Continuous-Thrust Analytical State Propagation for J₂-Perturbed Nonlinear Orbital Motion

This work presents an analytical method for propagating the continuous-thrust orbital state of a spacecraft under general thrust acceleration, accounting for nonlinear orbital motion perturbed by J₂ effects. The method approximates the real thrust acceleration using a truncated Fourier series in terms of eccentric anomaly for both periodic and nonperiodic cases. The approximated orbital motion is decomposed into two components: the secular motion and periodic perturbations relative to the secular trajectory. Analytical propagation of the secular orbital motion is derived using the orbital averaging method and the thrust series approximation. From the secular propagation, periodic motion equations are obtained via first-order Taylor expansion of the real motion around the secular solution. An analytical solution to the periodic motion is then obtained using linear system theory. A simple multirevolution orbital transfer design method for the boundary-value problem is further proposed based on the developed analytical state propagation. Numerical examples verify that including the periodic orbital variations in addition to the secular motion significantly improves the accuracy of the analytical state propagation compared to considering only the secular motion. The proposed approach enables efficient and accurate orbital state propagation for spacecraft subject to continuous thrust in J₂-perturbed orbits.