Answer to Question #314935 in Astronomy | Astrophysics for ziad

Question

Assumethat a gravitational anomaly inthe solar systemhas shied a field 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:

Show that the slow-down ∆v of the Earth due to the asteroid collisions is given by:

∆v = v 1 − 1 + πR12dρMm 

Answer 1

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