{"id":483,"date":"2007-08-06T09:33:39","date_gmt":"2007-08-06T09:33:39","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2007\/08\/06\/howling-at-the-moon-bad-gravitational-math\/"},"modified":"2007-08-06T09:33:39","modified_gmt":"2007-08-06T09:33:39","slug":"howling-at-the-moon-bad-gravitational-math","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2007\/08\/06\/howling-at-the-moon-bad-gravitational-math\/","title":{"rendered":"Howling at the Moon: Bad Gravitational Math"},"content":{"rendered":"<p><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" alt=\"PF_997949~Gray-Wolf-Howling-at-Moon-Posters.jpg\" src=\"https:\/\/i0.wp.com\/scientopia.org\/img-archive\/goodmath\/img_235.jpg?resize=145%2C212\" width=\"145\" height=\"212\" class=\"inset right\" \/><\/p>\n<p> There&#8217;s one piece of bad math that I&#8217;ve encountered relatively frequently in conversations. It&#8217;s<br \/>\nincredibly frustrating to me, because it&#8217;s just so crazy &#8211; but the way we teach math and physics, far to many people just don&#8217;t have enough of a clue to see how foolish it really is. <\/p>\n<p> This comes up in conversations with lay-people whenever a new space probe is launched. It&#8217;s generally presented in the form of a question; something like &#8220;That TV announcer said something about a point between the earth and the moon where gravity cancels, so there&#8217;s no gravitational pull towards either the earth or the moon. How can the moon cause tides if its gravity is cancelled all the way out there?&#8221;<\/p>\n<p> I&#8217;ve never found a form of this that was sufficiently mockable &#8211; in general, people who ask the question <em>know<\/em> that there&#8217;s something wrong with the question; they <em>know<\/em> that it&#8217;s stupid, but they don&#8217;t know why. I don&#8217;t like to make fun of that: people who ask a question because they know that their ignorant about something, and they&#8217;re trying to fix that patch of ignorance &#8211; they <em>don&#8217;t<\/em> deserve to be mocked. So I&#8217;ve avoided this. Until now: I&#8217;ve found the perfect mockable presentation of this problem. And wait till you see the wonderfully insane form I found it in!<\/p>\n<p><!--more--><\/p>\n<blockquote>\n<p>\tNo one would quarrel with the fact that there is a relationship between what the Moon does and what the Tides do. The Bible, after all, says that the Moon was designed to serve mankind through &#8220;signs&#8221; (which could certainly include Tidal phenomena), and through &#8220;seasons&#8221;, and by giving light.<\/p>\n<p>However, to say there is a relationship or connection between the Moon and Tides is one thing; to say that the Moon causes and controls Earth&#8217;s tides (as the whole world has been taught is a scientific fact) is quite another thing.<\/p>\n<p>\tIn the first instance&#8211;since God has said that one of His purposes for making the Moon and having it behave as it does is precisely for man&#8217;s aid in such things as gauging tides, planting, harvesting, etc.&#8211;we see the relationship as supernatural. These are &#8220;signs&#8221; and they have always worked and they work now for those who read them. Thus, there is a relationship or connection between the Moon&#8217;s behavior and supplying useful and necessary knowledge for man.<\/p>\n<p>\t\tIn the second instance, however&#8211;since &#8220;science&#8221; has said it will explain everything in natural terms without God and will designate all supernatural explanations as superstitions held by unenlightened people&#8211;we find that the obvious connections between the Moon&#8217;s behavior and certain phenomena such as Tides must be explained naturalistically by the science establishment.<\/p>\n<p>\t\tSo, God gave His supernatural explanation for Tides, which man has rejected. In its stead, man has come up with a purely naturalistic explanation for the tidal phenomena. In short, man&#8217;s &#8220;science&#8221; has declared that the Moon&#8217;s gravitational pull (assisted by the sun&#8217;s pull) causes the Tides. This declaration is now counted as a &#8220;fact&#8221; of science.