B-Plane Resonant Flybys: Theory Extension to Elliptical Orbits and Dynamic Programming Application

Abstract

A convenient formalism for the design of resonant flyby trajectories is the B-plane, where postencounter orbits with target resonance conditions or semimajor axes can be analytically mapped. This framework has been developed by many authors starting from the classical Öpik’s theory for close encounters, but it still relies on the approximation of circular orbits of the flyby bodies. In this work, the theory is analytically extended to account for elliptical planetary orbits. The classical and the extended formulations are tested and compared on two mission design applications, showing nonnegligible differences when the flyby body has a marked eccentricity. Further validation using a full three-body model confirmed the greater accuracy of the extended formulation. The second part of the paper proposes an efficient dynamic programming approach to the design of unperturbed resonant flybys. This problem has traditionally been addressed within broader optimization frameworks involving generic multiple gravity assists. However, focusing only on the resonant sequence allows the problem to feature a convenient structure for the implementation of dynamic programming. The developed algorithm is tested by reproducing the design of Solar Orbiter’s resonant phase with Venus, used in the actual mission to gradually raise the ecliptic inclination and reduce the distance at perihelion.