Can you explain this line from "A brief history of time"?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.