{"id":190354,"date":"2016-02-02T03:00:00","date_gmt":"2016-02-02T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=a96a804e954e46c0aabc8780decd8ebc"},"modified":"2016-02-02T03:00:00","modified_gmt":"2016-02-02T00:00:00","slug":"a-new-look-at-the-feynman-hodograph-approach-to-the-kepler-first-law-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=190354","title":{"rendered":"A new look at the Feynman ?hodograph? approach to the Kepler first law"},"content":{"rendered":"<p>Hodographs for the Kepler problem are circles. This fact, known for almost two centuries, still<br \/>\nprovides the simplest path to derive the Kepler first law. Through Feynman?s ?lost lecture?, this<br \/>\nderivation has now reached a wider audience. Here we look again at Feynman?s approach to this<br \/>\nproblem, as well as the recently suggested modification by van Haandel and Heckman (vHH), with two<br \/>\naims in mind, both of which extend the scope of the approach. First we review the geometric<br \/>\nconstructions of the Feynman and vHH approaches (that prove the existence of elliptic orbits without<br \/>\nmaking use of integral calculus or differential equations) and then extend the geometric approach to<br \/>\nalso cover the hyperbolic orbits (corresponding to ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/2\/025004\/ejpaa12c9ieqn1.gif] {$Egt 0$} ). In the second part<br \/>\nwe analyse the properties of the director circles of the conics, which are used to simplify the<br \/>\napproach, and we rela&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hodographs for the Kepler problem are circles. This fact, known for almost two centuries, still<br \/>\nprovides the simplest path to derive the Kepler first law. Through Feynman?s ?lost lecture?, this<br \/>\nderivation has now reached a wider audience. Here we loo&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-190354","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/190354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=190354"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/190354\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=190354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=190354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=190354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}