Thanks for taking my question. I'm taking AP Physics, and I recently came across a slightly-puzzling situation I was hoping you could clear up for me, as I am confused on this topic; I normally do really well in Physics, otherwise. My teacher is out sick with the flu this week, the substitute wasn't very helpful.
I know the speed of an object in circular motion is related to the amount of force needed for that motion. I also know that the force of gravity is the source of the centripetal force on a satellite in motion. If a satellite increases speed it goes to a higher orbit, if it loses speed it goes to a lower orbit. This seems to contradict the force on the satellite since lower orbits would have a larger gravitational force.
I was hoping you could explain this apparent contradiction between a satellite changing speed in its orbit and the force that keeps it in motion.
I reviewed my textbook and asked a friend, but I couldn't get any great answers; can you explain why this is? (Like I said, I'm a Senior taking AP Physics, so you might have to dumb it down *slightly*).
Thank you very much, I genuinely appreciate your help.
When the satellite goes into a higher orbit, it will be going against gravity. Therefore, it will actually lose energy/speed until it's settled into an orbit where the forces are balanced again. This makes shunting satellites tricky, you can't just fire a rocket for five seconds to give one a different orbit or the orbit becomes elliptical. So you slowly fire the rocket, and the change in gravitational energy is balanced by the energy of the rocket motor. It all works out, but it *does* seem counterintuitive on the face, so let me go through the higher-orbit thing.
You fire your rocket (or ion thruster) slowly to speed the satellite up. It will, indeed move to a higher orbit. But imagine if you *did* just fire it for a few seconds. It would be knocked into an elliptical orbit that would take it further away from Earth, where it has a component of motion straight away from the Earth. That will rob it of energy. No matter how you fire it, if you're increasing the orbital distance, there's a component of velocity away from the Earth (if there was none, the orbit would remain perfectly circular by the definition of a circle). Gravity will work against this component of velocity, and the satellite will lose energy/speed. So by carefully spiraling outward, you're giving gravity the chance it needs to slow the satellite down for the higher orbit. Too much, and you escape.
Circular orbits are simple, changing them is actually quite tricky. :)