<\/p>\n<p>\t\tVern, one of these explanations is the Truth and one is a lie. Let&#8217;s see if we can find out which is which&#8230;. First, let us look at some facts and see where they take us logically. For instance, there is a real fact about a neutral gravity zone between the Earth and the Moon. I quote from a letter from NASA dated April 5, 1990 addressing this matter:<\/p>\n<blockquote><p>\n&#8220;&#8230;On a direct line from the Earth to the moon, equal gravitational effects would be found at approximately 216,000 miles, given a mean<br \/>\ndistance of 240,000 miles between the two bodies&#8230;.&#8221;20 (Emph. added)\n<\/p><\/blockquote>\n<p>\tOther sources confirm this understanding. Figures XIV &amp; XV {reproduced in book only} are taken from one of famed rocket scientist Werner von Braun&#8217;s books. They illustrate this neutral gravity zone.\n<\/p>\n<p>\tOK. So all we are describing here is something that must logically be true if the statistics about the Earth and Moon gravitational pulls are fairly accurate. Earth&#8217;s gravity is said to be six times as strong as the Moon&#8217;s gravity, or said the other way, the Moon&#8217;s gravitational attraction is 1\/6 or about 17% that of Earth&#8217;s gravity.<\/p>\n<p> Somewhere between the two bodies the pull of one body has got to be overcome by the pull of the other<br \/>\none. At this point (which NASA says and von Braun confirms averages c. 216,000 miles from the Earth) there<br \/>\nis a neutral gravity zone where the Earth&#8217;s gravitational pull becomes weaker than the Moon&#8217;s gravitational<br \/>\npull and, at this same point, the Moon&#8217;s gravitational pull becomes weaker than the Earth&#8217;s gravitational<br \/>\npull.<\/p>\n<p>\tThis circumstance is demanded by the gravity concept and all the supposed facts and laws that describe the Earth and Moon gravitational fields. OK, Vern? Now keep that in mind as we read what &#8220;science&#8221; says about Tides on Earth&#8230;.<\/p>\n<p>\tWhat &#8220;science&#8221; says is that the Moon&#8217;s gravitational pull reaches out thru the neutral gravity zone (where it couldn&#8217;t attract a balloon full of feathers, a dead horse, or the Astrodome) and goes on beyond 50,000, 100,000, 216,000 miles and sucks the big ole Earth toward it like stretching a rubber ball! I know it&#8217;s incredible; I know it&#8217;s insane, but that&#8217;s what the naturalistic (i.e., &#8220;scientific&#8221;) explanation demands that the Moon must do. Read it for yourself from these examples (which are repeated in every book on the subject):<\/p>\n<blockquote><p>\n&#8220;Strange as it may seem [yeah!], what we normally think of as<br \/>\nthe solid body of the earth is also affected by the moon, so that it<br \/>\ntoo [the Earth, that is] has a tide. The landmass of the earth is elastic<br \/>\nand actually rises and falls about 4 1\/2 inches. We do not feel these<br \/>\nland tides&#8230;but they do take place.&#8221; 23 (Emph. added)\n<\/p><\/blockquote>\n<p> In his book, The Lunar Effect, author Lieber says:<\/p>\n<blockquote><p>\n&#8230;the pull of the moon distorts the earth as if it were a rubber<br \/>\nball. The North American Continent may rise so much as a foot<br \/>\nwhen the moon is overhead.&#8221;24\n<\/p><\/blockquote>\n<p>\tThe famous &#8220;science&#8221; writer Asimov says:<\/p>\n<blockquote><p>\n&#8220;&#8230;the earth, so to speak, is stretched in the direction of the moon.<br \/>\nThe solid earth does not stretch much, however (only about nine inches<br \/>\non each side), and only delicate measurements can show this stretch.&#8221;25\n<\/p><\/blockquote>\n<p> He&#8217;s lying about the &#8220;delicate measurements&#8221;, of course. No measurement shows this (and what the others said) or could show it. Mathematical decorations derived from and supportive of this crazy hypothesis might show a 9&#8243;stretch (twice what the other guy just said), but no measurement has or can show it.<\/p>\n<p> In a kid&#8217;s &#8220;science&#8221; book we read:<\/p>\n<blockquote><p>\n&#8220;Now the land of the earth does not move easily, but the waters do.