一道关于角动量的题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 s

一道关于角动量的题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 s
一道关于角动量的题
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
一定要用到角动量，希望大家再努力想想
是ucla的入学考试题，我小妹在美国，老师只提示要用角动量，其他没说。我知道的就这么多。

一道关于角动量的题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 s
angular momentum...who is rotating?
I think what I did was right.refer to 3,angular momentum is a MAYBE,not a must.I used momentum,which is in the list as well.
Firstly,energy is NOT conserved,because there is impact dissipation.
Secondly,angular momentum is conserved,but not useful,because the system is symmetric and no fixed point for rotation.
Finally,momentum is conserved,and the only way I can think of is F=dp/dt for the force.and of course I could be wrong,so just for reference:
F=dp/dt=d(mv)/dt=v d(ρ pi R^2 L)/dt=v ρ pi R^2 dL/dt =v^2 ρ pi R^2
Here's the complete problem.
1.The problem statement,all variables and given/known data
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
2.Relevant equations
Angular momentum => Li = Lf
Momentum => Pi = Pf
Energy including
Potential energy = GMm/R2
Kinetic Energy = 1/2 (mv2)
3.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