3. A rich Abell Cluster is observed to consist of 1200 galaxies and a radial size R 7 Mpc. The average dispersion speed associated with the galaxies moving randomly in the cluster is estimated to be ~ 1500 km/s. Assuming that the average baryonic mass of a galaxy in the cluster is Mbar-gal~ 5 x 1011 Mo, estimate the minimum amount of dark matter needed within a radius R to maintain virial equilibrium for the galaxy cluster. (b) While travelling in a train, which is moving fast along a straight track, when we look outside through the windows, we see trees, lamp posts, etc. moving in the opposite direction with respect to the train in motion. But the Sun or the Moon on the sky appear to be stationary relative to us sitting inside the moving train. Why? (c) A natural satellite SEP of a hypothetical exoplanet EP1 (which is spherical in shape, has a solid crust and spins about its axis at a slow rate) goes around EP1 in a circular orbit. A future hypothetical astronomer, A1, lands on the equatorial region of EP1. Al observes that the satellite SEP keeps rising on the horizon of EP1 earlier on every subsequent 'exoplanet day', by a constant interval of time.