Keplerian Map Theory for High-Fidelity Prediction of the Third-Body Perturbative Effect

This paper introduces an accurate model to monitor the motion of a particle of negligible mass under the simultaneous gravitational attraction of many celestial bodies, in the restricted three-body problem dynamical regime. It relies on the Lagrange planetary equations and applies the perturbation approach to the three-body potential. This approach benefits from a dynamical model based on the slow-varying Keplerian elements, with respect to the classical formulation of the N-body problem in Cartesian coordinates, which ensures a high computational efficiency. An extensive validation of the theory is presented, to test the accuracy of the model in different scenarios and prove its competitiveness from a computational point of view. The model is eventually adopted for computing a trajectory where the third-body perturbation plays a significant role; the target mission is a multi-flyby trajectory design in the Jupiter sphere of influence, where the gravity fields of the gaseous planet and the four Galilean moons are simultaneously considered.