Luke Peterson, Department of Aerospace Engineering Sciences, University of Colorado Boulder

Persistence of Resonant Orbits in Realistic Solar System Models

Resonant periodic orbits are often used in astrodynamics and space mission design due to their predictable and repeatable behavior. For example, the nominal orbit of Lunar Gateway--the next-generation space station--is a 9:2 halo orbit, i.e., the station orbits the Moon 9 times in the time it takes the Sun to “orbit” the Earth-Moon frame 2 times. In the Earth-Moon system, the dynamical model used for preliminary mission design is the Circular Restricted 3-Body Problem, an autonomous Hamiltonian system; however, there are significant periodically perturbing effects, from the ellipticity of the Earth-Moon orbit to the gravitational influence of the Sun, that must be incorporated to ensure mission success. Most periodic orbits persist as invariant 2-tori under certain non-degeneracy conditions prescribed by KAM theory; yet resonant periodic orbits persist as resonant periodic orbits, often multiple orbits of the same resonance, as determined by subharmonic Melnikov theory. In this talk, I will present recent progress in the application of subharmonic Melnikov methods to modern celestial mechanics problems, especially highlighting the open questions in dynamical systems arising from the motion of a satellite in our solar system.