Word Problems/Physics

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Question
Thank you for taking my question. I am taking an AP Physics course and I thought of a really interesting question, but my regular-teacher is out sick this week with the flu. The substitute wasn't able to help much.

The question is:

I know that 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.  

Can you explain/clear up the apparent contradiction between a satellite changing speed in its orbit and the force that keeps it in motion. (Like I said, I'm only a Senior taking AP Physics, so please *slightly* dumb-down your answer)

Thank you for your time, Clark

Answer
The question is not stated correctly.  The speed increases the closer two objects get.
This also makes objects that are closer take lest time to orbit.

Consider the moon and the planets.  The moon is relative close object,
and it only take roughly 27 days.  

The planets orbital speeds are in
planetfacts.org/orbital-speed-of-planets-in-order
As can be seen here, the closer a planet is, the faster it needs to go.

In other words, there's no contradiction in logic -
speed and closeness are really the way we think they should be.  

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