Question

can two particles be in equilibrium under the action of mutual gravitational force? Can three particles be? Can one of the three particles be?

Answer 1

It is a common situation for 2 particles to stay in equilibrium when it is under the action of a mutual gravitational force. It is a typical two-body state of equilibrium. Most of the natural examples of such bodies are - ellipses, circles, hyperbolas, etc.

It is difficult for 3 bodies to stay in an equilibrium state under mutual gravity. However, examples like the Lagrange points prove that it is possible in special cases.