Sweeping Satellite in Dust Cloud

MediumPhysElo Quiz #2

11.Sweeping Satellite in Dust Cloud

+10

A satellite of initial mass

m_0

is in a circular orbit of radius

R

around a star of mass

M

. The satellite travels through a vast cloud of dust that is stationary relative to the star. The satellite has a scoop of cross-sectional area

A

facing its direction of motion, and it sweeps up and retains all the dust it encounters. The dust has a uniform mass density

\rho

. The satellite's engines provide a thrust force to keep the satellite in exactly the same circular orbit at a constant speed. What is the magnitude of the thrust force provided by the engines as a function of time

t

after entering the dust cloud? (Assume the mass of the swept dust is much less than

M

, and neglect the self-gravity of the dust cloud).

\frac{1}{2} \frac{\rho A G M}{R}

\frac{\rho A G M}{R}

\frac{\rho A G M}{R} + \frac{m_0 G M}{R^2}

\frac{\rho A G M}{R} + \frac{\rho A t}{R} \left(\frac{G M}{R}\right)^{3/2}

\frac{m_0 G M}{R^2} + \frac{\rho A t}{R} \left(\frac{G M}{R}\right)^{3/2}

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