MOID-increasing disposal strategies for LPO missions

The issue on the final fate of Sun--Earth Libration Point Orbits (LPO) missions, commonly chosen to place space observatories, has recently drawn the attention of ESA. So far, the only disposal concept implemented at the end-of-life consists in moving the spacecraft on a heliocentric graveyard orbit. This idea requires that the spacecraft will never return to Earth after leaving its operational orbit. A na\"ive approach to fulfill this constraint is to close the zero velocity curves, in such a way that no physical motion is possible between the geocentric orbital regime and the heliocentric one. We propose here an alternative strategy: the disposal orbit is such that, despite the fact that the given bottleneck passage may remain open, it always has an increasing Minimum Orbit Intersection Distance (MOID) evolution. Two numerical procedures have been developed to this end: one considers the application of optimization techniques, the other uses the Newton's method. Both methodologies aim to design spacecraft--Earth encounters, which ensure that the variation of the average orbital elements are such that the MOID will increase. The evolution of the orbital elements as a function of the angle of encounter is first analyzed by means of a semi-analytical 3D extension of the Keplerian map \cite{RS}, which provides a first guess solution to the numerical procedures.