A photon rocket is a hypothetical rocket that uses thrust from emitted photons (radiation pressure by emission) for its propulsion.
Contents
Photons could be generated by onboard generators, as in the nuclear photonic rocket. The standard textbook case of such a rocket is the ideal case where all of the fuel is converted to photons which are radiated in the same direction. In more realistic treatments, one takes into account that the beam of photons is not perfectly collimated, that not all of the fuel is converted to photons, and so on. A large amount of fuel would be required and the rocket would be a huge vessel.
In the beamed laser propulsion, the photon generators and the spacecraft are physically separated and the photons are beamed from the photon source to the spacecraft using lasers.
In the photonic laser thruster, collimated photons are reused by mirrors, multiplying the force by the number of bounces.
Speed
The speed an ideal photon rocket will reach, in the absence of external forces, depends on the ratio of its initial and final mass:
where
The gamma factor corresponding to this speed has the simple expression:
Derivation
We denote the four-momentum of the rocket at rest as
squaring both sides (i.e. taking the Lorentz inner product of both sides with themselves) gives:
According to the energy-momentum relation (
We can now solve for the gamma factor, where beta represents the change in speed relative to the initial rest frame, by noting that the two four–vectors are:
As we start in the rest frame (i.e. the zero momentum frame) of the rocket the final–four vector is
with P being the final momentum vector. Therefore, taking the Minkowski inner product (see four-vector), we get the following after rearranging: