Low Energy Interplanetary Transfers Exploiting Invariant Manifolds of the Restricted Three-Body Problem
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Low Energy Interplanetary Transfers Exploiting Invariant Manifolds of the Restricted Three-Body Problem 1 Francesco Topputo," Massimiliano Vasile,3 and Franco Bernelli-Zazzera"
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 Poincare section of the manifolds. A merit function, defined on the Poincare 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.
Introduction A class of future interplanetary missions would require the maximization of the payload mass without any particular restriction on the transfer time. For instance, the construction of a permanent base on Mars will require many preparatory missions aimed at delivering experiments and robotic devices on the planet. Moreover, 1Presented in part at the AAS/AIAA Space Flight Mechanics Meeting, Maui, Hawaii, February 2004 as paper AAS 04-245. 2Ph.D. Candidate, Aerospace Engineering Department, Politecnico di Milano, Italy, [email protected]. 3Researcher, Aerospace Engineering Department, Politecnico di Milano, Italy, [email protected]. 4Full Professor, Aerospace Engineering Department, Politecnico di Milano, Italy, [email protected].
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a manned journey to Mars could involve several cargo missions to carry the facilities necessary to allow human survival in hostile conditions. Such missions could be carried out by following low energy interplanetary trajectories through the libration points. On the other hand, as recently demonstrated by the designers of the Bepi Colombo mission [1], a gravitational capture can be used to avoid a single point failure of a classical chemical orbit insertion burn typical of a hyperbolic
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