Integration of Deprit's radial intermediary

Abstract

In Artificial Satellite Theory, for the so called main problem (the two-body problem is only perturbed by the equatorial planet's bulge) Deprit's intermediary plays an important role because of its simplicity and integrability while maintaining a similar structure to the original Hamiltonian. To integrate it, we prove that there is no need to introduce a generalizad Kepler's equation, but the classical Kepler's equation, which has been extensively studied for more than three centuries.