{"id":290,"date":"2015-08-27T00:19:36","date_gmt":"2015-08-27T00:19:36","guid":{"rendered":"http:\/\/digitalobby.spu.edu\/energy\/?page_id=290"},"modified":"2020-12-16T05:09:42","modified_gmt":"2020-12-16T05:09:42","slug":"two-equations-for-gravitational-force-and-energy","status":"publish","type":"page","link":"https:\/\/scholars.spu.edu\/seeley\/lane-seeley\/physics-learning-resources\/categorizing-forces\/two-equations-for-gravitational-force-and-energy\/","title":{"rendered":"Two Models for Gravitational Force and Energy"},"content":{"rendered":"<p>Why do we have two completely different equations for gravitational force and two completely different equations for gravitational energy?&nbsp;&nbsp;<\/p>\n<p>.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-296 alignnone\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Satellite.jpg\" alt=\"Satellite\" width=\"365\" height=\"213\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-295 alignnone\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Pisa1.png\" alt=\"Pisa\" width=\"193\" height=\"225\" srcset=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Pisa1.png 359w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Pisa1-258x300.png 258w\" sizes=\"auto, (max-width: 193px) 100vw, 193px\" \/><\/p>\n\n\n<p class=\"wp-block-paragraph\"><strong>Newton&#8217;s Universal Law of Gravitation<\/strong> &#8211; One set of equations for force and energy is universal and applies whenever two massive objects are interacting with each other:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Grav-Force-Univ-3.gif\" alt=\"\" class=\"wp-image-787\" width=\"124\" height=\"47\" \/><figcaption>Universal equation for gravitational force<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-1024x329.png\" alt=\"\" class=\"wp-image-775\" width=\"153\" height=\"49\" srcset=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-1024x329.png 1024w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-300x96.png 300w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-768x247.png 768w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-830x266.png 830w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-230x74.png 230w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-350x112.png 350w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM-480x154.png 480w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Screen-Shot-2020-12-07-at-10.55.14-AM.png 1034w\" sizes=\"auto, (max-width: 153px) 100vw, 153px\" \/><figcaption>Universal equation for gravitational energy <\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"43\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Gravitation-Constant.gif\" alt=\"\" class=\"wp-image-782\" \/><figcaption>Universal gravitation constant<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In these equations, <em>m<sub>1 <\/sub><\/em>and <em>m<sub>2<\/sub><\/em> are the masses of the two objects and <em>R<sub>1,2<\/sub> <\/em>is the distance between their centers. Both equation have negative signs but these negative signs mean very different things. The negative sign in the gravitational force equation indicates that the gravitational force interaction is always attractive. The negative sign in the gravitational energy equation indicates that two objects have zero gravitational energy when they are infinitely far apart and their gravitational energy decreases (or becomes more and more negative) as they get closer together. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Gravitational Force and Energy Near Earth&#8217;s Surface<\/strong> &#8211; According to Newton\u2019s Universal Law of Gravitation the gravitational force decreases in magnitude as object get further apart. This is certainly true but it is not very noticeable for objects near Earth surface. The gravitational force interaction between Earth and everyday objects is nearly constant as the height of the object changes. Therefore, we often make the approximation that the gravitational force does not depend on height for objects near Earth\u2019s surface. This approximation leads to a set of equations which is very different from the universal equations above.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Grav-Force-Terr.gif\" alt=\"\" class=\"wp-image-788\" width=\"163\" height=\"33\" \/><figcaption>Gravitational force near Earth&#8217;s surface<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Grav-Energy-Terr.gif\" alt=\"\" class=\"wp-image-789\" width=\"190\" height=\"24\" \/><figcaption>Gravitational energy near Earth&#8217;s surface<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Grav-Accel-Terr.gif\" alt=\"\" class=\"wp-image-790\" width=\"84\" height=\"39\" \/><figcaption>Gravitational acceleration near Earth&#8217;s surface<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Near Earth&#8217;s surface the gravitational force does not change very much at all, so it is convenient to  the approximation that the gravitational force interaction between an object and the Earth does not change with height. According to this approximation the increase in gravitational energy of the Earth-object system is directly proportional to the increase in height. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2020\/12\/Change-in-Grav-Energy.gif\" alt=\"\" class=\"wp-image-794\" width=\"168\" height=\"20\" \/><figcaption>Change in gravitational energy<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"> In this approximation the zero point of gravitational energy is arbitrary. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Why do we have two completely different equations for gravitational force and two completely different equations for gravitational energy?&nbsp;&nbsp; . Newton&#8217;s Universal [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":0,"parent":246,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/page_fullwidth.php","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-290","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/comments?post=290"}],"version-history":[{"count":10,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/290\/revisions"}],"predecessor-version":[{"id":799,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/290\/revisions\/799"}],"up":[{"embeddable":true,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/246"}],"wp:attachment":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/media?parent=290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}