In the previous chapter, we noted that galaxies in rich clusters are poor standard candles because they tend to grow brighter as they merge with other galaxies. Let's estimate the galaxy merger rate in the Coma cluster to see whether it's truly significant. The Coma cluster contains N≈1000 galaxies within its half-mass radius of rh≈1.5 Mpc. What is the mean number density of galaxies within the half-mass radius? Suppose that the typical cross-sectional area of a galaxy is Σ≈10−3 Mpc2. How far will a galaxy in the Coma cluster travel, on average, before it collides with another galaxy? The velocity dispersion of the Coma cluster is σ≈880 km s−1. What is the average time between collisions for a galaxy in the Coma cluster? Is this time greater than or less than the Hubble time?