Use momentum transfer to calculate rocket recoil and photon impulses.
Method and worked examples
A rocket transfers backward momentum to expelled material and gains forward momentum. For the craft-plus-exhaust system, neglect external impulse and conserve total momentum. Air is not required. An ion thruster accelerates charged propellant electrically; the outgoing particles carry momentum. Thrust is momentum transferred per time, so a small mass flow can give small thrust even at high exhaust speed.
Photons also transfer momentum. For normal incidence, absorption of incoming photon momentum p gives an ideal sail impulse p. Perfect reflection straight backward reverses the photon momentum and gives sail impulse 2p. Divide impulse by elapsed time for average force, or by craft mass for a small velocity change.
Example 1
A craft ejects 0.0200kg of gas backward at 1000ms−1 in a short interval. Estimate craft impulse in the initial craft frame.
The exhaust momentum is approximately −20.0kgms−1. Neglecting external impulse, the craft gains +20.0Ns. This short-interval model neglects the small craft speed change while gas leaves.
Example 2
An ideal incident light pulse carries momentum 3.00×10−6kgms−1. Compare absorbed and normally reflected impulses.
Absorption gives 3.00×10−6Ns. Perfect backward reflection gives 6.00×10−6Ns because the photon momentum reverses.
Watch out:They exchange momentum with expelled propellant and operate in vacuum; external air is unnecessary.
6. Rockets, ion thrusters and solar sails | Year 12 Physics | Ascent Arcade