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Given the distance among stars (the most massive objective in the space) is so huge, the difference of order of magnitude is about 7. And also, since gravity is such a weak force, how is it likely for gravity to shape galaxy the way it is? Would it make more sense to say galaxy is collapsing?

I would like to know if my reasoning is improper, where goes wrong,

and how to test my reasoning or your reasoning with experiment?

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Actually, most research suggests that interactions of two galaxies (i.e., "mergers" or collisions) is what determines the shapes of galaxies, and not necessarily gravity alone. This Astronomy Now article from a few years ago goes a bit more into the details.

It is true that there is a strong force pulling us inwards (on the order of a billion Newtons), so you indeed could say that a galaxy is collapsing, but it would take something like $10^{100}$ years before the stars would fall into the supermassive black hole in the center. On that time-scale, it really isn't a statement worth making, IMO.

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    $\begingroup$ Ha, I like the emphasis on years beside $10^{100}$... makes it sound like the units are crucial, but $10^{91}$ Gyr, or $10^{107}$s... doesn't make much difference :) $\endgroup$
    – Kyle Oman
    Jan 15, 2014 at 21:55
  • $\begingroup$ @Kyle: I wish the $10^{100}$ part could be italicized too so that the emphasis is on the huge number part and not the unit part. $\endgroup$
    – Kyle Kanos
    Jan 16, 2014 at 1:24
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Gravity is indeed a relatively weak force, but it has two things going for it when it comes to creating galaxies. Firstly gravity is always attractive and additive, so the total attractive force scales up with the amount of matter. Secondly for a ball of stuff of radius $r$ the factor $M/r^2$ goes up linearly with $r$ i.e. make the ball big enough and it will always collapse.

Would it make more sense to say galaxy is collapsing

The angular momentum of the galaxy is conserved, so the galaxy can't just collapse into a point (or black hole). For this reason I don't think it's appropriate to say a galaxy is collapsing. At some point the angular velocity will increase enough to balance the gravitational attraction and the galaxy will stabilise. In principle galaxies can shed angular momentum by ejecting stars, but this is very slow on timescales like the lifetime of the universe.

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