Trapped satellites

If two material particles are to diverge to infinity, their total energy, i.e. the sum of both their kinetic and mutual gravitation energies must be non-negative. Similarly, when they speed towards each other from infinity, their energy is non-negative, the trajectories are open curves, so they can only meet once. Therefore no two such material particles can get caught in a closed orbit. To have open orbits become closed, the total energy of two bodies must become negative. Real bodies not being material particles, this is indeed possible. For instance, part of the energy can be transformed into rotation (because of the tidal effect) or thermal energy (for the same reason); one object can be hampered by the atmosphere of the other (which, in fact, also leads to a partial transformation of energy from mechanical to thermal), finally, part of the energy can carry a third body away, as it probably happens quite often in globular clusters densely filled with stars. Some satellites in the solar system are suspected to have been caught by planets, particularly so some satellites revolving around their planet in the direction opposite to that of the planet revolving around the sun. This problem, however, is far from being solved.

T.K.