Identifying Safe Zones for Planetary Satellite Orbiters

Abstract

This paper studies the dynamics of temporarily captured trajectories in the Hill 3-body problem, with application to orbits about Jupiter’s satellite Europa. Using a model that includes the tidal force of Jupiter, the phase space of capture trajectories is numerically determined and trajectories are identified that don’t impact with the planetary satellite or escape over long periods of time. These ‘safe zones’ in phase space are mapped out over dierent energy levels, identifying regions in phase space where an uncontrolled spacecraft would remain in orbit without impact or escape. The ‘distances’ of these safe trajectories from various frozen orbit trajectories are determined 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. I. Introduction In this paper, we study capture trajectories in the Hill 3-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 Scheeres 5 looked at escaping trajectories in the Hill 3-body problem, which are analogous to capture trajectories with time reversed. One particular feature of capture trajectories that we investigate is their lifetime. Unstabilized, these orbits can impact with the planetary satellite or exit the interior Hill region after vert short time spans. 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 controlled by chaotic dynamics. We develop a method which identifies sets of capture trajectories that do not impact or escape the planetary satellite for extended time periods. We call these ‘safe trajectories’ and the regions in which they lie ‘safe zones’. These safe low-energy trajectories may be useful for the proposed NASA Jupiter Icy Moons Orbiter (JIMO) mission. The plan for this mission is to orbit three of Jupiter moons, 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. In order to identify possible target long-term stable orbits, we turn to some previous work on orbits identified by using double averaging assumptions. There orbits are termed ‘frozen orbits’ and both circular and elliptic frozen orbits have been studied extensively. Broucke 1 identified and studied the long term eects