Smooth and continuous interplanetary trajectory design of spacecraft using iterative patched-conic method

Abstract

This paper is concerned with the transfer trajectory design among multiple planets using multiple flybys. The proposed trajectory design method consists of a semi-analytical tuning strategy and iterative patched-conic method. The tuning strategy refers to a method realizing the smooth connection between a hyperbolic trajectory near a planet and a trajectory obtained by Lambert's problem between the planet and another one. The proposed method iteratively solves Lambert's problem and the tuning strategy so that the arrival or departure velocity obtained by Lambert's problem coincides with the velocity at the corresponding point in the sphere of influence (SOI), assigned by the tuning strategy. Consequently, a smooth and continuous trajectory with multiple flybys can be obtained, where the SOI of each flyby planet and the flyby time are explicitly taken into account. Moreover, analytical conditions with respect to the orbital elements of the arrival and departure hyperbolas are provided to minimize velocity mismatch at the periapsis of a flyby planet. Through numerical simulation using the Cassini example, it is shown that the resultant trajectory by the proposed method is close to the optimal trajectory obtained by the n-body problem. Thus, a suitable approximate trajectory can be effectively generated without solving the n-body problem.