Question

A small spaceship whose mass is 1600 kg (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 13 kW laser beam, what speed will the ship attain in 5.0 days because of the momentum carried away by the beam?

Answer 1

The momentum of the light is equal (and opposite)to the momentum of the ship.

Momentum of light =   energy / c =   power * time / c

time is 1 day, or   86400 sec so

   momentum = 13000 W * 86400 sec / 3.0 x 10⁸ m/s =   3.744 kg m/s

This is also the momentum of the ship after one day so

   momentum = m v

3.744 =   1600 * v

   v = 0.00234 m/s =   2.34 mm/sec