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**1. Homework Statement**

A spherical satellite of radius r is moving with velocity v through a uniform tenuous atmosphere of density ρ. Find the retarding force on the satellite if each particle which strikes it (a) adheres to the surface and (b) bounces off it elastically.

I know the answer should be: -ρAv

^{2}

**2. Homework Equations**

I am not fully sure one what equations are relevant but I am thinking, for part (a) conservation of momentum and for part (b) conservation of kinetic energy.

**3. The Attempt at a Solution**

For part (a):

This is what I tried but it did not really lead to anything that makes sense, maybe I set it up wrong or took a wrong approach?

Mv + dm(v - u)= (M + dm)(v - dv)

For part (b):

I intended to use the conservation of kinetic energy but I ended up getting confused on the set up of it.