Invariant Funnels For Robust Interplanetary Transfer, Flyby, Capture, and Landing

NASA is exploring the idea of sending robotic probes to the ocean worlds orbiting the outer planets. The Europa Clipper, set to launch in 2024, will give us a deeper understanding of the icy surface of Jupiter’s moon Europa. Proposed missions to the surface of Europa, as well as Saturn’s moon Enceladus, are currently being considered as future flagship missions for NASA. Mission designers will be tasked with finding the most fuel-efficient route to these final destinations to save space for the scientific instruments that will probe for signs of life. Current best practices rely on using resonant orbits to perform multiple flybys of other moons to reduce orbital energy before taking advantage of three-body dynamics to approach the target moon. Since the design space is infinitely large, mission designers must often rely on Monte Carlo techniques, simulating millions of random trajectories to find a few that meet mission constraints. This process can be slow, stalling or preventing concurrent engineering efforts. Therefore, fast methods for identifying resonant orbits that reach specific landing sites are in high demand. I have discovered a simple, two-part solution to this problem. First, I apply a standard planar Poincare map in the spatial problem to identify a resonant landing orbit. Next, I generate an "invariant funnel" of trajectories that converge to the orbit, which acts as an attractor. The funnel has a wide mouth, thousands of kilometers wide, that shrinks to a small disc at a landing site only a few kilometers (or less) wide. This proposal seeks to develop these methods into technology that can be used in real-life applications. I will do this by characterizing the dynamical structures that make these methods possible, performing navigation analyses, applying them to the problem of flybys, and producing software and documentation for distribution.

Develop fast methods for identifying resonant orbits that reach specific landing sites.

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