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Natural Science Forum / Physics / Relativity / December 2005Falling Objects, How They Fall
To examine falling of objects, very heavy objects need to be dropped; With light objects, measurement can be made using either the center of mass, or the bottom edge. With very heavy objects, like the moon falling on Earth, or Mars faling on Earth, both the centers of mass and the closest surfaces must be used. It may be useful to use an alternate model of gravitation to visualize how heavy things fall before doing the math. So instead of Newtonian gravitation, let's use the Divergent Matter model, where objects expand, rather than "attract". If a small point particle is dropped on Earth, the distance between the particle and the surface of Earth is reduced at 981 cm/sec/sec. If the Moon is dropped, the distance between the near surfaces of the Earth and Moon is reduced at greater than 1000 cm/sec/sec. In the Divergent Matter model this is obvious, in Newtonian gravitation, it is not. In Divergent Matter, the centers of mass do not move, the surfaces do. If Mars is dropped, the distance between the near surfaces of Mars and Earth is reduced at even a greater rate than for the Earth and Moon. Newtonian gravitation also predicts this, but the math must be done. Joe Fischer Snip of pure crap... Blithering idiot! Paul Stowe > Snip of pure crap... > > Blithering idiot! > > Paul Stowe Is this where you learned how objects fall? http://www.lessonplanspage.com/ScienceExHeavyOrLightObjectsFallFasterMO68.htm Joe Fischer > Snip of pure crap... > > Blithering idiot! > > Paul Stowe to the contrary, snipping without arguing makes _you_ idiot > Snip of pure crap... > > Blithering idiot! > > Paul Stowe to the contrary, snipping without arguing makes _you_ idiot > To examine falling of objects, very heavy objects need to be dropped; > [quoted text clipped - 11 lines] > So instead of Newtonian gravitation, let's > use the Divergent Matter model, The Divergent Matter model is utter nonsense. Bill > where objects > expand, rather than "attract". [quoted text clipped - 20 lines] > > Joe Fischer >> To examine falling of objects, very heavy objects need to be dropped; >> With very heavy objects, like the moon falling on [quoted text clipped - 4 lines] > >Bill Another troll that can't do Newtonian math. Joe Fischer >>> To examine falling of objects, very heavy objects need to be dropped; >>> With very heavy objects, like the moon falling on [quoted text clipped - 6 lines] > > Another troll that can't do Newtonian math. Figured out Boyles law yet? Bill > Joe Fischer >Figured out Boyles law yet? > >Bill You are really a troll, Hobbit, and too lazy to snip. I took the information from a book, but I think it is much easier to visualize using Divergent Matter. Over the past 8 years I have written about how falling objects do also cause the Earth to accelerate toward them in Newtonian concepts, but it takes an asteroid the size of Eros to get the measurement within precision attained by Dicke with Eotvos type experiments. Two Earths will accelerate towards each other at twice the acceleration as the Earth and anything smaller than an automobile, at the same distance of separation. Anybody that wants to dispute that needs to show the math or the logical premise, just repeating rules or prior gossip level physics will not do it. AFAIK, no measurement of equal falling has ever exceeded a precision of 15 significant digits. Anything smaller than the asteroid Eros will require a better precision than that. Does that mean that all things fall equally, of course they do not. Many if not most experiments have not even tried to see if all things fall equally, they test to see if all elements and materials fall the same, but they still have not achieved better than 15 digit precision. If Newtonian gravitation math says that Eros will fall faster than a VW at the same altitude above the Earth, then it is at least true. But on any large object, a decision has to be made whether to use the center of mass or the near surfaces to measure the relative acceleration. This is not an attempt by me to invalidate anything, it is something I read in a well known book. In fairness, I think I found an error in the book, but it could be from an editor, instead of the author. There is a statement that a satellite in a 100 mile high orbit will fall 16 feet every second, and I don't think that is right, but I have not done the math. While objects fall 16 feet the first second after being dropped, the satellite is not starting from stationary. But one error, if there is one, does not make everything in the book wrong. I just posted the formula for relative acceleration of two objects in the last couple of days. It is from the book, and is A (Earth) + a (anything else) = G * ( M (Earth)) + ( m (anything else)) --------------------------------------------------- D^2 and acceleration is falling, using F(orce) to calculate falling just doesn't demonstrate clearly. Joe Fischer >>Figured out Boyles law yet? >> >>Bill > > You are really a troll, Hobbit, and too lazy to snip. Boyles law consists of one simple equation. Since you base your theory on 'gasses' it is obliviously needed. The fact you decided to give your usual incoherent rant instead of it is very revealing. Rest of junk snipped. Bill >"Joe Fischer" wrote: >>>Figured out Boyles law yet? [quoted text clipped - 4 lines] >'gasses' it is obliviously needed. The fact you decided to give your usual >incoherent rant instead of it is very revealing. "My Theory", whatever that means, has nothing to do with the subject matter I posted, I just think it is good way to think of certain processes in gravitation, especially where two objects can have a measurable effect. Boyles law may have been modified by Van der Waal, check it out. >Rest of junk snipped. >Bill Glad you finally learned to snip unless the subject line carries your name, it gives you an easy way to avoid discussing anything point by point. Joe Fischer > > To examine falling of objects, very heavy objects need to be dropped; > > [quoted text clipped - 15 lines] > > Bill joe has more brain in his eggy farts than you have in your head > > where objects > > expand, rather than "attract". [quoted text clipped - 20 lines] > > > > Joe Fischer >> > To examine falling of objects, very heavy objects need to be dropped; >> > [quoted text clipped - 18 lines] > joe has more brain in his eggy farts than you > have in your head Unlike you whose brain is egg farts. Bill >> > where objects >> > expand, rather than "attract". [quoted text clipped - 20 lines] >> > >> > Joe Fischer > To examine falling of objects, very heavy objects need to be dropped; > With light objects, measurement can be made using > either the center of mass, or the bottom edge. > With very heavy objects, like the moon falling on > Earth, or Mars faling on Earth, both the centers of mass > and the closest surfaces must be used. > It may be useful to use an alternate model of > gravitation to visualize how heavy things fall before > doing the math. > So instead of Newtonian gravitation, let's > use the Divergent Matter model, where objects > expand, rather than "attract". > If a small point particle is dropped on Earth, > the distance between the particle and the surface > of Earth is reduced at 981 cm/sec/sec. > If the Moon is dropped, the distance between > the near surfaces of the Earth and Moon is reduced > at greater than 1000 cm/sec/sec. Where did you get that number from? I know you do not do any math, so I assume you just made it up as per usual. Do you really think that the acceleration due to gravity 250,000 miles from the Earth is the same as as the acceleration on the surface of the Earth? If something was "dropped" 250,000 miles above the Earth it would fall towards the Earth with an acceleration of .26 cm/sec/sec. This is because it is roughly 62 times farther from the center of the Earth than an object on the surface, and therefore the accleration due to gravity is 1/62*62 as much. > In the Divergent Matter model this is obvious, > in Newtonian gravitation, it is not. In Divergent > Matter, the centers of mass do not move, the > surfaces do. Divergent Matter theory is obviously wrong, as we know that the acceleration due to Earth's gravity gets weaker the farther away you get. According to you model orbits are impossible, mass has no affect on gravity, and gravity is independent of distance. > If Mars is dropped, the distance between the > near surfaces of Mars and Earth is reduced at even > a greater rate than for the Earth and Moon. No. This is simply untrue. > Newtonian gravitation also predicts this, but > the math must be done. No it does