According to Newton's Laws of Gravitation,
$F=Gm_1 m_2/r^2$
So gravitational force F is directly proportional to $1/r^2$.
Now if we consider 2 point masses in vacuum at rest at a distance 'd' apart, gravitational attraction will cause them to move towards each other by the above force, whatever magnitude it maybe. As the masses move closer, the distance 'd' decreases and the force in turn increases. So 2 particles at rest with zero energy (nearly) start moving towards each other with increasing acceleration and collide with each other with almost infinite speed.
But this does not happen. Rather I find in books that in such a situation, 2 point masses will revolve about a common axis.
Did I go wrong anywhere? I mean I thought that the gravitational field was doing work here.But again it seems to work like a perpetual motion machine which does not exist in nature.
Answer
You're not wrong; if you had two isolated particles that both started as completely stationary (which, on a non-classical note, is impossible due to the Heisenberg uncertainty principle), they'd collide at very high speeds (limited by radius of the objects themselves).
However, remember that gravity is a central force. If two objects are moving in a circle or ellipse, (a direct line of approach is essentially impossible after things get tugged by other particles along the way) the gravitational force will pull on the two objects to change their direction of motion, but it can't directly act to change the component of the object's velocity that is not in the same, central direction as the force.
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