{"id":285,"date":"2010-12-14T13:24:55","date_gmt":"2010-12-14T18:24:55","guid":{"rendered":"http:\/\/www.fruechtetheory.com\/blog\/?p=285"},"modified":"2011-01-15T17:59:41","modified_gmt":"2011-01-15T22:59:41","slug":"independent-action","status":"publish","type":"post","link":"https:\/\/www.fruechtetheory.com\/blog\/2010\/12\/14\/independent-action\/","title":{"rendered":"Independent Action"},"content":{"rendered":"

In one of the FGT YouTube videos of February 2008 it was mentioned that unlike a tug of war where the tension in the rope is the same throughout when the rope is stationary, gravity is one mass acting independently on another.\u00a0 In the case of two masses of spherical shape the force is known to be F12<\/sub> = Gm1<\/sub>m2<\/sub>\/r12<\/sub>2<\/sup>, which we can equate to m1<\/sub>a or m2<\/sub>a, depending on whether we want to calculate the acceleration of m1<\/sub> or m2<\/sub>, and where r12<\/sub> is the distance between the centers of the two masses.\u00a0 With planetary masses that are close to spherical, and the objects they pull, this formula has been used most reliably, while it has been known for a long time by learned mathematical and scientific people that shape matters, and using center of mass with the standard physics book formula can cause increased error in some instances.<\/p>\n

As an analysis that has already been done, let us use Kline Chapter 16, Sections 5, 6, and 7.\u00a0 Starting with Section 5, \u201cGravitational Attraction of Rods\u201d, the example given is that of a \u201crod 6 feet long and of mass 18 pounds which is uniformly distributed\u201d and \u201cso thin that we think of it as extending in one dimension only.\u00a0 Three feet from one end of the rod and along the line of the rod is a small object of mass 2 pounds which we shall regard as located at one point.\u201d \u00a0\u00a0Kline first calculates the force that the rod exerts on the 2-pound mass as though the entire mass of the rod were concentrated at its center, according to the standard F12<\/sub> = Gm1<\/sub>m2<\/sub>\/r12<\/sub>2<\/sup> formula, which comes out as equaling G poundals.\u00a0 Then he does the calculation properly using an integration over the rod, showing that the force that the rod exerts on the 2-pound mass is actually (4\/3) G poundals.\u00a0 In Section 6, \u201cGravitational Attraction of Disks\u201d [1], again a difference from the standard formula is shown which for comparison includes Exercise 1 from that section.\u00a0 Finally, in Section 7 it is shown that the standard physics book formula can be used with spheres.<\/p>\n

Since the title of the referenced book includes \u201cAn Intuitive and Physical Approach\u201d, intuition may tell us that, since the rod was integrated along its length to obtain a correct answer, every piece of a nearly one dimensional rod in the limit of a Riemann sum exerts a gravitational force independently on a separate point mass.<\/p>\n

With General Relativity, unproven to date, a mass produces surface curvature in space, which may contact a series of points on other surfaces, due to another mass, through a tensor product [2] that reduces to a force vector. \u00a0This may be interpreted as space-time surface interaction, and not necessarily complete independent action.\u00a0 At least two multi-million dollar projects are built and running ([3], [4]) and at least one is being developed [5] in attempts to prove General Relativity.<\/p>\n

Special Relativity, on the other hand, E = mc2<\/sup>, has long been proven correct, and the gravitational theory presented on this web site would not work without it.\u00a0 Some physicists in their writings seem to make a transition from Special to General Relativity as though the two are somehow linked, and in reality they bear no relationship to each other.<\/p>\n

\u00a0<\/p>\n

[1] Kline, Morris, Calculus, An Intuitive and Physical Approach<\/span>, John Wiley and Sons, Inc., 1967, 1977; Dover (1998) unabridged republication.<\/p>\n

[2] Rainich, George Yuri, Mathematics of Relativity<\/span>, John Wiley and Sons, Inc., 1950, Chapter 4<\/p>\n

[3] http:\/\/www.ligo.caltech.edu\/<\/a><\/p>\n

[4] http:\/\/www.nasa.gov\/mission_pages\/gpb\/index.html<\/a><\/p>\n

[5] http:\/\/lisa.nasa.gov\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

In one of the FGT YouTube videos of February 2008 it was mentioned that unlike a tug of war where the tension in the rope is the same throughout when the rope is stationary, gravity is one mass acting independently on another.\u00a0 In the case of two masses of spherical shape the force is known […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,11],"tags":[],"class_list":["post-285","post","type-post","status-publish","format-standard","hentry","category-general-relativity","category-newtonian-mechanics"],"_links":{"self":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/comments?post=285"}],"version-history":[{"count":5,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/285\/revisions"}],"predecessor-version":[{"id":315,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/posts\/285\/revisions\/315"}],"wp:attachment":[{"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/media?parent=285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/categories?post=285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fruechtetheory.com\/blog\/wp-json\/wp\/v2\/tags?post=285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}