Extended Lambert-Based Approach for Ground-Track Adjustment with Specified Overflight Altitude

Abstract

This paper presents an extended Lambert-based approach for ground-track adjustment under J2 perturbation, aiming to achieve a satellite flyby over a designated ground location at a predetermined altitude. Extended equations are developed in the orbital plane based on Lagrange’s form for the unperturbed Lambert’s problem to address the J2-perturbed two-body motion. By combining them with the out-of-plane flight time equation constraint regarding the ground-track adjustment, a nonlinear system of equations with two unknowns and two equations is established and split into different modes. To solve these modes, a modified Newton–Raphson method is used, and a necessary condition is established to determine the maximum allowable number of revolutions. To enhance computational efficiency, a radius restriction method is proposed to narrow down the allowable range of the number of revolutions. The proposed algorithm is applicable to various scenarios, including single- or multiple-day flights, ascending or descending overflights, coplanar or non-coplanar transfers, and initial or reverse-initial directional transfers. The simulation results demonstrate that the proposed algorithm is effective and accurate for the perturbed adjustment problem.