Current measurements and cosmological theories suggest that only about 4% of the total mas...
Current measurements and cosmological theories suggest that only about 4% of the total mass of the universe is composed of ordinary matter. About 22% of the mass is composed of dark matter, which does not emit or reflect light and can only be observed through its gravitational interaction with its surroundings (see Chapter 12). Suppose a galaxy with mass MG is moving in a straight line in the x-direction. After it interacts with an invisible clump of dark matter with mass MDM, the galaxy moves with 50% of its initial speed in a straight line in a direction that is rotated by an angle θ from its initial velocity. Assume that initial and final velocities are given for positions where the galaxy is very far from the clump of dark matter, that the gravitational attraction can be neglected at those positions, and that the dark matter is initially at rest. Determine MDM in terms of MG, v0, and θ .
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