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

What is it about?

An extended Lambert-based approach is proposed for J2-perturbed ground-track adjustment with specified target-overfly altitude. Extended equations are developed in the orbital plane based on Lagrange's form for the unperturbed Lambert's problem to address the $J_2$-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. A radius restriction method is proposed to narrow down the allowable range of the number of revolutions. The proposed algorithm is effective and 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 results of this study may have important implications for Earth observing missions, especially those of emergency cases.

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