not. If you would learn some math you would realize that in a moment. The math is trivial. The closest Mars gets to Earth is 35 million miles. This is over 8000 times the distance from the center of the Earth to the surface, which means the gravitational pull Mars feels is 1/64000000 what we feel on the surface of the Earth. Trying to understand any of this stuff without even knowing the simple algebra needed to determine what Newtonian predicts is pointless. Stephen > > To examine falling of objects, very heavy objects need to be dropped; > [quoted text clipped - 26 lines] > 250,000 miles from the Earth is the same as as the acceleration > on the surface of the Earth? first of all there is not such an animal like "250,000 miles from the Earth" you understand sh.t, arent you? > If something was "dropped" 250,000 miles above the Earth > it would fall towards the Earth with an acceleration of > .26 cm/sec/sec. This is because it is roughly 62 times > farther from the center of the Earth than an object > on the surface, and therefore the accleration due to > gravity is 1/62*62 as much. now you confirme that you are stupid, thanks > > In the Divergent Matter model this is obvious, > > in Newtonian gravitation, it is not. In Divergent > > Matter, the centers of mass do not move, the > > surfaces do. > > Divergent Matter theory is obviously wrong, as we know but you are stupid, that is right > that the acceleration due to Earth's gravity gets weaker you are the first dickhead ever been defining "gravity" > the farther away you get. According to you model orbits > are impossible, mass has no affect on gravity, and gravity > is independent of distance. what is gravity? you fool > > If Mars is dropped, the distance between the > > near surfaces of Mars and Earth is reduced at even [quoted text clipped - 18 lines] > > Stephen >> To examine falling of objects, very heavy objects need to be dropped; > [quoted text clipped - 22 lines] > >Where did you get that number from? I made it up, it is not a number though, it is a minimum. It assumes dropping the moon as close as physically posssible to the Earth, which puts the moon's center of mass at least 1000 miles above the surface. I may have overestimated the acceleration of gravity at 1000 miles altitude though, sorrry, I probably should have said 1.012 times the acceleration of gravity at that altitude. I also may have been thinking of two Earths, instead of Earth and Moon. > I know you do not >do any math, so I assume you just made it up as per usual. Right. >Do you really think that the acceleration due to gravity >250,000 miles from the Earth is the same as as the acceleration >on the surface of the Earth? Where did you get 250,000 miles from? I did not specify dropping the moon from any particular altitude, and the moon is only 239, 000 miles away. >If something was "dropped" 250,000 miles above the Earth >it would fall towards the Earth with an acceleration of >.26 cm/sec/sec. This is because it is roughly 62 times >farther from the center of the Earth than an object >on the surface, and therefore the accleration due to >gravity is 1/62*62 as much. I have seen and posted the acceleration of gravity at the moon's orbital altitude as 1.37 cm/sec/sec, I don't know where you got .26 from. >> In the Divergent Matter model this is obvious, >> in Newtonian gravitation, it is not. In Divergent >> Matter, the centers of mass do not move, the >> surfaces do. > >Divergent Matter theory is obviously wrong, Nothing is obviously wrong if it is examined completely. >as we know >that the acceleration due to Earth's gravity gets weaker >the farther away you get. If you are a student, do not pay any attention to what I say, you may fail. But there is no "attraction", so the statement above is not how I would say it. Obviously, the Newtonian formula reflects an inverse square function, I am able to do 4th grade math. > According to you model orbits >are impossible, mass has no affect on gravity, and gravity >is independent of distance. You are imagining things, Divergent Matter treats orbits as General relativity does, as a straight line, except I don't proffer Parallel Transport or Schild's Ladder Math. Mass has a profound effect on gravity as a component of density and total energy. And the Divergent Matter model has the falloff with distance built in the sole postulate of "Matter Expands". This falloff reflects the entropic nature of gravity and is involved with the establishment of many constants in nature, sorry I have not put forth a formal presentation, I have been hoping somebody else will be able to think for themself and not just recite Newtonian concepts. >> If Mars is dropped, the distance between the >> near surfaces of Mars and Earth is reduced at even >> a greater rate than for the Earth and Moon. > >No. This is simply untrue. Why not, Mars has more mass than the Moon, perhaps I assumed wrong in thinking they could be dropped from the same altitude, which would have to be greater than the radius of Mars above the surface of Earth. >> Newtonian gravitation also predicts this, but >> the math must be done. > >No it does not. Well, the book I got the idea and most of the information from only gives the Newtonian treatment, so that author is mistaken. I may have made mistakes in trying to present the concept of things not falling equally, but I tried. >If you would learn some math you would >realize that in a moment. The math is trivial. I would say so, GM / d * d is not a very high level of math. >The closest Mars gets to Earth is 35 million miles. I assumed we could take it and place it or anything else at the closest point to Earth without surfaces touching. >This >is over 8000 times the distance from the center of the >Earth to the surface, which means the gravitational pull >Mars feels is 1/64000000 what we feel on the surface >of the Earth. Which is not pertinent to the premise stated. >Trying to understand any of this stuff without even knowing >the simple algebra needed to determine what Newtonian >predicts is pointless. >Stephen Algebra isn't needed for such simple things as falling in the presence of gravity. Trying to understand that freefall is inertial motion must be difficult for many people if I read the comments correctly though. And understanding that both objects do affect the apparent relative acceleration due to gravity is paramount to even thinking about gravity, just reciting a simplified formula that has been greatly simplified by greater minds than ours is not very understanding. If you are a student, please ignore everything I write about Divergent Matter, I may convince you and then you would fail in school. I don't now who my fan is in Malaysia, but I apologize to all if he said anything hostile. :-) Imagine, one real fan. :-) Joe Fischer >>> To examine falling of objects, very heavy objects need to be dropped; >> [quoted text clipped - 22 lines] >> >>Where did you get that number from? > I made it up, it is not a number though, it is > a minimum. > It assumes dropping the moon as close as > physically posssible to the Earth, which puts the > moon's center of mass at least 1000 miles above > the surface. Why would you assume that the moon is so close to the Earth? The moon is quite far away. Of course I do not see how the rate at which the Earth expands can be affected by how far away objects are. But more on that later. > Where did you get 250,000 miles from? I did > not specify dropping the moon from any particular > altitude, and the moon is only 239, 000 miles away. The altitude at which you drop something is very important for determining how fast it will fall. >>If something was "dropped" 250,000 miles above the Earth >>it would fall towards the Earth with an acceleration of >>.26 cm/sec/sec. This is because it is roughly 62 times >>farther from the center of the Earth than an object >>on the surface, and therefore the accleration due to >>gravity is 1/62*62 as much. > I have seen and posted the acceleration of > gravity at the moon's orbital altitude as 1.37 cm/sec/sec, > I don't know where you got .26 from. I misplaced a decimal point. I should have said 2.6 cm/sec/sec. As I said, the Moon is roughly 62 times as far away from the center of the Earth as the surface of the Earth is, therefore the acceleration due to gravity is 1/(62*62) times as much as the acceleration at the surface. This is roughly 10 m/sec/sec * 1/(62*62) = 2.6 cm/sec/sec. That is according that F = G M m / d^2 formula that you seem to dislike so much. >>> In the Divergent Matter model this is obvious, >>> in Newtonian gravitation, it is not. In Divergent >>> Matter, the centers of mass do not move, the >>> surfaces do. >> >>Divergent Matter theory is obviously