<br \/>\nThe waters on the side of the earth closest to the moon pile up in a<br \/>\n&#8220;bulge&#8221;, causing a high tide. But at the same time there is a high tide<br \/>\non the other side of the earth. What do you suppose is the reason for<br \/>\nthis? The answer is that, as the moon&#8217;s gravity pulls the water nearest<br \/>\nto it a little away from the earth, it also pulls the whole earth a little<br \/>\naway from the waters in the ocean on the farthermost side, setting up a<br \/>\nsecond high tide there.&#8221;26\n<\/p><\/blockquote>\n<p>\tIn The Moon: Earth&#8217;s Natural Satellite, author Branley says the same thing in explaining his diagram on the tidal phenomena:<\/p>\n<blockquote><p>\n&#8220;&#8230;the ocean at E [the furthermost from the moon], because it is so<br \/>\nmuch farther away is not pulled toward the moon as much as the solid<br \/>\nearth; the earth is pulled away from the water; and the water is therefore<br \/>\ndeeper during this part of the tidal cycle.&#8221;27 (emph. added)\n<\/p><\/blockquote>\n<p>\tBranley then gets into some numbers which grow out of the myth he believes, numbers so contradictory as to be comical if the world weren&#8217;t mesmerized by this deception:<\/p>\n<blockquote><p>\n&#8220;The tide-raising force of the moon is very small indeed, compared<br \/>\nto the force of gravity. The tide-raising force of the moon is about<br \/>\n1\/9,000,000 that of the earth&#8217;s gravity&#8230;.&#8221;28\n<\/p><\/blockquote>\n<p>\tWow. One nine millionth  Let&#8217;s see; that means the earth&#8217;s pull toward its own center on its own crust and oceans and seas is nine million times as great as the Moon&#8217;s pull on the same features, doesn&#8217;t it? Nine million to one. Whew! Amazing, isn&#8217;t it that nine million mule power could be pulling something one way and one mule power could overcome all that every hour of every day and stretch the Earth and cause zillions of cubic feet of water to shift around everywhere! Yes, just amazing, especially when that one mule power stopped out there at the 216,000 mile neutral gravity zone! Momma mia&#8230;\n<\/p>\n<\/blockquote>\n<p> Now <em>that<\/em> is truly first class insane crackpottery. Just off the wall.<\/p>\n<p> Yes, it&#8217;s <a href=\"http:\/\/www.fixedearth.com\/tides.htm\">an ultra-fundie geocentric lunatic.<\/a> (A particularly appropriate term given the subject.) See, the lunar tide thing is part of an elaborate conspiracy by<br \/>\nscientists to deny God&#8217;s role in causing the tides. In fact, it&#8217;s all tied in to evolution. But we won&#8217;t get to that bit today.<\/p>\n<p> This doesn&#8217;t even need me to mock it. Just read it yourself, and when you manage to pick yourself up off the floor, I&#8217;ll explain the math behind the error.<\/p>\n<p> It&#8217;s crazy, but it does contain that gravity question &#8211; just stretched out beyond the breaking point. But what makes it break in that loony-tune universe is the same thing that causes confusion back here in the real world.<\/p>\n<p> The &#8220;zero point&#8221; isn&#8217;t the point at which the moons gravity stops. It&#8217;s not the point at which<br \/>\nthe earths gravity overcomes the moons gravity so that the moons gravity can&#8217;t come any closer to the earth. It&#8217;s just the point <em>at which things balance<\/em>. <\/p>\n<p><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" alt=\"spring-wall.png\" src=\"https:\/\/i0.wp.com\/scientopia.org\/img-archive\/goodmath\/img_236.png?resize=193%2C158\" width=\"193\" height=\"158\" class=\"inset right\" \/><\/p>\n<p> Get two large springs &#8211; like a slinky. Attach each of them to opposite ends of a rubber ball. Then attach the other end of the springs to opposite walls of a room, and let go of the ball. The ball will<br \/>\noscillate back and forth for a while, but eventually, it will stop, in a configuration like the figure to the right: the two springs will each by stretched to the point where the force that each stretched spring applies to the ball is the same. The place it stops is the equilibrium point for the two springs in that space &#8211; it&#8217;s the point where the force exerted by the two springs is equal, and so they cancel out &#8211; the ball is effectively under no accelerating force. <\/p>\n<p> But &#8211; more importantly: the <em>walls<\/em> that the springs are attached to are still being pulled towards each other, even if the springs are in equilibrium. The fact that the tension in the springs<br \/>\ncreate forces that cancel out at the equilibrium point doesn&#8217;t mean that the forces have disappeared.