(a) Use the idea of escape velocity to show that, to prevent the 
galaxies in the universe from moving outward forever, the average
density of the universe would have to be at least

             3 * H^2
  (rho) =  ------------  where H is the Hubble constant.
            8 * pi * G

(b) Using H = 70 km s^(-1) Mpc^(-1), convert H into units of s^(-1) and
compute (rho) in units of kg/m^3 and in units of hydrogen atoms per
cubic meter.

(c) The best measurements to date show that the mass density of the universe,
including dark matter, averages about two hydrogen atoms per cubic meter.
Does this mean that, by your calculations, the universe will collapse
upon itself or expand forever?