My co-workers and I had a debate if there is an "orbital speed limit" for a given altitude over a celestial body. According to Kepler's laws it appears you cannot.
My co-worker proposed the following thought experiment to prove you could if you were also thrusting towards the planet. If you had infinite fuel, could you orbit around an arbitrary point in deep space (No gravity effects) with any given orbital radius? For example orbit a point going the nearly speed of light with a 1cm orbital radius as long as you had, and kept adjusting your thrust vector and had enough thrust to arrest and reverse your velocity.
We understand and agree if you turned you engines off you would fly away in a straight line.
However, I am under the impression that at any given speed you have a minimum orbital radius which you could never go under without slowing your orbital velocity down regardless if you are actively changing your thrust vector to achieve impossible natural orbits.
Am I correct?