A satellite in force-free space sweeps stationary interplanetary dust at a rate of $dM/dt = \beta v^

Question

A satellite in force-free space sweeps stationary interplanetary dust at a rate of $dM/dt = \beta v^2$, where $M$ is mass, $v$ is the speed of the satellite, and $\beta$ is a constant. The deceleration of the satellite is

Professor PC Thomas Classes · Answer

Rate of change of mass $\frac{dM}{dt} = \beta v^2$. Retarding force $F = -v_{rel} \frac{dM}{dt} = -v (\beta v^2) = -\beta v^3$. Deceleration is $a = \frac{|F|}{M} = \frac{\beta v^3}{M}$.