In order to accommodate a flat rotation curve, a density profile for a galaxy and its environs must be different than one that is centrally concentrated. Newton's version of Kepler's Third Law implies that the spherically symmetric, radial density profile ρ (r) is: ρ ρ ( r ) = v ( r ) 2 4 π π G r 2 ( 1 + 2 d log ⁡ ⁡ v ( r ) d log ⁡ ⁡ r ) where v (r) is the radial orbital velocity profile and G is the gravitational constant. This profile closely matches the expectations of a singular isothermal sphere profile where if v (r) is approximately constant then the density ρ ∝ r to some inner "core radius" where the density is then assumed constant. Observations do not comport with such a simple profile, as reported by Navarro, Frenk, and White in a seminal 1996 paper.