wrong, > Nothing is obviously wrong if it is examined > completely. So have you completely examined the aether and the space elevator? >>as we know >>that the acceleration due to Earth's gravity gets weaker >>the farther away you get. > If you are a student, do not pay any attention > to what I say, you may fail. > But there is no "attraction", so the statement > above is not how I would say it. > Obviously, the Newtonian formula reflects an > inverse square function, I am able to do 4th grade math. But you are unable to explain it at all using your model. Lets look at the simple problem of dropping two small objects, one 2000 miles above the surface of the Earth, and one 4000 miles above the surface of Earth. To simplify the math a little, lets assume that the radius of the Earth is 4000 miles and the acceleration at the surface is 10 m/sec/sec. How far will the two objects fall in one minute? At 2000 miles above the surface of the Earth, the acceleration is 4.44 m/sec/sec, and at 4000 miles above the surface of the Earth, the acceleration is 2.5 m/sec/sec. This is just a simple application of F = G M m / d^2. After one minute, the lower object will fall approximately 5 miles. The upper object will fall approximately 3 miles. This is just applying some simple calculus. The key thing, is that the lower object will fall farther than the upper object, and the distance between them will increase. This is predicted by Newtonian gravity and General Relativity. However, what happens according to your model? You claim that the Earth is expanding, and that the objects are not attracted towards the Earth. So the surface of the Earth will expand towards the two objects, but the distance of the objects will not change. They will remain 2000 miles apart, and will "fall" at the same rate. This is quite contrary to what Newton and Einstein predict. In fact your model actually predicts that the higher object falls faster. You claim that the Earth is expanding, but the reason that we do not notice it is because everything expands. So those 2000 miles that separate the two objects will shrink over time, so according to your model the two objects are actually approaching each other. This is only possible if the farther one is falling faster than the nearer one. So your model predicts that the force of gravity increases with distance. >> According to you model orbits >>are impossible, mass has no affect on gravity, and gravity >>is independent of distance. > You are imagining things, Divergent Matter > treats orbits as General relativity does, as a straight > line, except I don't proffer Parallel Transport or Schild's > Ladder Math. General relativity does not assume that the Earth is expanding. You cannot claim that gravity on the surface of Earth is caused by the expansion of the Earth and just fall back on GR to explain everything else. The two are not compatible. Stephen >>>Where did you get that number from? > [quoted text clipped - 7 lines] >Why would you assume that the moon is so close to >the Earth? I didn't assume anything, if I do a thought experiment, I can put the moon anyplace it will fit. > The moon is quite far away. I know where the moon is, I had 4 semesters of college astronomy and built telescopes from scratch, this during the 1950s, and I have had a sincere interest since. >Of course >I do not see how the rate at which the Earth expands >can be affected by how far away objects are. I didn't mean to infer that (if I did). > But more on that later. > [quoted text clipped - 4 lines] >The altitude at which you drop something is very important >for determining how fast it will fall. Right, if it were to "fall". >>>If something was "dropped" 250,000 miles above the Earth >>>it would fall towards the Earth with an acceleration of [quoted text clipped - 8 lines] > >I misplaced a decimal point. I should have said 2.6 cm/sec/sec. I didn't calculate it I got the number from a book. >As I said, the Moon is roughly 62 times as far away from >the center of the Earth as the surface of the Earth is, >therefore the acceleration due to gravity is 1/(62*62) >times as much as the acceleration at the surface. This >is roughly 10 m/sec/sec * 1/(62*62) = 2.6 cm/sec/sec. 1000 / 3600? >That is according that F = G M m / d^2 formula that >you seem to dislike so much. Sorry if my writing implied I don't like that formula, I think it is great, for what it is intended. But F (force) is not what is used in orbital mechanics, acceleration is. And the total acceleration is the acceleration of the moon plus the acceleration of the Earth. >>>> In the Divergent Matter model this is obvious, >>>> in Newtonian gravitation, it is not. In Divergent [quoted text clipped - 8 lines] >So have you completely examined the aether and the space >elevator? What aether? Please talk about physics. >>>as we know >>>that the acceleration due to Earth's gravity gets weaker [quoted text clipped - 8 lines] > >But you are unable to explain it at all using your model. I can explain a lot to my satisfaction. What should be appreciated by others is the fact that I do find the EDM model to approximate General Relativity in many/most cases. >Lets look at the simple problem of dropping two small >objects, one 2000 miles above the surface of the Earth, >and one 4000 miles above the surface of Earth. To simplify >the math a little, lets assume that the radius of the Earth >is 4000 miles and the acceleration at the surface is 10 m/sec/sec. Expansion is not and can NOT be calculated using acceleration alone. A physicist should know that intuitively. >How far will the two objects fall in one minute? At 2000 >miles above the surface of the Earth, the acceleration is >4.44 m/sec/sec, and at 4000 miles above the surface of the >Earth, the acceleration is 2.5 m/sec/sec. This is just >a simple application of F = G M m / d^2. I appreciate the discussion because it forces me to try to improve my explanation of the processes. >After one minute, the lower object will fall approximately >5 miles. The upper object will fall approximately 3 miles. >This is just applying some simple calculus. The key thing, >is that the lower object will fall farther than the upper >object, and the distance between them will increase. This >is predicted by Newtonian gravity and General Relativity. Right, but in different ways, I do not accept that General Relativity says freefall is "acceleration" or "falling". >However, what happens according to your model? You claim >that the Earth is expanding, and that the objects are not >attracted towards the Earth. Right (in the model), but all objects, including the meter stick also expand (in the model). The fact that objects are not "attracted" is what makes the model beautiful in my view. > So the surface of the Earth >will expand towards the two objects, but the distance of >the objects will not change. ^ substitute between? >They will remain 2000 miles >apart, and will "fall" at the same rate. You are assuming they can be "dropped" from those altitudes, I do not. I use a physically realistic method of placing the two objects where they need to be. And (in the model) there is no "attraction", this method is consistent (within the model). A catapult, mortar, or rockets impart a velocity upward, and the two objects rise to the specified altitude at a specified instant. They will NOT be rising at the same velocity at that instant. That instant must be when the upward acceleration of surface of the Earth (in the model) coincides with the upward motion of both objects. The surface then begins "catching up", and the different upward velocity of the two objects causes them to move apart. >This is quite >contrary to what Newton and Einstein predict. If modeled properly, the physics should be parallel to Newtonian mechanics, or rather General Relativity. >In fact your model actually predicts that the higher >object falls faster. Not hardly (in the model), the upper object has a greater upward velocity than the lower, else it could not have been at a higher altitude. This model is not only a good way to think of gravity so that the concepts in General Relativity can be accepted and visualized better, it is also a good way to practice thinking of dynamics. >You claim that the Earth is expanding, >but the reason that we do not notice it is because everything >expands. Right, except for surface gravity (and other subtle differences which need to be discovered). >So those 2000 miles that separate the two objects >will shrink over time, so according to your model the >two objects are actually approaching each other. Not so, unless my brain really works backwards. I have been lax for not creating some kind of video that shows the dynamics. >This is >only possible if