The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely provides the centripetal force needed for the rotation. (why? )
(a) show that the corresponding shortest period of rotation is t = √3π/grho, where rho is the uniform density (mass per unit volume) of the spherical planet.
(b) calculate the rotation period assuming a density of 3.0 g/cm³, typical of many planets, satellites, and asteroids. no astronomical object has ever been found to be spinning with a period shorter than that determined by this analysis.