Extension of the Kepler problem towards minimization of energy and gravity softening

The classical Kepler Problem consists in the determination of the relative orbital motion of a secondary body (planet) with respect to the primary body (Sun), for a given time. However, any natural system tends to have minimum energy and is subjected to differential gravitational or tidal forces (called into play mainly due to the finite size and deformability of the secondary body). We formulate the Kepler Problem taking into account the finite size of the secondary body and consider an approximation which tends towards minimum energy orbits, by increasing the dimensionality of the problem. This formulation leads to a conceivable natural explanation of the fact that the planetary orbits are characterized by small eccentricities. © 1997 Kluwer Academic Publishers.