Galaxy mergers in a rich cluster could impede their use as standard candles over time as they tend to brighten. The Coma cluster of galaxies contains N ~ 1000 galaxies within its half mass radius of rh ~ 1.5 Mpc.
a) What is the mean number density of galaxies within the half mass radius? Suppose the typical physical cross section of a galaxy is sigma ~ 10^-3 Mpc^2.