LEO--Lissajous transfers in the Earth--Moon system
- Paper number
IAC-08.C1.3.7
- Author
Ms. Elisa Maria Alessi, Universitat de Barcelona, Spain
- Coauthor
Prof. Gerard Gómez, University of Barcelona, Spain
- Coauthor
Mr. Josep J. Masdemont, Universitat Politècnica de Catalunya, Spain
- Year
2008
- Abstract
We apply the Circular Restricted Three–Body Problem (CRTBP) and the tools of Dynamical Systems Theory to the Earth–Moon system in order to construct transfer trajectories between a given Low Earth Orbit (LEO) and a Lissajous orbit around the collinear point L1.
Recently, a remarkable effort has been devoted to find optimal transfers in the Earth–Moon system. The Moon might be an ideal departure point for interplanetary missions and the study of its environment, origin and evolution still represents a challenge to the human’s knowledge. Within this framework, a space hub can be located around L1, serving as construction and repair facility.
It is well known that the CRTBP studies the behaviour of a massless particle affected by the gravitational attraction of two main bodies, which follow a circular orbit around their common barycenter. In a suitable reference system, this model admits five equilibrium points: L1 lies between the primaries on the axis joining them.
The centre × centre part associated with the linear behaviour in a neighbourhood of L1 defines its central manifold. Among the orbits filling it, we focus on the Lissajous ones, quasi–periodic orbits lying on invariant tori. The hyperbolic character of these orbits gives rise to stable and unstable manifolds.
As the stable manifolds of the Lissajous orbits around L1 do not reach the Earth, we need a transfer arc from the LEO to the manifold. This is established at least on two manoeuvres, one on the hyperbolic manifold and the other on the LEO. The main interest resides in seeing how the transfer’s total cost and time depend on the geometry of the arrival orbit, on the points at which the manoeuvres are performed and on the methodology used.
We take advantage of semi–analytical and numerical techniques. The computation of the transfer is achieved by exploiting different methods such as classical manoeuvres, differential correction procedures and other extended simulations. The Lissajous orbits and the corresponding stable manifolds are computed by means of an order 25 Lindstedt–Poincaré procedure, which takes in consideration higher order terms in the equations of motion and produces initial conditions with high degree of accuracy.
The results are an extension of the ones obtained by Born, Howell, Parker and Rausch for halo orbits.
- Abstract document
- Manuscript document
IAC-08.C1.3.7.pdf (🔒 authorized access only).
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