STATE TRANSITION MATRIX FOR RELATIVE MOTION INCLUDING HIGHER-ORDER GRAVITY PERTURBATIONS

This paper extends the prediction accuracy of the Gim-Alfriend-J(2)-based state transition matrix (GA STM) by including higher-order gravity perturbations due to J(2)(2), J(4), and J(6). In lieu of an analytical mean-to-osculating element transformation, consistent initial osculating elements for a given set of mean elements are obtained by a least squares approach. Numerical results show that the extended GA STM is more accurate than its original version, with a remarkable reduction obtained in the cross-track, over the J(2) model. It is observed that the along-track relative motion error does not monotonically decrease as the higher-order effects are included incrementally. These results are validated by the simulation package GMAT.