Show that keplerian rotation implies ~ ~ r-1/2. use kepler's third law: p2 ~ ay and assume perfectly circular orbits (i. e. write the rotation speed in terms of p and a) (b) show that a spherically symmetric mass distribution with constant density gives solid body rotation (v = const x r). (set the centripetal force on a star in a circular orbit equal to the gravitational force on that star and substitute for m in terms of the uniform density.)