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While I was trying to understand the three models that obey Friedmann's two assumptions of a non-static universe, I came across a line that says and I quote "It (referring to Big Bang) starts at time zero and eventually the galaxies are moving apart at steady speed." The question is - is it possible for two massive space bodies to move apart at a 'constant' speed? What do you say on account of the gravitational forces acting between the galaxies? And does it mean the universe will only expand and never come to rest? P.S. I am assuming 'steady' to mean 'constant'.

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The key word here is "eventually."

The strength of the gravitation felt between two objects is inversely proportional to the square of the distance between the two bodies. As a result of this, raising an object from a nonzero distance from object A to an infinite distance from object A requires a finite amount of energy.

In a Keplerian/Newtonian trajectory, the velocity of an object solely under the influence of gravity is governed by an exchange between gravitational potential energy, and kinetic energy. As a result of that, no matter how long their mutual gravity acts, there's a limit to how much kinetic energy gravitation can take from the object.

If the equations are balanced such that the object would come to rest at an infinite distance, the speed that the object has is called "Escape Velocity."

If the object is moving faster than escape velocity, it would wind up with a finite relative velocity at an infinite distance, and this value is called Hyperbolic Excess Velocity.

For instance, if the Sun and Voyager I were the only objects in the universe, and there were no other forces between them other than mutual gravity, the relative velocity between the two of them would never fall below 16.6 km/s.

A similar case holds for any two objects, regardless of mass; If they're moving relative to each other higher than their mutual escape velocity, considering only the two bodies, and only the gravitation between them they wind up asymptotically approaching a finite relative velocity.

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