B-plane and Picard–Chebyshev integration method: Surfing complex orbital perturbations in interplanetary multi-flyby trajectories

Orbital resonances have been exploited in different contexts, with the latest interplanetary application being the ESA/NASA mission Solar Orbiter, which uses repeated flybys of Venus to change the ecliptic inclination with low fuel consumption. The b-plane formalism is a useful framework to represent close approaches at the boundaries of the sphere of influence of the flyby planet. In the presented work, this representation is exploited to prune the design of perturbed resonant interplanetary trajectories in a reverse cascade, replacing the patched conics approximation with a continuity link between flybys and interplanetary legs. The design strategy splits the flyby time and state variables in a two-layer optimization problem. Its core numerically integrates the perturbed orbital motion with the Picard–Chebyshev integration method. The analytical pruning provided by the b-plane formalism is also used as starting guess to ensure the fast convergence of both the numerical integration and the trajectory design algorithm. The proposed semi-analytical strategy allows to take advantage of complex gravitational perturbing effects optimizing artificial maneuvers in a computationally efficient way. The method is applied to the design of a Solar Orbiter-like quasi-ballistic first resonant phase with Venus.