Retarded Force in Space and interstellar dust

[whiztle]

Homework Statement

A uniform, spherical planet of mass M and radius R moves SLOWLY with an essentially uniform speed v through a cloud of interstellar dust particles, whose density is ρ. The dust particles are attracted towards the planet, and some of them would eventually fall onto its surface.

Find the resulting retarding force on the planet due to the dust cloud.?
Since the planet moves slowly, initial speed and final speed can be assumed to be the same

Homework Equations

Angular momentum => Li = Lf
Momentum => Pi = Pf
Energy including
Potential energy = GMm/R²
Kinetic Energy = 1/2 (mv²)

The Attempt at a Solution

The clue is to use conservation of momentum, angular momentum, and energy.
Solution should be in terms of speed v, radius R, mass M, and density ρ.

 

[diazona]

Hmm... well, the clue you give suggests that maybe this isn't what is intended, but are you familiar with this equation?
F = \frac{\mathrm{d}p}{\mathrm{d}t}
That's my first thought...