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Einstein introduced the cosmological constant because without it, one cannot get a static universe - gravity would cause the universe to contract.

Given that, why is the Milky Way not contracting? For that matter, why isn't the Solar System contracting? It can't be because of dark energy, because dark energy's effect shouldn't manifest within over such short distances.

I'm guessing that the answer has something to do with rotation - after all both the Solar System & the Milky Way are rotating. However, the obvious "to conserve angular momentum" answer doesn't seem applicable, since the Milky Way (Solar System) could both collapse and conserve angular momentum as long as there is a very fast-rotating central black hole (Sun).

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    $\begingroup$ Related: Why doesn't the Moon fall onto the Earth? $\endgroup$
    – Qmechanic
    Commented Jun 28, 2021 at 4:15
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    $\begingroup$ Not duplicate - this question asks about structure formation, cosmology, dark energy, GR. $\endgroup$
    – Allure
    Commented Jun 28, 2021 at 4:35
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    $\begingroup$ @Allure Note that your question asks about GR, dark energy, etc but your question can be answered in the context of Newtonian gravity, and it doesn’t appreciably change when you move to GR. $\endgroup$
    – J. Murray
    Commented Jun 28, 2021 at 11:39
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    $\begingroup$ For the same reason that you can swing a ball tied to a piece of string over your head in circles and it stays up as long as your arm is swinging it. It has nothing to do with dark matter, dark energy, magic or God pushing them around. $\endgroup$ Commented Jun 28, 2021 at 15:19
  • $\begingroup$ Note: Gravity(acceleration) + transverse_momentum = Orbits $\endgroup$ Commented Jun 28, 2021 at 16:29

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Both energy and angular momentum must be conserved.

In the case of the Milky Way (and the Solar System), a more compact configuration would have a numerically smaller gravitational potential energy.

This means that get to the more compact configuration would require the system to lose energy. The question then, is how can that energy be lost and on what timescale?

In neither the cases of the Milky Way, where stars orbit in a collisionless fashion through a very sparse interstellar medium, or the Solar System, where planets orbit without direct interaction, is there an energy loss mechanism that is rapid enough to bring about significant contraction on interesting timescales.

In terms of cosmology - the idea of introducing a cosmological constant to get a static universe applies on cosmological scales when the matter is assumed to be isotropic and homogeneous and it only considers gravitational interactions. The applicability of some sort of scaled expansion or contraction of the universe on scales smaller than gravitationally bound structures is questionable and you can find several duplicates of that on Physics SE. However, we do know that energy within a closed system like the Solar System or the Milky Way must be conserved, so any contraction must be "paid for" by shedding that energy somewhere.

As a final point, both energy and angular momentum must be conserved. In Newtonian physics and GR, the components of the Milky Way and Solar System cannot move into more compact configurations without losing angular momentum as well as energy. Even the hypothesis that the Solar System could ultimately turn into a fast-spinning black hole requires both energy and angular momentum to be lost. The angular momentum of the Sun is about $J = 2\times 10^{41}$ kg m$^2$ s$^{-1}$. A maximally spinning black hole has $J = GM^2/c$, which is $ 8\times 10^{41}$ kg m$^2$ s$^{-1}$ for the mass of the Sun. Thus, whilst the Sun could collapse to a black hole whilst conserving angular momentum, it could not take the rest of the Solar System with it, because there is about 4 orders of magnitude more angular momentum in the Solar System as a whole, with very little additional mass.

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  • $\begingroup$ Hmm, if collapse is difficult to achieve in the first place, how did the Sun (and the planets) form? How did they lose energy? $\endgroup$
    – Allure
    Commented Jun 28, 2021 at 10:55
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    $\begingroup$ @Allure in the initial collapse the energy is dissipated through interactions in the gas and dust. i.e. Infrared radiation (predominantly) from the gas and dust carries away the energy. The loss of angular momentum is a more difficult problem. There are quite a few ideas including winds, viscosity, jets and various magnetic interactions, but the difficult in losing ang. momentum is why collapse to a disk occurs - the minimum energy configuration for a given angular momentum. $\endgroup$
    – ProfRob
    Commented Jun 28, 2021 at 11:25
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    $\begingroup$ Most of the solar system has already collapsed, we call this "sun". $\endgroup$
    – user132647
    Commented Jun 28, 2021 at 14:53
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    $\begingroup$ @user132647 The Sun contains a very small fraction of the mass of the "protosolar nebula" it also contains a lot less than 1% of the angular momentum of the Solar System even as it exists today. But yes, most of the mass in the Solar System we see today has already "collapsed" to close to a minimum-energy configuration and the mechanisms don't exist to complete the task on a short timescale. As Fraxinus points out, the Sun will, in around 7-8 billion years collapse to a white dwarf. $\endgroup$
    – ProfRob
    Commented Jun 28, 2021 at 15:00
  • $\begingroup$ Sun can itself collapse down to the Earth size, it will be an impressive feat (if looked at from a distance). $\endgroup$
    – fraxinus
    Commented Jun 28, 2021 at 15:00
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If all the planets in our solar system, and all the stars in the Milky Way, were to all contract into a smaller volume, we would have a huge loss of energy and angular momentum. These are conserved quantities, and so what you suggest would contradict the laws of conservation of energy and angular momentum.

First, you are correct in that planets continue to orbit the sun to conserve angular momentum. It is thought that the solar system began with a cloud of essentially gas and dust that over time condensed to form the planets and our sun. As this cloud began to collapse inward, all this matter began to settle into a spinning disc with a big lump in the center: the Sun. Further collapsing caused the formation of the planets. This process is called accretion. The point is, there was angular momentum present back then, and so there still is (conserved) now, meaning that the planets must maintain their stable orbits (and the sun keeps its own rotational angular momentum, as do all the planets as well).

The formation and motion of the Milky Way also relies on conservation of angular momentum (and energy and linear momentum), for objects in motion within it, though their formation is more complicated, and this time we have many stars (and perhaps planets revolving around them) revolving around the center of a black hole. Universal expansion probably has a little to do with the galaxy itself expanding from its center, though relative to the general expansion of the universe (that causes galaxies to move away from each other), the Milky Way is moving at $\approx 600 km/s$.

Whether dark energy is a significant contributing factor is unknown (I am not aware of any experiments or data that suggest dark energy causes some of the stability - or even expansion - of our galaxy or solar system), though its behavior on cosmological scales is more obvious (if it truly exists).

since the Milky Way (Solar System) could still collapse as long as there is a very fast-rotating central black hole (Sun).

A black hole is destructive only when bodies are close to the event horizon. A black hole from a great distance away is just like any other object that has the same mass. It will not crush things into it from such distances. Its gravitational force behaves the same as anything else with similar mass. If the sun was suddenly turned into a black hole, apart from darkness, nothing else would happen, and the Earth and all planets would continue to orbit it in exactly the same way as before this happens. The same logic would also apply to our galaxy with a black hole in the center of it. Black holes are destructive (in the sense of crushing things into them) only in regions close too, or at the event horizon.

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    $\begingroup$ About the last paragraph: I actually meant that it's possible to still conserve angular momentum by concentrating all the mass in the central black hole (or Sun) and having that object rotate very quickly. $\endgroup$
    – Allure
    Commented Jun 28, 2021 at 5:01
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    $\begingroup$ Yes, I noticed your edit, though the point remains that even though a black hole can "suck" massive objects into it, this will only happen if an object (planet, star etc.) came close to the event horizon. Because the objects circling the black hole/sun have constant angular momentum and average distance, they must maintain their orbital positions, and so whether the mass is a star or black hole, it wont make a difference, Cheers. $\endgroup$
    – joseph h
    Commented Jun 28, 2021 at 5:15
  • $\begingroup$ It is not necessary that a body moves in the direction of net acceleration (thus net force). Suppose a planet has a tangential component of velocity right from its formation then the acceleration due to gravitational pull changes the velocity vector which in turn decides where the body would be at the next instant. $\endgroup$ Commented Jun 28, 2021 at 5:35
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    $\begingroup$ I don't think OP suggested that the black hole should destruct the solar system. I think the OP tried to say that conservation of angular momentum does not prevent a collapse, because it could collapse into a black hole that has angular momentum. $\endgroup$
    – user132647
    Commented Jun 28, 2021 at 14:49
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One can think of a galaxy as an oversized accretion disk of its central black hole.

Eventually, in quite distant future, inner part of the galaxy matter will be accreted, outer part of it will carry away the extra angular momentum. Possibly, some of the matter will be thrown away by the polar jets. The extra energy will be radiated away as heat.

On the other hand, the timescale of this process is way longer than the presently accepted universe age.

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