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Cross section of a moving star

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A star of radius R and mass M is moving with velocity v through a cloud of particles of density rho.
If the particles that collide with the star are trapped by it, show that the mass of the star will increase at rate:

dM/dt = Pi * rho * v * (R^2 +2GMR/v^2)

Show how the cross sectional area compares with the geometric cross section of a hard sphere.

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