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Newton realized that, according to his theory of gravity the stars should attract each other, so it seemed they could not remain essentially motionless. Would they not all fall together at some point? In a letter in 1691 to Richard Bentley, another leading thinker of his day, Newton argued that this would indeed happen if there were only a finite number of stars, distributed over a finite region of space. But he reasoned that if, on the other hand, there were an infinite number of stars, distributed more or less uniformly over infinite space, this would not happen, because there would not be any central point for them to fall to.

Newton realized that according to his theory of gravity the stars should attract each other, so it seemed they could not remain essentially motionless. Would they not all fall together at some point?

Can you please explain this statement?

jng224
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Manny
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I understand it like that: If there was a finite number of stars evenly distributed in, let's say a spherical region of the universe. Then if we consider the stars on the "surface" of this sphere, there are no gravitational forces pulling them away from the center of the sphere. However, since there are many stars closer to the center of the sphere, the stars on the surface "feel" a net force pulling them towards the center. We can extend this logic for all the other stars and arrive at the conclusion that all stars will be pulled towards the center of mass of our sphere.

If there are however infinite stars in an infinite region of space, then there will always be other stars in every direction. Thus there will be no pull towards one single point since the gravitational forces on every star approximately cancel. The stars therefore won't collapse into one point.

jng224
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    Is your last paragraph just meant to describe what Newton's logic was, without suggesting that it was either right or wrong? It might be worth mentioning that Newton's logic and conclusion were both wrong, even within the context of his own $1/r^2$ theory of gravity, as explained here and here. – Chiral Anomaly Nov 15 '21 at 03:39
  • There are cosmological models that would allow for one spherical distribution of matter to pull stars gravitationally outward from a smaller spherical distribution of matter within it: An example is Nikodem Poplawski's "Cosmology with torsion", whose multiverse is described in 2010-2021 preprints freely visible on Cornell University's Arxiv website. – Edouard Nov 26 '21 at 16:24
  • Some recent observational effects tending to support such models (in a multiple collision of black holes construed to have resulted in a "Russian dolls" or "kitty-in-a-keg" assemblage of them), were reported in recent years, I believe by an observatory in Australia. – Edouard Nov 26 '21 at 16:44
  • At https://www.facebook.com/AustralianAcademyofScience/videos/2742756582607039/ , there's a brief description of the multiple BH collision: It was detected by gravitational-wave observation, although the AAS may have construed the subsequent arrangement of them hypothetically. – Edouard Nov 26 '21 at 16:51
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    A small moon may feel only a net force pulling it to a planet, yet it may never fall since it has tangential velocity, it will just orbit around. Couldn't this also happen to the stars on the surface of this 'sphere'? – Juan Perez Nov 26 '21 at 18:05
  • To clarify my own comments on Jonas' answer, I should add that the "local universes", in Poplawski's version of an inflationary multiverse, are each described by him as having the shape of "the skin of a basketball". (A "sphere", in postings on PSE, has occasionally been misconstrued as including the volume enclosed between opposite halves of its closed surface, but, in physics, the volume enclosed within the opposite halves of that surface is called a "ball".) – Edouard Nov 27 '21 at 02:58
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Newton thought that if the number of stars was finite they would all fall towards the centre of mass and all end up together there.

As that hasn't happened he argued that there could be an infinite number of stars.

John Hunter
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    @FluidCode it was an explanation of the printed section - there is another way the collapse can be avoided and that's that the universe is expanding, according to the print Newton was acknowledging the infinite universe possibility – John Hunter Nov 14 '21 at 15:55
  • but as an escamotage to avoid collapsing. I think Newton recognise that even in an infinite static universe there would have been infinite centres to collapse into. I believe I have read about a discussion he had with another scientist about the issue. (ref: the comment, not the answer). – Alchimista Nov 14 '21 at 16:46
  • This answer's correct as far as it goes, so I'm hoping it moves ahead of one of the others, but it doesn't answer the question about collapse that I've included in my request for clarification of the OP's overall question, which remains ambiguous at the moment. – Edouard Nov 26 '21 at 16:33
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The best description of Newton's conundrum, and its modern resolution, may be found on pages 295-297 in the 1997 Basic Books ed. of Guth's book titled "The Inflationary Universe", which uses simple algebra and one diagram to illustrate that resolution.

Newton's thinking (accurately described in John Hunter's answer) contained one flaw: He failed to consider the possibility that the collapse of even an infinite universe might occur "everywhere at once", in a reversal of the content in the phrase (much-used in modern classrooms) about our universe's "Big Bang happening everywhere at once". To use Guth's exact terminology about an observer in Newtonian space, "No matter where the observer might be in the infinite space, he would see all the rest of the matter in the universe converging towards him".

Of course, what we see through our telescopes is, happily, the physical reverse of that possibility: The observable region of our universe is expanding, away from us and away from everything else in it. That's usually presumed to be the case outside our observable region, under the assumption that the universe (whether it's a single universe, or a "local universe", causally-separated from other LU's basically similar to it, in an inflationary multiverse) is isotropic and homogeneous.

There are some more local exceptions, concerning astronomical bodies large enough for their gravitational attraction to overcome the expansion (whose main origin is most commonly supposed to be "Dark Energy"): For instance, when people refer to the fact that the Milky Way Galaxy will eventually collide with the Andromeda Galaxy, they're referring to one of those exceptions. More extremely "local" exceptions occur at microscopic scales: Dark energy has not been observed to tear molecules apart.

Edouard
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  • In fact, except for the indirect observation that it might account for the actual redshift of light from astronomical objects receding from each other, Dark Energy has not been observed at all, for reasons perhaps bearing on the nature of time, whose conjugate in the Heisenberg Uncertainty Principle is energy. – Edouard Nov 26 '21 at 01:09
  • Expansion and collapse are, unfortunately, often misconstrued as constrained to a rate no more rapid than the speed of light: As has repeatedly been stressed, both on this site and in the 1916 edition of General Relativity, the expansion of an object (in this case, space) is entirely different from the motion of any object relative to that of any other object, and has no such constraint. – Edouard Nov 26 '21 at 04:48
  • I'm sorry if I seem to be splitting hairs, but, in physics, gravity is not considered to be energy. It's occasionally described as "negative energy", because its effects can reverse effects of energy. However, that usage can interfere with understanding of some of the "singularity theorems" that were written by Hawking and Penrose. "Gravity" CAN be understood as a form of "acceleration". – Edouard Nov 26 '21 at 15:50