Different perspectives on the b-plane: perturbation effects and use for resonant flyby design

Abstract

Orbital resonances can be leveraged in the mission design phase to target planets at different energy levels. On the other side, precise models are needed to predict possible threatening returns of natural and artificial objects closely approaching a target planet. To this aim, we propose a semi-analytic extension of the b-plane resonance model to account for perturbing effects inside the planet’s sphere of influence. We compute the actual values of the perturbing coefficients by means of precise numerical simulations, whereas their expression stems from the properties of hyperbolic trajectories and asymptotic planetocentric velocity vectors. We apply the proposed b-plane model to design ballistic resonant flybys by solving a multilevel mixed-integer nonlinear optimization problem.