In a question, I'm shown that the orbital time period of a satelite is given by a formula:
T = 4pi^2 (R + h)^3 / GM, where R = radius of planet, h = height above surface of planet
and I'm asked to use it to prove that the period of orbit around the earth cannot be less than 85mins.
Basically the way to answer this question is to sub in h = 0, and assume that the orbit is literally just above the the earth's ground.
However I was just thinking, why would this be sufficient proof, doesn't the actual speed of the satellite need to be taken into account?
surely time period of orbit would vary with a given distance from the centre of earth, depending on how fast the satellites are orbiting, for example isn't it theorectically possible to take less than 85mins to orbit the earth if the satelitte is powered by some sort of mega rocket engine?