Chapter 41: Problem 44

Question: A small spaceship whose mass, with occupant, is $M=1500~{\rm kg}$ is drifting in outer space, where the gravitational field is negligible. If the astronaut turns on a $P~=~10.0~{\rm kW}$ laser beam, what speed would the ship attain in one day because of the reaction force associated with the momentum carried away by the beam?

Solution: The force arising from the laser beam is

$$\vert F\vert~=~{P\over c} \ \ \ ,$$ (20)

which leads to an acceleration of |a|=F/M, and hence a change in velocity of $\vert\Delta v\vert=(\Delta t)F/M$ during a time interval $(\Delta t)$, hence

$$\vert\Delta v\vert~=~(\Delta t) {P\over c M }~=~ 2\times 10^{-3}~{\rm m/s} \ \ \ .$$ (21)