QUESTION #523

# If a spacecraft was fitted with a laser would the photons emitted push the craft upwards as in the solar sail or beamed energy propulsion concepts?

First, let me say that you do not _really_ need a laser to achieve this effect; any strong source of light could be used to the same effect. A laser differs from ordinary light because it is coherent light, but that is pretty much irrelevant for propulsion purposes.

Second, I want to compare a 'photon engine' to a regular 'exhaust gas' rocket engine, in terms of efficiency. Note that in a rocket-propelled spacecraft, the exhaust gases are moving nowhere near relativistic speeds with respect to the spacecraft. Therefore we can use classical mechanics to analyze that situation. On the other hand, the proposed photon engine is patently relativistic, so we will treat that relativistically.

For propulsion, all that we care is how much _momentum_ (denoted p) we can gain for the energy (denoted E) we spend. I will assume an ideal rocket, where all the molecules moving in the same direction. In this case, the energy of the gas is given by:

E = 1/2 m v2

The momentum of the gas is

p = m v

which is also the momentum that will be transferred to our spacecraft once this gas is exhausted. The quantity p/E which is a sort of efficiency is:

p/E = 2/v

So, the efficiency of our energy use is inversely proportional to the gas speed we use. The faster you exhaust the gas, the faster you accelerate, but the more wasteful you are in terms of energy. So, if you have a lot of time, it is best to exhaust gas at small speeds over a long time to use the energy efficiently to gain momentum.

For photons the situation is different, they always move at the speed of light. The energy-momentum relationship for a photon is:

E = pc

Thus, our efficiency figure is:

p/E = 1/c

Once again, it is inversely proportional to speed, but this time this is the speed of light we have here. And that is quite a large number (3x108 m/s) compared to gas exhaust speeds. Thus, our efficiency is way smaller compared to a gas exhaust rocket engine. (As a side note, having a 1 here instead of the 2 is due to the effect of relativity.)

So is a photon engine totally useless? Well, maybe not, because 'matter' is conserved (well, more or less), while photons can be created out of nothing... But you still need energy.

So how is this different from a solar sail? Not much, except that in a solar sail you are not supposed to be generating the energy, you just use the photons from the sun. However if you collected that energy, and used it to throw massive (as opposed to massless, not to mean heavy) particles out of the spacecraft you could do much better. Then again, you will inevitably run out of things to throw at some point... Hard to create a win-win situation in a spacecraft!
Answered by: Yasar Safkan, Ph.D., Software Engineer, Noktalar A.S., Istanbul, Turkey