if we assume our desired orbit to be at an altitude of 320 kilometers and our orbital velocity to be 7 kilometers per second; and we assume that air resistance

if we assume our desired orbit to be at an altitude of 320 kilometers and our orbital velocity to be 7 kilometers per second; and we assume that air resistance decreases as a proportion of the cube of velocity inside the troposphere, proportional to the square of velocity inside the stratosphere, proportional to velocity inside the mesosphere, and discount air resistance above the mesosphere, we can begin to set up a differential equation to solve the problem. I'll be back, if anyone wants to follow along at home, post your answers when you are ready.