I am curious about a system of gravitating bodies with particular characteristics. Before describing the characteristics of the system, let me say what I want to know about it:
- Can this be a solution?
- Is it a stable solution?
- Can the orbiting objects all lie on the same elliptical orbit?
Here are the characteristics of the system: It is a system of 3 bodies of negligible mass in closed orbits around a central massive object. The three bodies of negligible mass orbit such that their distances to the central massive object and to each other are always changing, BUT the sum of their inverse distances (i.e. the sum of their individual potential energies) is constant. In this system energy is conserved, therefore it follows that the sum of the objects' squared velocities (i.e. their kinetic energies) is also always constant, even though the individual velocities are always changing.