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Let's say the objects are marble size or even single atoms or quarks. They are placed in an otherwise empty universe(expanding or non-expanding) at opposite ends of the universe with an arbitrarily large distance between them. With a combination of great enough distance and small enough mass will the gravitational pull between the two objects ever equal zero or merely approach it? Given an infinite amount of time would they ever meet?

user38296
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    An empty universe wouldn't expand at all.This can be easily seen from the first Friedman equation. – Sandesh Kalantre Jan 27 '14 at 07:43
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    To make this question interesting you need to expand it. Can you write down an equation for the interaction between the two objects? If so, can you work out what will happen? You can ignore the expansion of the universe because as described in this question, an empty universe does not expand or contract. At the moment I have voted to close your question because it needs more work, but if you revise the question I will withdraw the vote to close. – John Rennie Jan 27 '14 at 07:45

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Being "at rest" always means "at rest relative to a given reference frame". When both masses are "at rest" in the same reference frame, they start with a relative velocity of 0 to each other.

Newton's law of universal gravitation says that every mass in the universe attracts every other mass with a force of $F = G \frac{m_1 m_2}{r^2}$ where G is the universal gravity constant, m1 and m2 are the masses of the objects and r is the distance between them.

As long as the masses are larger than zero and the distance is smaller than ∞, there will be a force between the two masses, which will accelerate them towards each other. When they have no initial velocity relative to each other, this acceleration will cause them to meet.

However, when there would be an initial velocity (which isn't exactly into the direction of each other), they will never meet. When the velocity is smaller than the escape velocity in the initial configuration, the two masses will orbit each other without ever meeting. When the velocity is larger than the escape velocity, they will escape from each other.

Philipp
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