Designing Capture Trajectories to Unstable Periodic Orbits Around Europa

摘要

The hostile environment of third body perturbations restricts a mission designer's ability to find well-behaved reproducible capture trajectories when dealing with limited control authority as is typical with low-thrust missions. The approach outlined in this paper confronts this shortcoming by utilizing dynamical systems theory and an extensive pre-existing database of Restricted Three Body Problem (RTBP) periodic orbits. The stable manifolds of unstable periodic orbits are used to attract a spacecraft towards Europa. By selecting an appropriate periodic orbit, a mission designer can control important characteristics of the captured state including stability, minimum altitudes, characteristic inclinations, and characteristic radii among others. Several free parameters are optimized in the non-trivial mapping from the RTBP to a more realistic model. Although the ephemeris capture orbit is ballistic by design, low-thrust is used to target the state that leads to the capture orbit, control the spacecraft after arriving on the unstable quasi-periodic orbit, and begin the spiral down towards the science orbit. Despite the limited control authority and the highly unstable dynamical environment, the method provides structure and controllability to the design of the ephemeris model capture trajectories at Europa.