the farther one is falling faster than >the nearer one. Sorry, you are just not representing the dynamics of the model. >So your model predicts that the force >of gravity increases with distance. No, it predicts there is no "force" until or unless the objects have a contact interaction with the Earth (and/or the atmosphere). >>> According to you model orbits >>>are impossible, mass has no affect on gravity, and gravity [quoted text clipped - 6 lines] > >General relativity does not assume that the Earth is expanding. Right, it assumes objects in freefall and that objects in freefall are in inertial motion. I don't know how or why that can be resolved with the Earth remaining a constant size. >You cannot claim that gravity on the surface of Earth >is caused by the expansion of the Earth and just fall back >on GR to explain everything else. The two are not compatible. >Stephen I assume that spacetime curvature explains how objects in freefall can be in inertial motion without the surface of the Earth accelerating upward. But in the Electromagnetic Divergence of Matter model, the meter stick and the length of the second are constantly lengthening, and that should surely represent "spacetime curvature". I don't really know if the model will ever prove to have any merit, or if it will be useful, but it already is for me. It seems to definitely show that the moon and Earth both expanding would cause the distance between them to diminish faster than if only the Earth expanding. So if you don't start with the vis viva equation, or use Keplerian formulas with an orbital velocity of zero, you won't get the right answers of "falling". If falling could be measured to more than 25 significant digits, I think heavier things would be seen to fall faster. But only if they are not part of the Earth's mass, and only if they are dropped one at a time and the acceleration measured. If they are dropped side by side, they will appear to fall the same because, they mass of both will "attract" the Earth, and the relative acceleration will not be seen. Joe Fischer snip << 0x20,0x20,0x20,0x20 If falling could be measured to more than 25 significant digits, I think heavier things would be seen to fall faster. So a kg lead bar will overtake a kg of lead shot. The bird shooters won't like that if blimps are the blind and penguins are the prey. That is probably why the wardens in Antarctia won't let ya hunt with a 9 pounder. :o) > But only if they are not part of the Earth's > mass, and only if they are dropped one at a time [quoted text clipped - 3 lines] > both will "attract" the Earth, and the relative > acceleration will not be seen. Well... the 9 pounder *will* hit the bird harder than a single lead shot so there might be some support that the bird and planet have some attraction to large artillery rounds and rush to greet it. The 25 significant digits would seem to be needed to express how far the planet's barycentre moves. You can make the argument for either the larger or the smaller object, depending on how you choose barycentres to use as reference points. Sue... > Joe Fischer >>>>Divergent Matter theory is obviously wrong, >> [quoted text clipped - 3 lines] >>So have you completely examined the aether and the space >>elevator? > What aether? Please talk about physics. What divergent matter? Aether is much more a part of physics than divergent matter is. At least some of the people championing aether theories understand some math. Stephen >>>So have you completely examined the aether and the space >>>elevator? [quoted text clipped - 3 lines] >What divergent matter? Aether is much more a part of physics >than divergent matter is. In a pigs eye (an old saying), and only to those unable to count successes and progress. > At least some of the >people championing aether theories understand some >math. >Stephen And that makes aether more real? Divergent matter is about real matter, not some imaginary magical non-material. [Fire] [Earth] [Water] [Aether] Get serious. Joe Fischer >>>>So have you completely examined the aether and the space >>>>elevator? [quoted text clipped - 3 lines] >>What divergent matter? Aether is much more a part of physics >>than divergent matter is. > In a pigs eye (an old saying), and only to those > unable to count successes and progress. >> At least some of the >>people championing aether theories understand some >>math. >>Stephen > And that makes aether more real? Divergent > matter is about real matter, not some imaginary > magical non-material. Real matter does not diverge. > > [Fire] [Earth] [Water] [Aether] > Get serious. I am serious. Real matter does not diverge. Gasses do not diverge. Boyle's law is quite simple and well understood. Stephen >> And that makes aether more real? Divergent >> matter is about real matter, not some imaginary >> magical non-material. > >Real matter does not diverge. Not according to the meter stick, even in the model Divergent Matter. But a model is what a model is, "spacetime" does not exist in nature, but it does describe. >> [Fire] [Earth] [Water] [Aether] > >> Get serious. > >I am serious. More pessimistic and sarcastic than serious. >Real matter does not diverge. Like you know real truth? > Gasses do not diverge. I have assumed they do, if you can recite a reference to anything that shows that a gas in free space will liquify, I will reconsider. If it will not liquify at any temperature, then it diverges. >Boyle's law is quite simple and well understood. >Stephen You can do better than copy Bill Hobba's invalidation statement. It should be easy to find out if you and Hobba are correct, I believe the toilet waste from some spacecraft was ejected into space, and was ice when ejected. If that ice boiled off and the vapor did disperse, that would seem to mean it diverged. Joe Fischer >>> And that makes aether more real? Divergent >>> matter is about real matter, not some imaginary >>> magical non-material. >> >>Real matter does not diverge. > Not according to the meter stick, even in the > model Divergent Matter. > But a model is what a model is, "spacetime" > does not exist in nature, but it does describe. So you are claiming that matter does not really diverge? > >>> [Fire] [Earth] [Water] [Aether] >> >>> Get serious. >> >>I am serious. > More pessimistic and sarcastic than serious. You are the one who is refusing to seriously think about your model, or to seriously think about Newton or any physics. >>Real matter does not diverge. > Like you know real truth? The universe we observe is not at all consistent with your model. >> Gasses do not diverge. > I have assumed they do, if you can recite > a reference to anything that shows that a gas in > free space will liquify, I will reconsider. Gasses do not accelerate, unless a force is applied to them. If you have two "balls" of gas, one twice the diameter of the other, it is true that they will expand as the gas molecules spread out, but they will not maintain that two to one ratio. The ratio will approach 1 as time goes on. So gasses do not "diverge" in the way your model requires. Go read about Boyle's law. There is lots of stuff on the web and it is not hard to understand. Stephen > >>>>So have you completely examined the aether and the space > >>>>elevator? [quoted text clipped - 23 lines] > > I am serious. Real matter does not diverge. now it makes sense go away you stoopid mothofaka > Gasses > do not diverge. Boyle's law is quite simple and > well understood. > > Stephen >Lets look at the simple problem of dropping two small >objects, one 2000 miles above the surface of the Earth, >and one 4000 miles above the surface of Earth. To simplify >the math a little, lets assume that the radius of the Earth >is 4000 miles and the acceleration at the surface is 10 m/sec/sec. Ok, if anybody wants to help with math concepts, assume there is no Newtonian attraction, and all matter expands with an acceleration. Using the numbers above, assume the surface of the Earth has an upward _velocity_ of UVE. After all, if it has been accelerating, it must have a velocity. The object that will be at 4000 miles up when the math starts will have an upward velocity UVE + OHV. The object that will be at 2000 miles up when the math starts will have an upward velocity UVE + OLV. OHV is considerably greater than OLV, so the distance between objects will increase (until the surface of Earth strikes the Lower Object. The lengthening of the meter stick and the second can be ignored and still get a feel for the dynamics. The dropped objects need not expand. Anybody like math? A computer program would be better. Joe Fischer Only a fool. >>Lets look at the simple problem of dropping two small >>objects, one 2000 miles above the surface of the