{"id":239,"date":"2018-12-30T15:11:57","date_gmt":"2018-12-30T20:11:57","guid":{"rendered":"http:\/\/josmfs.net\/wordpress\/?p=239"},"modified":"2018-12-30T15:13:55","modified_gmt":"2018-12-30T20:13:55","slug":"keplers-equal-areas-law","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2018\/12\/30\/keplers-equal-areas-law\/","title":{"rendered":"Kepler\u2019s Equal Areas Law"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-232\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2018\/12\/Keplers-Equal-Areas-Law-Newton-Fig.jpg\" alt=\"\" width=\"200\" height=\"207\" \/>I have long been fascinated by Newton\u2019s proof of Kepler\u2019s Equal Areas Law and wanted to write about it. Of course, others have as well, but I wanted to emphasize an aspect of the proof that supported my philosophy of mathematics.<\/p>\n<p>Before I get to Newton, however, I wanted to discuss how Kepler himself justified this law, since his approach has a number of fascinating historical aspects to it. I have previously discussed Kepler\u2019s ellipse and in the process of doing that research, I came across a number of articles about how Kepler arrived at his equal areas law. One notable result is that even though now we call the idea that a planet orbits the Sun in an elliptical path with the Sun at one focus, Kepler\u2019s First Law, and the idea that the line from the Sun to the planet sweeps out equal areas in equal times, Kepler\u2019s Second Law, Kepler actually discovered these laws in reverse order. See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2018\/12\/Keplers-Equal-Areas-Law-170329.pdf\">Kepler\u2019s Equal Areas Law<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have long been fascinated by Newton\u2019s proof of Kepler\u2019s Equal Areas Law and wanted to write about it. Of course, others have as well, but I wanted to emphasize an aspect of the proof that supported my philosophy of mathematics. Before I get to Newton, however, I wanted to discuss how Kepler himself justified [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[20,19,10,11,21,7,14,13],"class_list":["post-239","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-angular-momentum","tag-equal-areas-law","tag-newton","tag-kepler","tag-law-of-ineertia","tag-math-history","tag-physics","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/239","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=239"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/239\/revisions"}],"predecessor-version":[{"id":241,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/239\/revisions\/241"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}