A mapping approach to the dynamics of closely-spaced planets

Abstract: Understanding the gravitational dynamics of bodies orbiting around a dominant central mass has applications to the study of exoplanets, satellite systems, and beyond. Treatments of these dynamics often involve complex mathematical machinery such as Hamiltonian perturbation theory and specialized disturbing function expansions that can obscure a clear physical picture of the dynamics. I will present a simple iterated map that can be used to model the dynamics of a pair of closely spaced planets by approximating their gravitational interactions as successive impulsive kicks imparted at conjunction. In addition to providing a clear physical picture of the dynamics, this mapping approach can be used to understand the pendulum-like dynamics of mean motion resonances and elucidate how the onset of dynamical chaos depends on planets’ spacing and eccentricities.