Assume that a gravitational anomaly in the solar system has shifted a field of asteroids into Earth’s orbit, and the field is no
w moving directly towards Earth. The asteroid field has a density of rho (asteroids/volume), and each asteroid has an average mass of m. The asteroid field stretches over a distance d in Earth’s path. Assume that the Earth moves with a velocity of v, the asteroids with u, and that be the radius of the Earth. The Earth collides with the asteroid field: Show that the slow-down ∆v of the Earth due to the asteroid collisions is given by:
