On page 125 of Moons and Planets, Problem 14 is about a planetesimal with radius R sweeping with velocity V through a swarm of smaller planetesimals. You can assume that the smaller planetesimals are distributed uniformly throughout space. Do this problem. All that I am really asking you to do is DRAW THE PICTURE of what is happening, and show how the relations presented in the problem come out of examining the picture. It is NOT quite enough simply to force the answer to have the right units - you have to think about where the pi comes from.

Part a: Ignore the notation dn/dt and just work with the right side of the equals sign. Think about the volume of space swept out by the planetesimal's area pi*(R²) in some time t. This requires careful thinking, but no difficult arithmetic.

Part b: Ignore the notation dM/dt and just work with the right side of the equals sign. Think about how the result of part a is modified when you consider the mass of each small planetesimal instead of just counting the collisions.

p.s. The first sentence includes the phrase "... of fixed size with velocity V, show that...". It is correct in the 4th edition; in the 5th edition the V has been left out.