JP

You raised a very relevent point ie the efficiency of the propulsion system, I had not considered this and had unconsciously assumed 100%, maybe Puck could use a photon drive or something similar

Even outside of the efficiency, you need to know something about the mass being ejected or its velocity. Since this isn't an energy conservation problem (the energy added to the orbiting body is zero!) you can't answer it by only knowing details about the orbits. Your answer could be zero (in the case BC talks about) or non-zero (in the case of a rocket engine providing the thrust). Because you can't get the energy from only knowing the orbit, you need to specify details about the source of the force holding Puck in place instead.

Let's check the 100% efficient rocket engine case, and assuming that the rocket fuel doesn't actually carry any mass away from Puck (which obviously is just an approximation). If he's shooting out particles with momentum, p, at a rate of N particles per second, then the force provided is pN. This isn't enough to answer the question unless you know something else, since you basically know the ejected momentum now, which is mv, but you can't get energy from this, since it's mv

^{2}/2. However, if you're assuming that you're ejecting photons, then you know that p=E/c for each photon, So...

pN=EN/c=F

_{grav}More interestingly, since c is a constant and F

_{grav} is constant for this particular orbit, that means that it's the product of E (energy per photon) and N (number of photons per second) that matters. You can eject more photons at lower energy or fewer photons at higher energy.

At any rate, the total rate of energy you're releasing here is EN, so in that case

EN=F

_{grav}c≈10

^{10} Joules per second per kilogram.