State Transition Matrix for relative motion including J2 and third-body perturbations

The paper extends the fidelity of the Gim-Alfriend State Transition Matrix (GA STM) by incorporating the effects of third-body gravitational perturbations. A doubly-averaged lunar potential, accounting for the lunar orbit's inclination and eccentricity, is adopted to obtain the secular rates for the orbital elements. The state vector of the Moon with respect to the Earth is obtained from ephemerides data. Consistent initial conditions for the averaged model are determined by a least squares method. The results for an example involving a reference orbit of high eccentricity show that the accuracy of the GA STM is significantly improved by the inclusion of the lunar perturbation model.

State Transition Matrix for relative motion including J2 and third-body perturbations Conference Paper