u5f27 $$AC$$ \u8207 $$BD$$ \u5728\u7403\u5fc3\u6240\u5f35\u7684\u89d2\u5ea6 $$\\phi_1$$ \u8207 $$\\phi_2$$ \u96d6\u7136\u4e0d\u76f8\u7b49\uff0c\u4f46\u5728 $$C$$ \u8207 $$D$$\uff0c\u5176\u5317\u6975\u4ef0\u89d2 $$\\lambda$$ \u8207 $$90^\\circ-\\lambda$$ \u8981\u4e92\u88dc\u3002<\/p>\n

\u7d93\u904e\u4e00\u4e9b\u8a08\u7b97\u53ef\u5f97<\/p>\n

$$\\displaystyle\\phi_1\\approx \\frac{b^2}{a^2}\\lambda$$\uff0c$$\\displaystyle\\phi_2\\approx \\frac{a^2}{b^2}\\lambda$$\uff0c<\/p>\n

$$AC$$ \u5f27 $$:$$\u00a0$$BD$$ \u5f27 $$\\displaystyle\\approx a\\phi_1:b\\phi_2=\\frac{b^2}{a}\\lambda:\\frac{a^2}{b}\\lambda=b^3:a^3$$<\/p>\n

\u4ea6\u5373\uff0c\u5982\u679c\u725b\u9813\u7684\u4e3b\u5f35\u6b63\u78ba\uff0c\u7def\u5ea6\u5dee\u76f8\u540c\u7684\u5f27\u9577\uff0c\u5728\u8d64\u9053\u9644\u8fd1\u8f03\u77ed\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002<\/p>\n

1730\u5e74\u4ee3\uff0c\u6cd5\u570b\u79d1\u5b78\u9662\u6d3e\u4e86\u5169\u7d44\u4eba\u99ac\uff0c\u5206\u5225\u5230\u5357\u7f8e\u6d32\u7684\u8d64\u9053\u9644\u8fd1\uff0c\u4ee5\u53ca\u82ac\u862d\u7684\u5317\u90e8\u5730\u5340\uff0c\u7528\u4e09\u89d2\u6e2c\u91cf\u6cd5\uff0c\u5404\u91cf\u5f97\u4e00\u7def\u5ea6\u7684\u5f27\u9577\uff0c\u7d50\u679c\u8b49\u660e\u725b\u9813\u7684\u9810\u6e2c\u662f\u5c0d\u7684\u2500\u2500\u5730\u7403\u6bd4\u8f03\u50cf\u6a58\u5b50\uff0c\u800c\u4e0d\u50cf\u6ab8\u6aac\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u672c\u6587\u4ee5\u4e00\u7def\u5ea6\u7684\u5f27\u9577\u5927\u5c0f\uff0c\u8aaa\u660e\u5730\u7403\u7684\u5f62\u72c0\u662f\u50cf\u6a58\u5b50\u7684\u6a62\u5713\u9ad4\uff0c\u800c\u4e0d\u662f\u50cf\u6ab8\u6aac\u7684\u6a62\u5713\u9ad4<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[226,224,111],"tags":[395,385,394,393],"class_list":["post-14620","post","type-post","status-publish","format-standard","hentry","category-math04-02","category-math04","category-mathematics00","tag-395","tag-385","tag-394","tag-393","loop-entry","cat-226","cat-224","cat-111","no-thumbnail"],"views":13638,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/14620","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=14620"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/14620\/revisions"}],"predecessor-version":[{"id":89359,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/14620\/revisions\/89359"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=14620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=14620"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=14620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}