Two Newtonian point particles, A and B, with mass 1kg are at rest separated by a distance of 1m. They are influenced only by the other’s gravitational attraction. Describe their future motion. In particular do they ever return to their original positions, and after how long?
A different question in the same vein:
The collision of two “infinitely small” points is quite another problem. Have some similarities, too.
For two points on a colliding path, the action and reaction force are present and of equal size and oppposite directions.
My example can have finite size balls or zero size mass points, but there is no reaction force to be seen. At least, I don’t.