Coplanar ground-track adjustment using time difference

The coplanar ground track adjustment problem is studied for both impulsive and continuous low-thrust maneuvers considering the J2J2 perturbation. For the initial orbit, semi-analytical solutions of the flight time and the longitude difference are obtained for an assigned ground-site latitude. Based on the time difference, the flight time for the two-body model is derived. This avoids directly solving the transfer orbit with the J2J2 effect. Then two methods including single-impulse method for free final orbit and shape-based low-thrust method for an assigned final orbit are proposed. For the single-impulse method, the analytical approximate solution is obtained by solving a cubic equation. For the low-thrust method, the shape-based approach is used with a combined inverse polynomial and trigonometric function. The results of several numerical examples show that the final longitude errors of the proposed methods are less than 0.04 deg for the nonlinear J2J2 model.