Dynamics about Uniformly Rotating Triaxial Ellipsoids: Applications to Asteroids

Abstract

The general problem of satellite and particle dynamics about a uniformly rotating triaxial ellipsoid with constant density is formulated. The study of this problem can shed light on the dynamics of particles and satellites when orbiting irregularly shaped bodies such as asteroids. The physical specification of an asteroid modeled as a triaxial ellipsoid can be reduced to two nondimensional shape parameters (the eccentricities of the triaxial ellipsoid) and one nondimensional parameter which is a function of the body density, shape, and rotation rate. All these parameters may be measured or inferred from groundbased observations. Using these three parameters, the rotating ellipsoid may be classified into Type I or Type II ellipsoids depending on whether or not all synchronous orbits about the body are unstable. This classification of the ellipsoid has significant consequences for the dynamics of bodies in orbits which are near-synchronous with the asteroid rotation. Asteroids classified as Type I have stable motion associated with near-synchronous orbits. Asteroids classified as Type II have unstable motion associated with near-synchronous orbits. Families of planar periodic orbits are computed for two specific ellipsoids based on the asteroids Vesta and Eros. The stability of these families are computed and related to the type classification of the ellipsoid. Notes are also made on the existence of stable and unstable periodic orbits about the asteroid Ida. Analytic approximations are also introduced under some assumptions, leading to a simplified description of orbits about a triaxial ellipsoid. Finally, a table of parameters and classifications for a few known asteroids and comets are given.