Computing Natural Transfers Between Sun-earth And Earth-moon Lissajous Libration Point Orbits
- Paper number
IAC-07-C1.3.10
- Author
Ms. Elisabet Canalias, Universitat Politecnica de Catalunya, Spain
- Coauthor
Mr. Josep J. Masdemont, Universitat Politecnica de Catalunya, Spain
- Year
2007
- Abstract
The use of libration regions as suitable locations for spatial missions has been increasing in the last 30 years. Space transportation between libration point orbits can use the so-called homoclinic and heteroclinic connections, which are asymptotic trajectories arising from the hyperbolic character of the aforementioned orbits in the frame of the Restricted Three Body Problem. Several studies have dealt with the computation of these kinds of connections in the last years, because they follow the natural dynamical channels of the problem, consequently providing very low cost transfers between libration orbits.
More recently, the idea of computing such natural transport channels has been extended to the 4 body problem Sun-Earth-Moon-spacecraft, modelled as two coupled restricted three body problems. Using the hyperbolic manifolds of the libration orbits of both problems and intersecting them in an adequate way, trajectories joining the libration regions of the Sun-Earth and Earth-Moon problems can be found, which use a very small Δv budget. The use of two restricted three body problems is convenient, because in this way one can take advantage of the knowledge of the dynamics in the libration regions and the high order analytical expansions defining the Lissajous orbits and their manifolds. Unfortunately, the coupling of two three body problems does not correspond exactly to the physical reality of the Sun, Earth and Moon relative motions. Therefore, another step has to be taken before being able to use the transfer trajectories in real mission design: the refinement to more realistic models.
A method for finding connecting trajectories between Lissajous type orbits around the L 2 point of the Sun-Earth and Earth-Moon restricted three body problems has been recently presented by the authors. Not only has this method proved to be efficient for transfer computation, but also convenient for mission prototyping, as it is easilly adaptable to important design parameters such as orbit sizes and relative configurations of Sun, Earth and Moon. In the present paper, a method for refining the connecting trajectories to JPL ephemeris is presented. To this aim, a modification of the classic multiple shooting algorithm is used, in order to slowly reduce the maneuver at the coupling point. Our goal is to obtain zero cost real transfers. However, it is also important to mantain the refined trajectory close to the original one, in order to keep the aforementioned adaptability of the methodology to mission requirements, which mainly depends on the control that the mission analyst has over the design parameters. Therefore, a trade between low cost and resemblance to the original trajectories has to be found. Whenever the maneuver can be reduced to 0 cost and the trajectory is still close to the original one, the method is iterated until free tranfers are obtained. On the other hand, when the resemblance to the coupled trajectory is threatened, the refinement procedure is stopped when the cost has been reduced to an affordable Δv but the refined trajectory is still considerably similar to the original one.
- Abstract document
- Manuscript document
IAC-07-C1.3.10.pdf (🔒 authorized access only).
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