{"id":75187,"date":"2015-03-24T03:00:00","date_gmt":"2015-03-24T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=44de4b1fcb33c91e761dadbd5e43266e"},"modified":"2015-03-24T03:00:00","modified_gmt":"2015-03-24T00:00:00","slug":"a-novel-study-on-keplers-law-and-inverse-square-law-of-gravitation-2","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=75187","title":{"rendered":"A novel study on Kepler?s law and inverse square law of gravitation"},"content":{"rendered":"<p>The Udwadia?Kalaba equation is a simple, aesthetic, and thought-provoking description of the world<br \/>\nat a very fundamental level. It is about the way systems move. In this paper, we creatively apply<br \/>\nthe Udwadia?Kalaba approach to study heavenly bodies? movements (especially on Kepler?s law and the<br \/>\ninverse square law of gravitation). In an alternative way, we show that a heavenly body?s motion<br \/>\norbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular<br \/>\nmomentum. Furthermore, by applying the Udwadia?Kalaba approach, we use the constraint of motion<br \/>\norbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint<br \/>\n(or energy conservation constraint) and easily verify that any heavenly body?s motion complies with<br \/>\nthe inverse square law of gravitation. That is, we study Kepler?s law and Newton?s inverse square<br \/>\nlaw in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move<br \/>\nand also&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Udwadia?Kalaba equation is a simple, aesthetic, and thought-provoking description of the world<br \/>\nat a very fundamental level. It is about the way systems move. In this paper, we creatively apply<br \/>\nthe Udwadia?Kalaba approach to study heavenly bodies?&#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-75187","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\/75187","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=75187"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/75187\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=75187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=75187"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=75187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}