Could a large panel of LEDs be used for station keeping in earth orbit?

Question

Hall effect and other ion thrusters require propellant to operate and thus have a limited usable lifespan in orbit.

In typical operational use, the force they produce is in the 25mN - 250mN range. It's not much, but it is enough to do station keeping for satellites.

We know photons have momentum and we also know that LEDs can produce photons from electricity. No propellant needed, just electricity.

I attempted to do some calculations, but my high school physics from a couple of decades ago has failed me. Here are some of the assumptions I was working with:

• The smallest wavelength for commercially available LEDs is about 250nm.
• The momentum of a photon at 250nm is ~$2.65×10^{-27}$ N•s
• Ion thrusters typically have a power range of 1-7kW, so assume that is the power available to an LED panel.

My questions are:

1. How large/powerful would an LED panel need to be replace a 100mN ion thruster on a satellite?

2. If even doable, would this give the satellite an effectively unlimited lifespan, assuming no other parts failed?

3. Are there better/more efficient light sources that would make this feasible? A photon's a photon's a photon, so I suspect not.

Answer 1

The relation between energy and momentum for electromagnetic radiation is $$E = pc$$ where $E$ is the energy, $p$ the momentum, and $c$ is the speed of light.

So the relation between force $F$ provided by a beam of light with power $W$ is $$W= Fc.$$ ​ You chose a force of 100 mN. I'm supposing that means micro Newtons, or $$100 \times 10^{-6} \text{ Newtons} = 10^{-4} \text{ Newtons.} $$

So the power you require is $$ W = 10^{-4} \text{ Newtons} \times c = 3 \times 10^{4} \text{ Watts.}$$ Note that this is the power that must be in the light, not just the power provided to the LEDs. If they were 33% efficient, you would need three times that in electrical power. Also note, if mN meant milli-Newton rather than micro-Newton, you would need 1000 times more.