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SOLUTIONS TO EXERCISE 12
(a) The spread of velocities is best explained as peculiar velocities among the galaxies in the cluster - that is, the velocity added to the galaxies' motions by gravity. Peculiar velocities mimic the velocity caused by the expansion of the universe; so if they are not properly accounted for, the distance to each galaxy will be systematically wrong. The large spread suggests that the galaxies in Abell 2218 are interacting gravitationally; and some intermediate value of these peculiar velocities would indicate how much matter is actually contained within the cluster. (b) The escape velocity of any object from this cluster, at a distance of 1000 kpc, would be 2 * 6.67 * 10^(-11) * 2.4 * 10^43 kg v = sqrt(2GM/r) = sqrt(------------------------------------) 1000 kpc * (3.1 * 10^19 m/kpc) = 3.1 * 10^5 m/sec = 310 km/sec. (Remember that the above equation requires r in meters for that value of G.) Since this galaxy is moving 950 km/sec, this galaxy should in fact be able to escape the cluster's gravity, and would thus NOT be bound to Abell 2218. |