Earth, >>and one 4000 miles above the surface of Earth. To simplify >>the math a little, lets assume that the radius of the Earth >>is 4000 miles and the acceleration at the surface is 10 m/sec/sec. > Ok, if anybody wants to help with math concepts, > assume there is no Newtonian attraction, and all matter > expands with an acceleration. > Using the numbers above, assume the surface > of the Earth has an upward _velocity_ of UVE. > After all, if it has been accelerating, it must > have a velocity. > The object that will be at 4000 miles up when > the math starts will have an upward velocity UVE + OHV. > The object that will be at 2000 miles up when > the math starts will have an upward velocity UVE + OLV. Do you think the Earth's gravity only affects objects that came from the Earth? There is no reason an object has to be lifted 4000 miles above the Earth's surface to be located 4000 miles above the Earth's surface. The affect of gravity does not depend on the history of an object. Imagine two meteors are heading towards Earth, and at some instance in time one is 2000 miles above the surface, and one is 4000 miles above the surface, and they both have the same velocity with respect to the Earth. According to Newton and Einstein the distance between the two meteors will increase. According to your model, it will decrease, although you seem incapable of understanding that. There is absolutely no reason to assume that two meteors will have any 'upward' velocity. The Earth is not the center of the universe, and requiring that all objects have a velocity away from the Earth in order to explain gravity just does not work. > OHV is considerably greater than OLV, so the > distance between objects will increase (until the > surface of Earth strikes the Lower Object. I see no reason why a higher object will have a higher velocity. You need to spell out exactly what you even mean by 'velocity', as clearly it is entirely possible for both objects to have zero velocity relative to the surface of the Earth. > The lengthening of the meter stick and the second > can be ignored and still get a feel for the dynamics. > The dropped objects need not expand. > Anybody like math? > A computer program would be better. > Joe Fischer Only a fool. I have explained the math to you. You choose to be a fool and ignore it. Stephen >Do you think the Earth's gravity only affects objects that came >from the Earth? No, do you think that because I study something dumb that I am stupid? > There is no reason an object has to be >lifted 4000 miles above the Earth's surface to be >located 4000 miles above the Earth's surface. You wanted to "drop" two objects, which means they must at the same instant be "stationary" at the point they are "dropped". What do you propose will make them lose all velocity relative to that point? >The >affect of gravity does not depend on the history of an object. No, but the path and speed does! >Imagine two meteors are heading towards Earth, and at >some instance in time one is 2000 miles above the surface, >and one is 4000 miles above the surface, and they both >have the same velocity with respect to the Earth. They will have a path and speed that does not match anything previously mentiioned. That does not fit your original 'invalidating" thought experiment. Is your desire to prove it isn't valid numbing your sense of logic? >According to Newton and Einstein the distance between >the two meteors will increase. If they both had the same path and speed and one preceeded the other, sure. > According to your model, >it will decrease, although you seem incapable of understanding >that. You are not trying to see the expansion as it has to be if it were to exist. The time required between the instant the math starts and the instant the surface strikes the first object will be much greater than the time till the surface strikes the second object. If circles are drawn representing an expanding Earth at equal time periods (current time), the distance between them increases as time passes. Isn't a square function expansion "hyperbolic"? >There is absolutely no reason to assume that two >meteors will have any 'upward' velocity. Right, although they could have missed the Earth and be moving away, but at an angle. You specified the dropping, and I described what is needed to accomplish it. If you want to use the two meteors, you will need rockets to change their path and speed to make them be "stationary" relative to the surface at any time. Which would take more energy than sending them up from the surface, and would require that they have an upward velocity relative to the center of an expanding Earth. > The Earth is not >the center of the universe, and requiring that all objects >have a velocity away from the Earth in order to explain >gravity just does not work. Change your specification any way you want, and I will try to describe what the model requires. This is not like some math models where you have all kinds of degrees of freedom. >> OHV is considerably greater than OLV, so the >> distance between objects will increase (until the >> surface of Earth strikes the Lower Object. > >I see no reason why a higher object will have >a higher velocity. The "velocity" is relative to the center of the Earth, I should have stated that, if it is the Earth's gravity we are talking about (Earth centric motion). The surface must have an outward/upward velocity if it has had an upward acceleration. Past history must be considered because this is dynamics, not a "fixed" Earth. >You need to spell out >exactly what you even mean by 'velocity', as >clearly it is entirely possible for both >objects to have zero velocity relative to >the surface of the Earth. Ok, have rockets take the two objects to the desired location and hold them there with zero velocity relative to the surface. Since the surface is accelerating upward and has been, the rockets need to continue to fire until you say "drop". It doesn't matter where they came from, they will have the same upward velocity when you say "drop" as they would the way I stated before. >> The lengthening of the meter stick and the second >> can be ignored and still get a feel for the dynamics. [quoted text clipped - 10 lines] >be a fool and ignore it. >Stephen You have recited Newtonian math, and this is not Newtonian gravitation. It can be Newtonian mechanics if all the expansions are considered. Anything that does not have an upward velocity (in the model) is in danger of colliding with the surface. Since there is a finite escape velocity for the Earth, and it is a constant for the Earth, the upward velocity of the surface could be the escape velocity. And the lengthening second would be what allows an object to escape, allowing more distance to be covered second. (In the model), there is no "attraction", so a different viewpoint/explanation is needed for almost everything. This is 4-D dynamics, and will require the mechanics to be different. Joe Fischer << There is no reason an object has to be lifted 4000 miles above the Earth's surface to be located 4000 miles above the Earth's surface. >> There certaintly is a reason. You don't get a charge pair separated by some distance without burning some fuel. http://laser.phys.ualberta.ca/~egerton/pair-p&a.htm << The bigger the mass of the particle, the bigger the energy needed to produce a particle-antiparticle pair. Electrons are the easiest particles to generate, and the energies go up from there. Quarks require more energy to create than electrons do, and different types of quarks require different amounts of energy, as they have different masses. >> http://www.steelypips.org/principles/2003_07_06_principlearchive.php http://www.mpe.mpg.de/~rod/tvuniv.htm The forces acting between massive bodies don't begin and end when your experiment begins and ends. Sue... >>I have explained the math to you. You choose to >>be a fool and ignore it. >>Stephen > You have recited Newtonian math, and this > is not Newtonian gravitation. I have to use "Newtonian" math to find out what Newton predicts, but I did not use "Newtonian" math to determine what your model predicts. I have shown that your model predicts things that are radically different than what Newton predicts. However Newton predicts what we see with amazing accuracy. > It can be Newtonian mechanics if all the > expansions are considered. You have yet to explain how. > Anything that does not have an upward > velocity (in the model) is in danger of colliding [quoted text clipped - 3 lines] > the upward velocity of the surface could be > the escape velocity. Escape velocity is impossible in your model, unless you assume a mechanics totally unlike anything we observe. The escape velocity at the Earth's