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 J₂ 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 J₂ 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 J₂ model.