Orbital resonance widths in a uniformly rotating second degree and order gravity field
Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway e-mail: firstname.lastname@example.org
Accepted: 6 December 2005
Aims.In this work I seek to derive analytical expressions for the widths of mean motion resonances in uniformly rotating second degree and order gravity fields.Methods.A Deprit perturbation series is used to derive Hamiltonians valid close to mean motion resonances. These expressions are reduced to the Hamiltonian of a pendulum through canonical transformations.Results.Analytical expressions for the orbital resonance widths in uniformly rotating second degree and order gravity field are derived and tested against numerical simulations. The widths of these mean motion resonances are independent of the rotation rate and the mass of the central body. The general stability of retrograde orbits are explained by the overlap criteria.
© ESO, 2006