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The tentative position of the next habitable space station could be a southern L2 Near Rectilinear Halo Orbit (NRHO) of the Earth Moon System. To bring crew and cargo to the station, a safe and efficient rendezvous methodology has to be established. However, a significant body of work remains to be done on the design of the rendezvous procedure between halo orbits. Given fixed start and end halo orbits, direct transfers (such as Lambert arcs) between the two can produce simple strategies with short transfer time at the cost of relatively high velocity increment Δv, measured in m/s [1].

When longer transfer time is allowed, as with some cargo, lower energy transfers, taking advantage the natural dynamics of the Earth-Moon system, can be used. The most commonly used topological objects are the stable and unstable manifold of a given orbit. These trajectories can lead a spacecraft very far from the original orbit at very low maneuver cost. One strategy is to insert into the unstable manifold of the initial orbit, making the spacecraft leave the starting orbit. After an optimized flight time T_F, a maneuver Δv is performed to insert into the stable manifold of the final orbit, and thus converging to the final orbit [2]. This procedure, however, requires the existence and explicit construction of physical intersections of the stable and unstable manifolds of the original orbits.

In this article, a method is presented to generate the manifolds along with an approximation of the set of their intersections by triangulating the surface and applying a modified Moeller’s method [3]. The most promising points are then further refined into true intersections and the lowest Δv is chosen. The article considers transfer between regular halo to halo, NRHOs to NRHOs and halo to NRHOs. Analysis shows that for several configurations the maneuvers cost can be sizably reduced as compared to fully optimized Lambert arcs.

References:

[1] S. K. Wang, et al. Dynamical Systems, the Three-Body Problem and Space Mission Design Caltech, (2000)

[2] S. Lizy-Destrez, Rendezvous Optimization with an Inhabited Space Station at EML2, 25th International Symposium on Space Flight Dynamics, ISSFD, (2015).

[3] T. Moeller. A Fast Triangle-Triangle Intersection Test, Stanford University, (1992)