I am not a physicist.
Suppose a body A is falling towards body B in a vacuum. We know that A's speed will increase. However, as A draws near to B, the force of gravity will increase so the rate at which A accelerates will increase. Also we can presume that B's motion is affected by A. So now we have multiple levels of acceleration.
I understand that, for practical purposes we can usually neglect smaller effects. My question is: In Nature do we ever get to the end of this apparently bottomless pit of derivatives?
A and B are of comparable but non-identical mass. They will therefore accelerate towards one another at differing rates.
When they get close enough, they can no longer be assumed to be a dimensionless point wrt gravity.