Low Energy Interplanetary Transfers Exploiting Invariant Manifolds of the Restricted Three-Body Problem

Abstract

In this paper, a technique for the analysis and the design of low-energy interplanetary transfers, exploiting the invariant manifolds of the restricted three-body problem, is presented. This approach decomposes the full four-body problem describing the dynamics of an interplanetary transfer between two planets, in two three-body problems each one having the Sun and one of the planets as primaries; then the transit orbits associated to the invariant manifolds of the Lyapunov orbits are generated for each Sun-planet system and linked by means of a Lambert’s arc defined in an intermediate heliocentric two-body system.

The search for optimal transit orbits is performed by means of a dynamical Poincaré section of the manifolds. A merit function, defined on the Poincaré section, is used to optimally generate a transfer trajectory given the two sections of the manifolds. Due to the high multimodality of the resulting optimization problem, an evolutionary algorithm is used to find a first guess solution which is then refined, in a further step, using a gradient method. In this way all the parameters influencing the transfer are optimized by blending together dynamical system theory and optimization techniques.

The proposed patched conic-manifold method exploits the gravitational attractions of the two planets in order to change the two-body energy level of the spacecraft and to perform a ballistic capture and a ballistic repulsion. The effectiveness of this approach is demonstrated by a set of solutions found for transfers from Earth to Venus and to Mars.