Sliding on a Massive Spinning Asteroid

While Newton’s sphere theorem allows us to model spherically symmetric objects as points, a spherical approximation is insufficient for some objects, such as irregular asteroids. Even Earth is not a true sphere but is closer to an oblate spheroid. We study the trajectory of a point mass sliding on a massive rotating ellipsoidal asteroid by numerically integrating the equations of motion in Mathematica. We calculate the maximum Lyapunov exponent and plot Poincare sections for the motion. We find that the system exhibits a variety of chaotic and regular behaviors and that its chaotic nature is closely related to the centrifugal and Coriolis pseudoforces and to the asteroid's gravity.