A satellite in force free space sweeps stationary interplanetary dust at a rate of (dM)/(dt)=α v, where M is mass and v is the speed of satellite and alpha is a constant. The acceleration of satellite is

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(4) -(α v²)/M. The satellite picks up dust that was at rest, so the dust has to be accelerated up to the satellite's speed. The retarding force is the rate at which momentum is handed over: F=-v(dM)/(dt). Substituting the given rate, F=-v(α v)=-α v². Acceleration is that force divided by the satellite's mass. a=-(α v²)/M, the minus sign showing it is a deceleration.

A satellite in force free space sweeps stationary interplanetary dust at a rate of (dM)/(dt)=α v, where M is mass and v is the speed of satellite and alpha is a constant. The acceleration of satellite is

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