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{"ops":[{"insert":"Assume that a gravitational anomaly in the solar system has shi\u001ced afield of asteroids into Earth\u2019s"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"orbit, and the field is now moving directly towards Earth. The asteroid field has a density of \u03c1"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(asteroids\/volume), and each asteroid has an average mass of m. The asteroid field stretches"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"over a distance d in Earth\u2019s path. Assume that the Earth moves with a velocity of v, the asteroids"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"with u, and that v \u001d u. Let R be the radius of the Earth. The Earth collides with the asteroid field:"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"v u"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Show that the slow-down \u2206v of the Earth due to the asteroid collisions is given by:"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"\u2206v = v"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"\u0012"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"1 \u2212"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"1"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"1 + \u03c0R2d\u03c1 m"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"M"},{"insert":"\n"}]}

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