Numerical integration of the satellites of the outer planets
The formulation of a numerical integration program, used to construct ephemerides for satellites of the outer planets, is described. The equations of motion are derived, including (1) n massive integrated satellites, (2) m massive perturbing planets, (3) J2, J4 oblateness coefficients of the primary and each satellite, and (4) a barycentric coordinate system. Variational equations are also found: (1) 6n initial states and n masses of the integrated satellites, (2) J2, J4 of the primary planet, (3) the mass of the system, and (4) right ascension and declination of the pole. The formulation was used to construct the satellite ephemerides of Saturn for the Voyager mission.