surface is about 7 miles per second if we ignore air friction. An object moving upwards at that speed will never fall back to the Earth's surface again. The higher up you are, the lower the escape velocity is. According to your model, at the time an object is launched its 'real' velocity with respect to the center of the Earth will be the velocity of the Earth's surface plus the objects velocity relative to the Earth's surface. In other words V = V_s + V_o where V_s is the velocity of the Earth's surface, and V_o is the velocity of the object relative to the surface. Now if we assume Newtonian mechanics, which is what you are presumably doing, then the object will move at a constant speed, as there are no forces acting on it. This means that at time t its distance from the center will simply be Vt. If you are not assuming Newtonian mechanics than your model is meaningless until you precisely describe your mechanics. So at time t, the object will be at a distance Vt from the center of the Earth, and it will be moving at a constant velocity. The surface of the Earth however is accelerating outward. The velocity of the surface is always increasing, and it will eventually exceed V, not matter how big V_o originally was, and the surface of the Earth will catch up with the object. No matter how fast the object was originally moving it will fall back to Earth. According to you the radius of the Earth is R = R_o * 2^(t/C) where R_o and C are some constants that depend on what units we choose. This grows much faster than Vt. At some time t, R_o * 2^(t/C) > Vt, no matter how large V is. Escape velocity is impossible. In order for escape velocity to work in your model, objects would actually have to accelerate away from the Earth. You would have to some sort of anti-gravity force that acts at a distance that pushes objects away from the Earth. However the whole apparent point of your model is to do away with a force that acts at a distance > And the lengthening second would be > what allows an object to escape, allowing > more distance to be covered second. But that also allows the Earth's surface to cover more distance. > (In the model), there is no "attraction", > so a different viewpoint/explanation is needed > for almost everything. If you are to explain everything differently, it is really not much of an explanation. > This is 4-D dynamics, and will require > the mechanics to be different. Does Newton's first law hold or not? With respect to "real" time and "real" space, do objects move at a constant velocity when not being acted on by a force? Stephen >Now if we assume Newtonian mechanics, which is what >you are presumably doing, then the object will move >at a constant speed, Thanks for writing this, I do use a form of modified Newtonian mechanics, primarily because I can't do anything more. Not doing math forces me to devise methods to estimate or approximate problems, which I enjoy as much as a Martin Gardiner fan would enjoy doing math proofs. I will respond to this later tonight, but I would appreciate it if you or anyone else could look at http://en.wikipedia.org/wiki/Reduced_mass where I found [QUOTE] " Applying the gravitational formula we get that the position of the first body with respect to the second is governed by the same differential equation as the position of a very small body orbiting a body with a mass equal to the sum of the two masses, because . The reduced mass is always less than the mass of each body" [UNQUOTE] The formulas in the above were images so you would need to look at the link. As I read the above, it says the two body problem can be worked as a one body problem if the main body mass is the sum of the masses of both bodies, with a small body of insignificant mass orbiting it. I don't see how the last statement can be true if that is the case, the sum of both bodies is surely not less than the mass of either body. The reduced mass problem presentation is complicated by using a negative value for the acceleration of the second (main) body, which woul seem to cause a problem with my clumsy attempt to explain what I assume after reading The Attractive Universe by Valens. I need to find more on the work of Percy Robertson who is supposed to have applied reduced mass to General Relativity, print it all out and study it to find out if I need to change my impression. Joe Fischer >>Now if we assume Newtonian mechanics, which is what >>you are presumably doing, then the object will move >>at a constant speed, > Thanks for writing this, I do use a form of > modified Newtonian mechanics, primarily because > I can't do anything more. You need to describe what the rules of your mechanics are before doing anything else. However once you step outside of Newtonian mechanics, you have kind of lost any claim to providing a "mechanical" explanation for gravity. You will likely have to hypothesize behavior as strange or stranger than action at a distance. > Not doing math forces me to devise methods > to estimate or approximate problems, which I enjoy > as much as a Martin Gardiner fan would enjoy doing > math proofs. > I will respond to this later tonight, but I would > appreciate it if you or anyone else could look at > http://en.wikipedia.org/wiki/Reduced_mass > where I found > [QUOTE] > " Applying the gravitational formula we get that the position of the > first body with respect to the second is governed by the same > differential equation as the position of a very small body orbiting a > body with a mass equal to the sum of the two masses, because . > The reduced mass is always less than the mass of each body" > [UNQUOTE] > The formulas in the above were images so you > would need to look at the link. > As I read the above, it says the two body problem > can be worked as a one body problem if the main body [quoted text clipped - 3 lines] > if that is the case, the sum of both bodies is surely > not less than the mass of either body. The reduced mass is just a mathematical trick to simplify solving the two body problem. It also is a simple trick to solve how one object orbits relative to another, as opposed to relative to the center of mass. In a two body problem the two objects are both accelerating towards each other. The second derivative of the distance between the objects with respect to time is equal to G*(m1+m2)/r^2 This is because the first object accelerates towards the second at a rate of G*m2/r^2 and the second object accelerates towards the first at a rate of G*m1/r^2. In the reduced mass problem we use the same force, F=G*m1*m2/r^2 but we assume one object does not move, and we use the reduced mass m1*m2/(m1+m2) to determine the acceleration of the second object relative to the unmoving first object. So we apply F=m*a and get G*m1*m2/r^2 = (m1*m2)/(m1+m2) * a so a = G*(m1+m2)/r^2 which is exactly the same as we got before. Note this is just a mathematical trick. Noone is claiming that the sum of the two bodies is less than the mass of either body. Another way to think about this in the two body problem we choose the center of mass as the origin, and both bodies orbit around the origin. In the reduced mass problem we choose the location of one of the objects as the origin, and the other object orbits around the origin. In both problems the relative positions of the two objects are identical. > The reduced mass problem presentation is > complicated by using a negative value for the > acceleration of the second (main) body, which > woul seem to cause a problem with my clumsy > attempt to explain what I assume after reading > The Attractive Universe by Valens. The reason they use a negative value is because the acceleration is in the opposite direction of the position vector. The acceleration is towards the center. The positions are away from the center. Stephen >> Thanks for writing this, I do use a form of >> modified Newtonian mechanics, primarily because >> I can't do anything more. > >You need to describe what the rules of your mechanics >are before doing anything else. It is difficult to present because it is very different. > However once you >step outside of Newtonian mechanics, you have kind >of lost any claim to providing a "mechanical" >explanation for gravity. The mechanics is simply the dynamics with the effect of expansion on measurements and the effect of those effects on definitions of motion. > You will likely have >to hypothesize behavior as strange or stranger >than action at a distance. It is to avoid action at a distance, but the primary objective is to describe the effects of gravity based on a literal interpretation of what I interpret as Einstein's Principle of Equivalence. I feel the idea of relativity of size by itself is very strange because it hasn't