If gravity clumps matter together into galaxies, why are there separate galaxies? Wouldn't all matter in the universe be in one clump?
Angular Momentum of the system checks the gravitational collapse beyond a point.
When a system collapses gravitationally, it starts spinning faster because of Angular Momentum conservation. Further collapse is arrested when it gains enough angular speed that its centripetal force is exactly equal to the gravitational force. This is the same reason why planets do not fall into the sun and why galaxies in a galaxy cluster do not collapse further. Gravitational force is a central force that pulls things radially inward, but objects generally have non-zero tangential components that contribute to their Angular Momentum.
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Gravity not only pulls matter together into galaxies but also acts on a larger scale to create voids and filaments in the universe due to the uneven distribution of matter and the expansion of space. Additionally, the initial conditions of the universe, such as density fluctuations from the Big Bang, play a significant role in the formation of separate galaxies rather than one massive clump of matter.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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