  Gravitational and electronic forces produce a correlation between the mass
and shape of objects in the universe. For example, at an average radius of ~
200 km - 300 km, the icy moons and rocky asteroids of our Solar System
transition from a rounded potato shape to a sphere. We derive this
potato-to-sphere transition radius -- or "potato radius" -- from first
principles. Using the empirical potato radii of asteroids and icy moons, we
derive a constraint on the yield strength of these bodies during their
formative years when their shapes were determined. Our proposed ~ 200 km potato
radius for icy moons would substantially increase the number of trans-Neptunian
objects classified as dwarf planets.
