If I put a flashlight in space, would it propel itself forward by "shooting out" light?
Yes, light has momentum and can generate thrust.
For example, https://en.m.wikipedia.org/wiki/Solar_sail
So if I had a flashlight in space and I turned it on, I could see it moving relative to me?
Yes, if you are in free fall and you turn on a flashlight and then let go of it, it will accelerate slightly. However, the operative word here is "slightly", as the force involved is extremely small - it's a good exercise to try calculating it for yourself, but for reasonable assumptions about the size and power of a flashlight I'm getting a micro-newton or thereabouts, which is well and thoroughly negligible.
The real appeal of light propulsion is that you can use a fixed power source to illuminate a solar sail, so the propulsion system doesn't have to accelerate itself and its fuel supply. You attach the sail to the payload, and then send it on its way using a powerful earth-based laser.
. . . or light from a nearby star.
Another advantage of light propulsion is that, if you use an on-board torch (X1000000, say), you are imparting momentum to your craft without using up any of its mass which is what always happens with a rocket engine. Even Ion Drive engines end up depleting their mass.
Ummm, shining a light out the back does deplete mass. The required energy has a mass equivalent.
relevant to thread;
True, in principle but there is a factor of c2 in there somewhere. Not sure where the photon momentum (hc/λ) would affect the effective ratio of ejected mass and ejected photons but the mass defect would still be tiny.
Yes, but there is a trade-off. The thrust per unit energy is also tiny.
The sweet spot for exhaust velocity depends on the energy density of your fuel. A photon drive is in the sweet spot for an antimatter fuel source. With less energy density than that, a lower exhaust velocity is better -- eject the expended fuel as reaction mass.
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