Frozen orbits for satellites close to an Earth-like planet (Q1341297)

This paper concerns the satellite motion around a planet with a dominant second order zonal harmonic, and all other perturbations are excluded. A Lie transformation is used to average over the mean anomaly to second order. The Hamiltonian is developed as a Fourier series in the argument of perigee with coefficients as algebraic functions of eccentricity. Frozen orbits are located by solving the equilibria equations by analytical and numerical means. The analytical solutions are provided in full. The manner in which the odd zonal J3 breaks the discrete symmetry is illustrated by color diagrams of the phase space Three families of frozen orbits in the full zonal problem are discovered and also illustrated by color phase space diagrams. These families are: 1) stable equilibria from the equatorial plane to the critical inclination, 2) an unstable family from the bifurcation at the critical inclination, and 3) a stable family from that bifurcation and terminating with a polar orbit. Except for orbits near the critical inclination, the stable orbits have small eccentricities and are well suited for survey missions. The paper is very analytical and includes the Hamiltonian in Delaunay variables and spherical coordinates. The color phase space diagrams add to the clarity.