Dynamics of Mutual Attraction: Gravitational Coupling of Rotation and Translation

Daniel J. Scheeres, University of Michigan, Aerospace Engineering

The dynamics of mutually gravitating mass distributions are discussed. When the interacting bodies are non-spherical, angular momentum and energy can be freely exchanged between their relative translational and rotational motions. Such situations occur in binary asteroid systems, and can end in mutual escape and rotational de-spinning of the bodies. A detailed study of these interactions leads to a number of analytical results that give insight into these exchanges, and relates them to resonant interactions between translational and rotational motion. Taking a different approach, this same problem can also be analyzed starting from the classical $n$-body problem. Applying some well-known results from that problem gives rise to a number of sharp stability results for the interaction of two mass distributions. This work has application to solar system dynamics, including the formation of asteroid binaries, the disruption of comets, and the evolution of small body spin states, and has application to astrodynamics, including gravity gradient satellites and space missions to asteroids and comets.