<\/p>\n<p> Gravity operates in the same way. As you move away from the moon, the force of the moons gravity decreases &#8211; every time you double the distance from the center of the moon, the moons force of gravity on you decreases by a factor of four. But it <em>never<\/em> disappears. The force doesn&#8217;t stop at equilibrium &#8211; it just balances there. If you move closer to earth than the equilibrium point, then the earth&#8217;s attraction is <em>stronger<\/em> than the moon&#8217;s. But it still exists.<\/p>\n<p> Just to hammer the point home a bit more, let&#8217;s look at the math. Let&#8217;s look at the gravitational forces on a person on the surface of the earth. We&#8217;ll just do it approximately, to keep the calculations simple, so we&#8217;ll do it for a person standing on the equator, and we&#8217;ll pretend that the moon orbits right above the equator.<\/p>\n<p> We&#8217;ll start by just laying out the basic data that we&#8217;ll need to do the calculation. I&#8217;ll use my own weight for the person; I weigh about 84 kilograms. The radius of the earth at the equator is about 6,350 kilometers. The mass of the earth is about 6.0&times;10<sup>24<\/sup>. The mass of the moon is about 7.4&times;10<sup>22<\/sup>. The distance from the earth to the moon (surface to surface) is about 384,000 kilometers. The radius of the moon is about 1,700km.<\/p>\n<p> Newton&#8217;s equation for calculating the gravitational force between two objects is F=Gm<sub>1<\/sub>m<sub>2<\/sub>\/r<sup>2<\/sup>, where the ms are the masses of the two objects, r is the distance between their centers of mass, and G is the gravitational constant 6.7&times;10<sup>-11<\/sup>m<sup>3<\/sup>\/(kg sec<sup>2<\/sup>).<\/p>\n<p> So &#8211; the force of gravity from the earth on the person (with all numbers rounded to two significant figures) (6.7&times;10<sup>-11<\/sup>)&times;(6.0&times;10<sup>24<\/sup>)&times;84\/(6.5&times;10<sup>6<\/sup>)<sup>2<\/sup> = 800 newtons.<\/p>\n<p>\t The force of gravity from the moon is calculated the same way. But we need the distance from the center of the moon to the surface of the earth, and our distance figure is surface to surface, so we need to add the radius of the moon &#8211; so the distance is 385,000km. So &#8211; the gravitational force from the moon on the person is  (6.7&times;10<sup>-11<\/sup>)&times;(7.4&times;10<sup>22<\/sup>)&times;84\/(3.9&times;10<sup>8<\/sup>)<sup>2<\/sup> = 2.7&times;10<sup>-3<\/sup> newtons.<\/p>\n<p> The force of the moon on the person on earth is very small &#8211; on the order of 1\/300,000th the gravitational force of the earth on that same person. But it&#8217;s definitely there &#8211; real, and measurable. And that kind of force is more than enough to produce the very modest effect of tides.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There&#8217;s one piece of bad math that I&#8217;ve encountered relatively frequently in conversations. It&#8217;s incredibly frustrating to me, because it&#8217;s just so crazy &#8211; but the way we teach math and physics, far to many people just don&#8217;t have enough of a clue to see how foolish it really is. This comes up in conversations [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-483","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-7N","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/483","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=483"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/483\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=483"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=483"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}