A satellite in force-free space sweeps statio | vedclass

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(A) The satellite is moving in force-free space,so the only force acting on it is the retarding force due to the accretion of dust.According to Newton

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$\frac{-\alpha v^{2}}{M}$

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(A) The satellite is moving in force-free space,so the only force acting on it is the retarding force due to the accretion of dust.According to Newton's second law,the force $F$ is equal to the rate of change of momentum: $F = \frac{d p}{d t} = \frac{d}{d t}(Mv)$.Since the satellite is moving at speed $v$ and collecting mass at a rate $\frac{d M}{d t} = \alpha v$,the retarding force is $F = -v \frac{d M}{d t}$.Substituting the given rate of mass change: $F = -v (\alpha v) = -\alpha v^{2}$.Using $F = Ma$,we have $Ma = -\alpha v^{2}$.Therefore,the acceleration $a = \frac{-\alpha v^{2}}{M}$.

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t} = \alpha v$,where $M$ is the mass,$v$ is the speed of the satellite,and $\alpha$ is a constant. The acceleration of the satellite is:

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