1. The problem statement, all variables and given/known data "Consider a perfectly homogeneous and isotropic universe filled with dust of uniform density ρ(t). Let universe expand, dust is carried radially outward from origin. Conservation of total energy E. E = K(t) + U(t) K(t) = (1/2)*mv^2(t) and U(t) = -GMm/r(t) where M = 4/3*∏r^3(t)ρ(t). Let E = -1/2*mkc^2s^2 with k a constant and s labelling a shell" 2. Relevant equations I am at loss as to where that last line came from. 3. The attempt at a solution From the information given it is easy to show that v^2 - 8/3*∏Gρr^2 = -kc^2s^2 and therefore determine what values of k allow a bounded or unbounded universe but I just don't get that last conclusion in the introduction.