{"id":726,"date":"2022-07-27T14:26:37","date_gmt":"2022-07-27T18:26:37","guid":{"rendered":"http:\/\/people.clas.ufl.edu\/ufhatch\/?p=726"},"modified":"2026-03-19T09:03:23","modified_gmt":"2026-03-19T13:03:23","slug":"keplers-planetary-laws-so-called","status":"publish","type":"post","link":"https:\/\/people.clas.ufl.edu\/ufhatch\/2022\/07\/27\/keplers-planetary-laws-so-called\/","title":{"rendered":"Kepler&#8217;s Planetary Laws &#8211; So-Called"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Kepler&#8217;s Planetary Laws &#8211; So-Called<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1st Law<\/strong> (1609): Each planet (P) revolves around the Sun in an <strong>elliptical orbit<\/strong>, with the Sun at one focus of the ellipse.<\/p>\n\n\n\n\n<div class=\"wp-block-image\">\n<figure class=\"size-full aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"250\" height=\"170\" src=\"http:\/\/people.clas.ufl.edu\/ufhatch\/files\/keplerPlanetLawsSoCalledTop.jpg\" alt=\"\" class=\"wp-image-727\" style=\"width:250px;height:auto\"><\/figure>\n<\/div>\n\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2nd Law<\/strong> (1609): A radius vector from the Sun to any particular planet sweeps out equal areas in equal times. (The hatched-in areas are equal.)<\/p>\n\n\n\n\n<div class=\"wp-block-image\">\n<figure class=\"size-full aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"250\" height=\"178\" src=\"http:\/\/people.clas.ufl.edu\/ufhatch\/files\/keplerPlanetLawsSoCalledMiddle.jpg\" alt=\"\" class=\"wp-image-728\" style=\"width:250px;height:auto\"><\/figure>\n<\/div>\n\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3rd Law<\/strong> (1618):  The squares of the periods of revolution (T1,T2) of the planets (P1,P2) are proportional to the cubes of their mean distances (d1,d2) from the Sun. (Note: the &#8216;mean distance&#8217; of a planet from the Sun is the semi-major axis of its elliptical orbit.)<\/p>\n\n\n\n\n<div class=\"wp-block-image\">\n<figure class=\"size-full aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"320\" height=\"265\" src=\"http:\/\/people.clas.ufl.edu\/ufhatch\/files\/keplerPlanetLawsSoCalledBottom.jpg\" alt=\"\" class=\"wp-image-729\" style=\"width:320px;height:auto\" srcset=\"https:\/\/people.clas.ufl.edu\/ufhatch\/files\/keplerPlanetLawsSoCalledBottom.jpg 320w, https:\/\/people.clas.ufl.edu\/ufhatch\/files\/keplerPlanetLawsSoCalledBottom-300x248.jpg 300w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/figure>\n<\/div>\n\n\n\n\n<p class=\"wp-block-paragraph\">The Planetary Times (PT, in Earth Years) and Mean Distances from the Sun (MD, in Earth-Sun ratios) are given below along with the easily multiplied results.  Notice the relationship between the Times Squared and the Distances Cubed.  Newton would eventually demonstrate that Kepler&#8217;s &#8216;Harmonic Law&#8217; (like Kepler&#8217;s First and Second &#8216;Laws&#8217;) was a necessary consequence of the inverse-square relationship associated with Newton&#8217;s principles of Universal Gravitation.<br>\n<\/p>\n\n\n\n<center><br>\n<strong>PT<\/strong>: M: 0.24; V: 0.615; E: 1.00<br>\n    M: 1.88; J: 11.68; S: 29.457<!--PARAGRAPH_SEPARATOR--><p><strong>MD<\/strong>: M: 0.387; V: 0.723; E: 1.00<br>\n    M: 1.524; J: 5.203; S: 9.539<\/p><!--PARAGRAPH_SEPARATOR--><p><strong>T2<\/strong>: M: 0.058; V: 0.38; E: 1.00<br>\n    M: 3.354; J: 140; S: 868<\/p><!--PARAGRAPH_SEPARATOR--><p><strong>D3<\/strong>: M: 0.058; V: 0.38; E: 1.00<br>\n    M: 3.54 J: 140; S: B68<br>\n<\/p><\/center>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1262,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"featured_post":"off","footnotes":"","_links_to":"","_links_to_target":""},"categories":[4,5],"tags":[],"class_list":["post-726","post","type-post","status-publish","format-standard","hentry","category-history-of-science","category-study-guide"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/posts\/726","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/users\/1262"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/comments?post=726"}],"version-history":[{"count":6,"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/posts\/726\/revisions"}],"predecessor-version":[{"id":1385,"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/posts\/726\/revisions\/1385"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/media?parent=726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/categories?post=726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/ufhatch\/wp-json\/wp\/v2\/tags?post=726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}