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The only Force acting on the masses is the gravitational force between them.

After what time do they collide?

Gravitational Force F = Gm

_{1}m

_{2}/(2s)

^{2}where m is the mass and s the distance to the center of both masses (Hence 2s the distance between them). G is the gravitational constant.

F = G*1*1/(2*0.5)

^{2}= G

As F = ma and m is 1, a = G at the initial position.

As the masses dont change I can say for all moments: a(s) = G(2s)

^{-2}

The acceleration a is a function of s, the distance, and not time, as usual.

From there on I was stuck.

My guess was that a(s) = dv/ds

And as a(t) = dv/dt = dv/ds*ds/dt and ds/dt = Velocity v

a(t) = a(s)*v

But I have no clue what velocity this is? Is this a totally wrong approach?

Another thought was to take the average acceleration and use it for my calculations.

When s = 0.5m the acceleration is 1G, and when s = 0.25m it is 4G.

Is 4G the average acceleration?

t = √(2s/a) = √(1/4G) = 61221.94s = 17 hours

If this average acceleration is wrong, how do I calculate it?

I would thank you for any help :S