Low Energy Transfers to the Moon Exploiting the Hyperbolic Dynamics of L1
- Paper number
IAC-05-C1.6.06
- Author
Mr. Francesco Topputo, Politecnico di Milano, Italy
- Coauthor
Mr. Franco Bernelli-Zazzera, Politecnico di Milano, Italy
- Coauthor
Mr. Massimiliano Vasile, Politecnico di Milano, Italy
- Year
2005
- Abstract
In the frame of the lunar exploration, numerous future space missions will require the maximization of the payload mass, while simultaneously achieving reasonable transfer times. To fulfil these requests, low energy non-Keplerian orbits could be used to reach the Moon’s neighborhood instead of the common conic paths.
In the past, several authors have faced the problem of finding efficient solutions to the issue stated above. The general idea has been the exploitation of intrinsic features derived by the assumption of n-body model for the description of the spacecraft dynamics. Only in these broader contexts, in fact, some new dynamical behaviors, as the ballistic capture or the chaotic regime, can be appreciated and used to improve the performances of the transfer trajectory.
The low energy solutions can be split into two main categories depending on the nature of the trajectory approaching the Moon: the transit orbits, approaching the Moon from the interior equilibrium point L 1 and the Weak Stability Boundary (WSB) transfers, reaching the Moon after a L 2 close passage. The latter technique, developed by Belbruno citebelbruno, exploits the chaotic dynamics characterizing the equilibrium region of the Sun-Earth-Moon-Spacecraft restricted four-body problem to perform a ballistic capture that reduces the hyperbolic excess velocity at Moon arrival. On the other hand, the study on the transit orbits, defined in the frame of the Earth-Moon-Spacecraft circular restricted three-body problem, begun with Conley citeconley who was the first to propose the use of such solutions as transfer trajectory to the Moon. Nevertheless, in more recent years, several authors citepernicka, bolt, schroer, macau, ross have demonstrated that the use of transit orbits brings about very high times of flight caused by the nature of the apogee raising mechanism due to the Moon resonances. Furthermore, a substantial Delta v saving could be accomplished only if the transfer links two high altitude parking orbits around the Earth and the Moon, clearly of less practical use for space purposes.
This paper proposes an alternative way to exploit the potentiality associated to the transit orbits for the Earth-Moon transfers. First, in a neighborhood of the L 1 point, the full three-body dynamics is linearized and written in normal form; then the whole family of transit orbits (from the Earth to the Moon and vice versa) is obtained by selecting the appropriate non-trivial multipliers associated to the hyperbolic part. Each hyperbola is parameterized and integrated backward and forward until the Earth/Moon regions are reached. In a second step, two selected low altitude parking orbit around the Earth and the Moon are linked with the transit orbit by means of two three-body Lambert’s arcs, solutions of two two-point boundary value problems.
The resulting four-impulse lunar transfer connects two low altitude orbits allowing a propellant mass saving with realistic transfer times making such trajectories of practical interest.
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- Abstract document