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The dynamics of temporarily captured trajectories in the Hill three-body problem is studied, with application to orbits about Jupiter's satellite Europa. By the use of a model that includes the tidal force of Jupiter, the phase space of capture trajectories is numerically determined and trajectories are identified that do not impact with the planetary satellite or escape over long periods of time. These safe zones in phase space are mapped out over different energy levels, identifying regions in phase space where an uncontrolled spacecraft would remain in orbit without impact or escape. Finally, transfers from these safe trajectories into long-term stable frozen orbits are identified, and the cost to transfer into these orbits is evaluated. Resulting from this analysis is the identification of robust capture trajectories and criteria on placing them into long-term stable orbits. N this paper, we study capture trajectories in the Hill three-body problem. Capture trajectories are trajectories that begin in the exterior region of Hill's problem and enter the region to orbit the planetary satellite at least one time. Previous work has been done on these types of orbits. In particular, Villac and Scheeres1 exam- ined escaping trajectories in the Hill three-body problem, which are analogous to capture trajectories with time reversed. One particular feature of capture trajectories that we investigate is their lifetime. Uncontrolled, these orbits can impact with the planetary satellite or exit the interior Hill region after very short timespans. Koon et al.2 investigated orbits that travel between the interior and exterior Hill regions and showed that the amount of time a trajectory spends orbiting the planetary satellite is determined by chaotic dynamics. We develop a method that identifies sets of capture trajectories thatdonotimpactorescapetheplanetarysatelliteforextendedtime periods.Wecallthesesafetrajectoriesandtheregionsinwhichthey lie safe zones. These safe low-energy trajectories may be useful for theproposedNASAJupiterIcyMoonsOrbitermission.Theplanfor thismissionistoorbitthreeofJupiter'smoons,Callisto,Ganymede, and Europa. We focus our attention on Europa; however, our results can be applied to the other moons as well. With the science goals of this mission being such that a low-altitude, high-inclination stable orbit about Europa is desirable, we examine low-cost methods to transfer from a safe capture trajectory to a long-term stable orbit. To identify possible target long-term stable orbits, we turn to some previousworkonfrozenorbitsidentifiedbyusingdoubleaveraging assumptions. Broucke3 identified and studied the long-term behav- ior of both the circular and elliptic frozen orbits. Scheeres et al.4

Robust Capture and Transfer Trajectories for Planetary Satellite Orbiters