Two-target interception problem with a single impulse

Abstract

This paper proposes a numerical method to solve the two-target interception problem with a single impulse. Free impulse position and free interception position are considered. Both elliptic and hyperbolic transfers are analyzed. Under the two-body model, by using the Gibbs method for orbit determination from three position vectors, the problem is transformed into solving nonlinear equations of only two independent variables. Newton-Raphson iterations associated with analytical Jacobi matrix are adopted to solve the nonlinear equations. The initial guesses are obtained by the Porkchop plot method. By using the solutions under the two-body model as the initial values, the solutions under the J2-perturbed model are obtained by combining the homotopy technique and the differential correction method. There are many solutions for the problem even for the zero-revolution case. Numerical examples are provided to verify the effectiveness of the proposed methods for the two-body model and the J2-perturbed model, respectively.