Answer to Question #339932 in Engineering for Nadim

Question

Assume that a gravitational anomaly in the solar system has shied afield of asteroids into Earth’s orbit, and the field is now moving directly towards Earth. The asteroid field has a density of ρ (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 v  u. Let R be the radius and M the mass of the Earth. The Earth collides with the asteroid field: v u Show that the slow-down ∆v of the Earth due to the asteroid collisions is given by: ∆v = v  1 − 1 1 + πR2dρ m M