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As all of you know, in the Milky Way galaxy, the Solar System revolves around the Milky Way to complete the Galactic year (because we have the supper massive black hole in our Milky Way galaxy) then the Earth revolves around the Sun, and the Moon revolves around the Earth. This is due to Einstein's theory which suggests that anything with mass in the universe will bend the spacetime fabric and due to its gravitational pull, another object will attract and they will revolve around that object because that object bent the spacetime fabric.

I read somewhere about the collision of Andromeda and the Milky Way galaxy in some billions of years. According to my knowledge if objects in galaxies will have some mass then the galaxies will have some cumulative mass.

So my question is simple: according to Einstein anything in the universe with mass will bend the spacetime fabric. Will the Milky Way revolve around the Andromeda galaxy or vice versa?

So if they will collide then why won't they revolve?

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The statement that one thing revolves around another isn't true in a 2-body system. Both objects orbit their common centre of mass. When one object is much more massive than the other, then the centre of mass is almost coincident with the centre of the most massive object.

What decides whether orbiting objects will orbit or collide? In Newtonian and "Einsteinian" gravity (General Relativity really isn't required to describe the dynamics of any of the scenarios in your question), the properties of orbits are defined by the total energy of the system ($E$) and the total angular momentum ($L$).

If $L$ is large then there is a potential barrier that prevents the two objects getting close together - you can think of that as a centrifugal force if you like, that counteracts the mutual gravitational contraction.

To get two objects to collide requires either a low value of $L$ to begin with or some additional means of removing angular momentum from the system, since both $E$ and $L$ are conserved quantities in an orbit.

In the case of the Milky Way and Andromeda, the $E$ and $L$ values of the system indicate that they will pass close to each other in about 5 billion years time. There is still some uncertainty about how close, but it is likely that their discs will overlap. It is this overlapping that gives the system a chance to lose both energy and angular momentum because the gas in their discs will collide, be compressed and heated. This exerts a torque and dissipation of energy. As a result it is likely that the system will lose enough energy and angular momentum to merge about 5 billion years after the initial glancing collision.

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    $\begingroup$ You're ignoring the effects of dark matter and dynamical friction, which on galactic scales are much more important ways of reducing $E$ and $L$ than gas-disk collisions. $\endgroup$ Mar 11, 2023 at 13:55
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(because we have the supper massive black hole in our Milky Way galaxy)

This is not correct. The supermassive black hole is a very small part of the total mass of the galaxy. Then solar system orbits in the gravitational field of the galaxy, and it would continue to orbit if there was no black hole.

Any two objects with mass will orbit around each other. If the two bodies have about the same mass, neither object will remain motionless; both will move. If one object is much more massive (like a star is more massive than a planet) then that massive object will move only a little bit and the lighter object will move a lot. This is why it is correct to say that the Earth orbits the sun.

But Andromeda and the Milky way are different. They have similar cumulative mass, and they are spread out widely, and they are not rigid. They can interact with each other in a soft collision. So they will be distorted by tidal effects, spread out. They will orbit each other for a while, losing energy through interactions between their dark matter halos. They will become increasingly turbulent, and end up as an elliptical galaxy, with very low rates of star formation.

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    $\begingroup$ They will lose far more energy via dynamical friction (due to the dark matter in the intergalactic medium and in their halos) than through "interactions between the gas in their disks". $\endgroup$ Mar 11, 2023 at 13:58

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