# Achieving relativistic speeds with the use of lasers

Basically, were using a laser as an engine.

1. Mass: 1000 tons.
2. Electrical power for the laser: 10 GW.
3. Efficiency of the laser(s) : 50%.

So first I calculated the kinetic energy the laser would give to the ship:

$$E = P \cdot t \cdot L_e$$

where $$P$$ = electrical power, $$t$$ = time, $$L_e$$ = laser efficiency (0.5).

Then based of that I calculated velocity:

$$v = \sqrt{\frac{2E}{m}}$$

If these calculations are correct, a 1000 ton ship will reach 6000 m/s after 1h of acceleration using that engine.

The 10GW could be generated by a fusion reactor e.g.

The reasons why I wouldn't use the fusion reactor directly as an engine is:

1. the nuclear waste it produces, so we couldn't use it around Earth;
2. the exhaust velocity isn't $$c$$, the max top speed will be lower than 0.999$$c$$.

My question is, if my calculations are correct, and if my assumption of using the nuclear reactor as an engine directly will result in a lower top speed?

And is this engine a good option for reaching relativistic speeds?

• A nuclear powered photonic rocket has a Max speed: en.m.wikipedia.org/wiki/Photon_rocket Dec 8, 2018 at 0:17
• Fusion reactors don't produce nuclear waste. Dec 8, 2018 at 1:02
• @RussellBorogove well it really does. D+D makes radioactive tritium, and both D+D and D+T make fast neutrons which make "other stuff" radioactive. D+3He doesn't do either but it is hard to suppress D+D also occurring in parallel that mixture.
– uhoh
Dec 8, 2018 at 10:29

For propulsion you have to think momentum rather than energy. In this case almost all of the optical energy output of the laser remains in the emitted photons. Whomever is unlucky enough to find themselves in that beam will tell you that, just before they vaporize!

So what's the momentum of a photon? Since photons don't have rest mass, a photon with energy $$E$$ has momentum $$E/c$$.

Thrust, which is momentum per second, would be energy per second (power) divided by $$c$$, or $$P/c$$ where $$P$$ is power in watts.

If you have 5 GW of laser power then thrust would be $$\frac{5 \times 10^9}{3 \times 10^8} = 16.7$$ newtons. Yep, it's very tiny.

You can then get your acceleration from $$F=ma$$$$a=F/m$$ which is tiny, but after months or years can add up. Final velocity would be $$v=at$$ after a time $$t$$ in seconds.

So in two years you get a little past 1 kilometer/second.

I'll leave that up to you if it's good or not for your application. If you don't mind waiting ten thousand generations, then this might be fine.