We consider the application of interferometry to measuring the sizes and shapes of small bodies in the solar system that cannot be spatially resolved by todays single-dish telescopes. Assuming ellipsoidal shapes, our results indicate that interferometers can measure the size of an object to better than 15% uncertainty if the limb-darkening is unknown. Assuming a Minnaert scattering model, one can theoretically derive the limb-darkening parameters from simultaneous measurements of visibilities at several different projected baseline lengths to improve the size and shape determination to an accuracy of a few percent. With a 3-D shape model for the dwarf planet Haumea, we demonstrate that when photometric light curve, visibility light curve, and visibility phase center displacement are combined, the rotational period and sense of rotation can all be derived, and the rotational pole can be estimated. Because of its elongated shape and the dark red spot, the rotation of Haumea causes its optical photocenter to move in a loop on the sky, extending of ~80 muas without the dark red spot, and ~200 muas with it. Such movements are easily detectable by space-based astrometric interferometer designed e.g. for planet detection. As an example, we consider the possible contributions to the study of small bodies in the solar system by the Space Interferometry Mission. We show that such a mission could make substantial contributions in characterizing the fundamental physical properties of the brightest Kuiper Belt Objects and Centaurs as well as a large number of main belt asteroids. We compile a list of Kuiper Belt Objects and Centaurs that are potentially scientifically interesting and observable by such missions.
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