been studied much and since it hasn't been studied much it will be considered to be stranger than any mechanics developed so far. Joe Fischer >>> Thanks for writing this, I do use a form of >>> modified Newtonian mechanics, primarily because >>> I can't do anything more. >> >>You need to describe what the rules of your mechanics >>are before doing anything else. > It is difficult to present because it is very different. Start with Newton's three laws, and explain what the corresponding laws in your dynamics are. >> However once you >>step outside of Newtonian mechanics, you have kind >>of lost any claim to providing a "mechanical" >>explanation for gravity. > The mechanics is simply the dynamics with > the effect of expansion on measurements and > the effect of those effects on definitions of > motion. That does not really mean anything, I'm afraid. Do objects require forces in order to accelerate? Do Newton's laws hold? >> You will likely have >>to hypothesize behavior as strange or stranger >>than action at a distance. > It is to avoid action at a distance, but the > primary objective is to describe the effects of > gravity based on a literal interpretation of what > I interpret as Einstein's Principle of Equivalence. In order to explain escape velocity, it seems necessary in your model that objects accelerate away from the Earth, or any massive object, even when there is no observable force present. Likewise in order for the moon to orbit the Earth, it must also be accelerating away from the Earth, despite the absence of an observable force. Your mechanics has to explain this. I doubt however that any sort of intuitive mechanics can explain it. You might also want to think about the mechanism that presumably causes matter to expand. And no, it is cannot be anything like the expansion of gasses. > I feel the idea of relativity of size by itself > is very strange because it hasn't been studied > much and since it hasn't been studied much > it will be considered to be stranger than any > mechanics developed so far. Why not just study GR then? If your model requires us to abandon any sort of intuitive mechanics in order to explain gravity than it really has no advantage over GR. Stephen >>>> Thanks for writing this, I do use a form of >>>> modified Newtonian mechanics, primarily because [quoted text clipped - 7 lines] >Start with Newton's three laws, and explain what >the corresponding laws in your dynamics are. Thanks for the advice. The problem, or rather the advantage, is that the Divergent Matter model exists as a result of the postulate that matter is expanding. I haven't tried to define any laws. I suppose Newton's laws apply with whatever needs to be done to make motion subject to the expansion and the lengthening units. >>> However once you >>>step outside of Newtonian mechanics, you have kind [quoted text clipped - 7 lines] > >That does not really mean anything, I'm afraid. Possibly not. >Do objects require forces in order to accelerate? Of course, but there is no acceleration in freefall or orbital motion or any inertial motion. >Do Newton's laws hold? As modified, think so. >>> You will likely have >>>to hypothesize behavior as strange or stranger [quoted text clipped - 9 lines] >away from the Earth, or any massive object, even when there is >no observable force present. "Appear to accelerate"! Once an object is in free motion there is no acceleration reading on an accelerometer on the object. If the length of the second increases, an object in motion can travel farther (in starting math units), so they appear to accelerate. Obviously if the model says there is no attractive gravitational field and no gradient field, then something has to repace the apparent reduction in relative velocity when an object leaves the Earth. > Likewise in order for the moon to >orbit the Earth, it must also be accelerating away >from the Earth, despite the absence of an observable >force. Right, but at the same time be in inertial motion, not to correspond with concepts in GR, but just because of the path vector and lengthening units. >Your mechanics has to explain this. It is difficult because of the entrenched concept of Euclidean space. > I doubt >however that any sort of intuitive mechanics can >explain it. I need to do some drawing, I can probably do it better with vector graphics than raster, so I will try this week. >You might also want to think about the mechanism >that presumably causes matter to expand. It would just be the lack of something that is in current atomic and molecular theory. Maybe not a total lack, just not as much attraction to hold things together. Anything that is proportional to mass might be a suspect at the quantum or atomic level. If this is the case and the "gravitational force" can be eliminated in the model, it is a reduction in complexity in physics. >And no, >it is cannot be anything like the expansion of gasses. Expandion has to be expansion due to repulsion, which is why molecules bounce, rebound, and diverge, in any way that they do. I still don't know if a gas can condense to liquid in free space, and that is of considerablr interest, even though it may not be relevant to the model/ >> I feel the idea of relativity of size by itself >> is very strange because it hasn't been studied [quoted text clipped - 3 lines] > >Why not just study GR then? I was 7 or 8 years into this before I ever heard of GR. Yes, I think I heard of Einstein during the 1930's and then read about him and the letter he wrote to FDR a couple of days after Hiroshima. But I didn' t know anything about GR and it being a gravity theory until the two books by Einstein were taken out of the vaults and put back on the shelf. > If your model requires >us to abandon any sort of intuitive mechanics in >order to explain gravity than it really has no >advantage over GR. >Stephen It never will have an advantage over GR unless there is some simplified math that will make it useful. But it will have some value in having an alternate model to use when designing experiments. I think (although I may be mistaken) that it has given me some insight to space physics. I was on the phone several times to contractor physicists when the astronauts tried to first tried to capture a satellite for repair or return to Earth. I had to do some considerable arguing to convince them that one man with a thruster back pack could not stop the rotation of a rotating satellite, it requires at least two. Luckily, they had a backup plan, that satellite had just enough orientation capability to reduce rotation to zero without hands on. Then on the following missions they used two or three people in the payload bay. The most important thing in any physical model is to have freefall and orbits be inertial motion, and not to have action at a distance. In expanding matter, the enabling mechanism has to be at the quantum or atomic level, and all else is dynamics. That would seem to make expanding matter a quantum theory, proportional to number of atoms, atomic mass, binding energy, and heat energy. I suppose binding energy could be positive or negative signed, but this model seems to involve too many different specialties for a hick mechanic to study. Joe Fischer >> I will respond to this later tonight, but I would >> appreciate it if you or anyone else could look at [quoted text clipped - 28 lines] >orbits relative to another, as opposed to >relative to the center of mass. My problem was with the last statement in the link above, and until somebody says otherwise, I assume that the reduced mass equation gives the same answer as Valens with the a + A formula. >In a two body problem the two objects are both accelerating >towards each other. The second derivative of the [quoted text clipped - 3 lines] >second at a rate of G*m2/r^2 and the second object accelerates >towards the first at a rate of G*m1/r^2. I think that is what I was saying, but it seems the only case I have found where the a + A formula was used as applied to a falling object rather than orbiting objects was in Valens "Attractive Universe". This makes sense because nobody has ever had any reason to drop a moon size object before. >In the reduced mass problem we use the same force, > F=G*m1*m2/r^2 [quoted text clipped - 9 lines] > a = G*(m1+m2)/r^2 >which is exactly the same as we got before. Which is the same as Valens said, I think, except he wrote it for the case where the two objects were falling toward the center of mass of the system rather than orbiting. I did find one thing I wanted, the criteria for saying a system is a planet with a moon vs a double planet is if the center of mass of the system is within the surface of the larger body or outside it. This is almost the case