Trajectory correction maneuver design using an improved B-plane targeting method

Abstract

A spacecraft for interplanetary mission is usually perturbed by some disturbance sources. The trajectory correction maneuver (TCM) is required to adjust this trajectory error, and the B-plane targeting method is widely used in this field. However, this B-plane targeting method is based on the differential correction algorithm, and a numerical Jacobian matrix is usually used for this algorithm. Therefore, our main goal in this paper is to suggest the improved B-plane targeting method to overcome the disadvantages of the conventional B-plane method which requires a numerical Jacobian matrix for the initial perturbation selection and iterations. For this improvement, an analytical Jacobian matrix is introduced instead of the numerical Jacobian matrix. Then, another B-plane approach that offers an analytical solution is suggested using the target eccentricity instead of the target time of closest approach (TCA). Using a modified Kepler's equation, the previous B-plane targeting approach can be replaced with the new method through the analytical solution.