Answer to Question #302059 in Engineering for Harsh

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 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

Answer 1

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