The optimized approach to get the fundamental property of the gravity assists maneuvers from the Jacobi integral

Abstract

Abstract The design of interplanetary trajectories using a series of gravity assists maneuvers begins with the ballistic mission design. It is reasonable to construct the corresponding initial approximation using the patched conics method within the model of the circular restricted three-body problem. Such a construction requires the calculation of the “transfer parameter” Vinf - the dimensionless asymptotic velocity of the spacecraft relative the target planet, when switching from heliocentric arcs to planetocentric segments and vice versa. In the circular restricted three-body problem model, Vinf can be calculated using the Jacobi integral J (or using it’s analogue - the Tisserand parameter TTiss and the basic property of the Jacobi integral for the gravity assists maneuvers within the framework of the circular restricted three body problem: const J ≈ TTISS ≈ 3 – Vinf Vinf . According to this property, the J value does not change during the multiple gravity assists maneuvers that preserve the Jacobi integral constant are performed. This fact is known in astrodynamics but it is classically derived in a rather cumbersome method. In this study, a shorter method for its obtaining is proposed. The modifications of the representation of the Jacobi integral in the circular restricted three-body problem for the various configurations of three bodies are presented.