The jeans equations: (a) consider the dark matter density profile p(r) (5) 4πgr2 which gives rise to constant rotation curves mal" and isotropic suppose that the dark matter is "isother- so that the 1d velocity dispersion o2 = a^0,d the jeans equation analog for "hydrostatic equilibrium" in spherical coordinates and =const. wvrite down v2/2 for this system show o2 galaxy at large radius r 3.5, but they contribute mass to the system. again using the jeans equations (but using gravity set (b) next consider their distribution is approximately spherical with p. c population of stars which orbit the same a negligible by the dark matter of equation 5), solve for o2