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BigD
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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/R
Kinetic Energy = 1/2 (mv2)
The Attempt at a Solution
I assumed the planet would consume all the dust within a circular cross section. By using conservation of energy and angular momentum, I got the radius of this circle to be
R' = (R^2 + 2RGM/v^2)^1/2
Then I used
dm = ρAdx = ρ(πR'^2)dx
to get
F = dp/dt = (dm/dt)v = ρπR^2(v^2 + 2GM/R).
I was told this wasn't right. Can someone give me a hint as to what I did wrong?