Interplanetary transfers employing invariant manifolds and gravity assist between periodic orbits

Abstract

The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application. This paper focuses on the interplanetary transfers between periodic orbits of two different three-body systems, whose invariant manifolds have no intersection in phase space. A novel design method is proposed to obtain the optimal transfer employing the invariant manifolds and planetary gravity assist. The periapsis Poincare map is used to analyze the periapsides of invariant manifolds. On the basis of hyperbola approximation, the impulses performed on the periapsis of invariant manifolds are calculated with a simple iterative algorithm. The propellant-efficient escape and capture trajectories can be found by comparing the impulses magnitudes corresponding to different invariant manifolds, which can provide the appropriate initial guess for optimization. Further, the trajectory design is formulated as an unconstrained optimization problem under the perturbed restricted three-body model. An efficient algorithm combining simplex method and differential correction is adopted to obtain the optimal solution. The validity of the proposed approach is demonstrated through several interplanetary low energy transfer trajectories.