Analytical Estimation of the Velocity Increment in J2-Perturbed Impulsive Transfers

Abstract

It is essential when planning multitarget missions to rapidly and accurately estimate the velocity increments of target-to-target transfers. An analytical method is proposed to estimate the optimal velocity increment of a multirevolution impulsive transfer, taking account of the $J_2$ perturbation. First, for a phasing problem where the differences in semimajor axis, inclination, ascending node, and argument of latitude at the termination of the transfer are eliminated, two linear equations derived from the first-order necessary conditions are solved to determine the normal components of the impulses. Then, the radial and tangential components of the impulses are determined by solving another two linear equations, thereby eliminating the difference in the eccentricity vector. In a classical debris removal scenario, the proposed method shows better accuracy than previous analytical methods and even a method based on a deep neural network. The computational efficiency of the method is also much higher than that of the existing semi-analytical method. In addition, the estimated transfer process is in good agreement with the exact one in some cases, and so the method shows potential for preliminary designs of impulsive trajectories.