The equilibrium configurations of rotating fluid masses is a classical problem first studied by Newton in the context of the figure of the Earth. Equilibrium configurations for synchronous, uniform, binary systems were computed by Roche, under the assumption that the resulting configurations are ellipsoids orbiting in a Keplerian orbit. In modern astrophysical research these classical Roche ellipsoidal solutions are used in the study of a wide range of contact binaries, including binaries in the Kuiper belt. In this talk, I will describe the classical analytical approximations, and I will then present exact numerical computations of the equilibrium configurations of synchronous binaries, self-consistently taking into account the tidal and rotational deformations of both components, and relaxing the assumptions of ellipsoidal configurations and Keplerian rotation. The numerical models
result in non-ellipsoidal configurations in non-Keplerian orbits, but indicate that the analytical ellipsoids are, in most cases, a fair approximation. I will show the light curves resulting from the numerically computed equilibrium configurations, and compare these light curves with those computed using the
Roche approximations. Finally, I will demonstrate how these models can be
used to infer the physical properties of observed Kuiper Belt binaries by fitting the observed light curve of QG298.