for the Earth, but not quite. >Note this is just a mathematical trick. Noone >is claiming that the sum of the two bodies is >less than the mass of either body. I thought that one web site did, >Another way to think about this in the two body >problem we choose the center of mass as the origin, [quoted text clipped - 4 lines] >In both problems the relative positions of the >two objects are identical. Which is especially acceptable because the observers are usually on the origin body >> The reduced mass problem presentation is >> complicated by using a negative value for the [quoted text clipped - 9 lines] >from the center. >Stephen Which seems to me what Valens was saying, except it was worded differently. When solving for the "falling", the sum of the accelerations should be used. The negative sign confuses things even though the accelerations are in different directions, The accelerations are toward the center of mass of the system, and are also toward each other, so they need to be summed to represent the total acceleration toward each other. Which seems to be the same as the reduced mass method as long if expressed as the sum of the accelerations toward each other. Which seems to mean that heavier objects fall faster. Hopefully there won't be a moon size object fall. But even on small objects, the same math applies, and the acceleration of only the origin object is used. And without 25 digit precision, it is impossible to measure the difference between saying "all bodies fall the same", and "heavier bodies fall faster". Which is what I was saying, and several people disagreed and even abused me for saying what I said. :-) Joe Fischer >>> As I read the above, it says the two body problem >>> can be worked as a one body problem if the main body [quoted text clipped - 9 lines] >>orbits relative to another, as opposed to >>relative to the center of mass. > My problem was with the last statement in > the link above, and until somebody says otherwise, > I assume that the reduced mass equation gives > the same answer as Valens with the a + A formula. >>In a two body problem the two objects are both accelerating >>towards each other. The second derivative of the [quoted text clipped - 3 lines] >>second at a rate of G*m2/r^2 and the second object accelerates >>towards the first at a rate of G*m1/r^2. > I think that is what I was saying, but it seems > the only case I have found where the a + A formula > was used as applied to a falling object rather than > orbiting objects was in Valens "Attractive Universe". > This makes sense because nobody has ever > had any reason to drop a moon size object before. There really is no difference between falling and orbiting. This was one of Newton's great insights. The math that describes falling and orbiting is the same. >>In the reduced mass problem we use the same force, >> F=G*m1*m2/r^2 [quoted text clipped - 9 lines] >> a = G*(m1+m2)/r^2 >>which is exactly the same as we got before. > Which is the same as Valens said, I think, > except he wrote it for the case where the two > objects were falling toward the center of mass > of the system rather than orbiting. There is no difference between falling and orbiting. The math I used above would work equally well in both cases. Actually as written it is more appropriate for 'falling', because I ignored the direction component necessary to handle the general case. Stephen > >> I will respond to this later tonight, but I would > >> appreciate it if you or anyone else could look at [quoted text clipped - 67 lines] > objects were falling toward the center of mass > of the system rather than orbiting. Orbiting IS falling toward a center of mass. It just also includes a component of motion transverse to that inward direction. > I did find one thing I wanted, the criteria > for saying a system is a planet with a moon vs [quoted text clipped - 4 lines] > This is almost the case for the Earth, > but not quite. The center of mass of the Earth-moon system is within the surface of the Earth. It qualifies. > >Note this is just a mathematical trick. Noone > >is claiming that the sum of the two bodies is [quoted text clipped - 13 lines] > Which is especially acceptable because > the observers are usually on the origin body That's irrelevant. You can apply exactly the same analysis to the Sun-Earth system, where the observers are on the smaller body. > >> The reduced mass problem presentation is > >> complicated by using a negative value for the [quoted text clipped - 28 lines] > fall faster. Hopefully there won't be a moon > size object fall. I don't know why you say that heavy objects fall faster. Let's take the Earth acting on light object with mass m and Earth acting on heavy object with mass M. Call the mass of the Earth ME. Force acting on light object is F = G(ME)m/r^2 Force acting on heavy object is F = G(ME)M/r^2 The acceleration of the Earth will be whatever it will be, lets call it AE, toward the center of mass. The acceleration of the light object is F/m = G(ME)/r^2 toward the center of mass. The acceleration of the heavey object is F/M = G(ME)/r^2 toward the center of mass. The relative acceleration of the light object and Earth is AE + G(ME)/r^2. The relative acceleration of the heavy object and Earth is AE + G(ME)/r^2. These look the same to me. > But even on small objects, the same math > applies, and the acceleration of only the origin [quoted text clipped - 8 lines] > > Joe Fischer >> Which seems to mean that heavier objects >> fall faster. Hopefully there won't be a moon >> size object fall. > >I don't know why you say that heavy objects fall faster. Because Newtonian gravitation math says they do, and because it is obvious that two objects having the same mass accelerate toward each other with greater acceleration than one of them an a small mass, and because the Divergent Matter model requires it. There may be other reasons. >Let's take the Earth acting on light object with mass m >and Earth acting on heavy object with mass M. Call the mass of the >Earth ME. > >Force acting on light object is F = G(ME)m/r^2 >Force acting on heavy object is F = G(ME)M/r^2 Right, two forces acting in opposite directions, but I did not say anything about force (except for brain/finger slips), it is acceleration that is relevant, in the Divergent Matter model there is no force acting on objects in freefall or orbit. >The acceleration of the Earth will be whatever it will be, lets call it >AE, toward the center of mass. If this means the Earth accelerates a very small amount, that is what I was saying. >The acceleration of the light object is F/m = G(ME)/r^2 toward the >center of mass. Does F / m mean a for acceleration? Force(on small mass) / small mass = acceleration? >The acceleration of the heavy object is F/M = G(ME)/r^2 toward the >center of mass. Force on Earth / Mass(Earth) = acceleration? >The relative acceleration of the light object and Earth is AE + >G(ME)/r^2. >The relative acceleration of the heavy object and Earth is AE + >G(ME)/r^2. In opposite directions, right? So that means the two accelerations should be added together to represent how fast they accelerate towards each other? >These look the same to me. Yes, the force is on both, that force is the same, that is Newtonian gravitation, it complies with Newton's third law, it is two forces for the price of one, same force acting on both bodies, the small body accelerates at 981 cm/sec/sec, the Earth accelerates a minuscule amount, the two accelerations need to be added together, the reduced mass discussions use a negative sign to show that the accelerations are in opposite directions, and the ultimate outcome is that heavier bodies fall faster. >> But even on small objects, the same math >> applies, and the acceleration of only the origin [quoted text clipped - 6 lines] >> people disagreed and even abused me for saying >> what I said. :-) That negative sign and other statements in the reduced mass discussions threw me for a loop, but adversity makes the learning process better and longer lasting, thanks all. I don't expect to ever see an experiment that shows that heavier things fall faster, but Newtonian gravitation says they do in my view, and the Divergent Matter model requires the same thing, but for different reasons. In my opinion, Dicke knew all this when he did the Eotvos experiments that raised the precision from 11 or 12 digits to 15 digits, and even at that precision, actual measurement of any parameters was difficult or impossible to that precision, the torsion balance works by resonance of many cycles, and I think Dicke used the sun and a 24 hour cycle to look for any change in motion. It was stated that t |
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