2. (100) Galactic rotations don't match what we understand about Newtonian gravity based on the visible sources of mass (the stars) within the galaxies. This is one of the motivations to believe in dark matter - something that has no light signature that nonetheless contributes to the gravitational attraction within galaxies. For the sake of this problem, suppose the following: A spherically-symmetric galaxy (not common) has stars from the nearest to the core to the farthest from the core, all orbiting with the same period. If we assume the galactic mass density (made of stars) to be like a continuous fluid with density p, what functional form must p(r) have in order for this to work out? T is the, distance from the galactic core. Please comment on physical implications of the functional form you arrive at