# Is there any recoil from turning on a flashlight?

Going from an “equal and opposite reactions” standpoint, is there any recoil when you turn on a flashlight and send a stream of photons shooting out? I’m guessing that there probably is – albiet it’d be a bilionth of a billionth of a Newton (or whetever unit you’d measure flashlight micro-movement with).

Also: if I were to click on a magic Maglite (which has magic batteries that never run out and a bulb that never burned out) in a vacuum, in the middle of deep space, would the power of the beam ever be able to counteract the flashlight’s intertia and send it moving?

Yes, photons have momentum p=h/lambda, where h = 6.62 x 10[sup]-34[/sup] Joule-seconds, and lambda is the wavelength of the photon. So, as soon as you turn on the flashlight, you are shooting little packets of momentum out. Doing this exerts a reactive force on the flashlight and thus on you.

One nice thing about photons is that their energy is strictly proportional to their momentum. Specifically, the energy of a photon is p*c, where c is the speed of light. Additionally, the force exerted by the beam of photons (or the reaction mass of any rocket), is just the momentum change per unit time. In this case, that would be the total light output power divided by the speed of light.

So, assume that we’re using a flashlight that puts out 1 Watt of light power. The momentum change per unit time is thus 1 Watt/(10[sup]8[/sup] m/s)=10[sup]-8[/sup] Newtons.

So, if you’re out in space with this flashlight thruster, and you and your super-lightweight spacesuit weigh about 100 kg, your acceleration is 10[sup]-10[/sup] m/s[sup]2[/sup], or 1 Angstrom per second per second. At this rate, you’ll be moving at 10 cm/s after about 30 years of acceleration.

Geez, I hope I got those orders of magnituder right.

Rick

Oops, the denominator there should be 3 x10[sup]8[/sup], so the force is actually approximately 3 x 10[sup]-9[/sup] Newtons. So, after 30 years you’re only going about 3 cm/sec.

Apparently I didn’t.

Rick

You can never overcome intertia… No matter what you do, it’s always there. However, you don’t need to overcome it, either. If you exert one microNewton of force on a one kilogram object for one millisecond, then your object will be moving at one nanometer/second. At that rate, it’ll take quite a while to build up any significant speed, but any force applied for any period of time will produce some change in speed.