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This is something that really bothers me...First of all let me say that I know what the terms centripetal and centrifugal stand for.

What's the problem then?

The problem is that I've always read that the centripetal force is an actual force and that the centrifugal force is a fictitious one. Why does this bother me?

Let's say that a satellite orbits around a planet. Why doesn't this satellite fall towards the planet? You would say that it doesn't fall because of the centripetal/centrifugal force. ( I don't know which of the two terms I should use...That's why I am here...)

Now, if I say that the satellite doesn't fall because of the centripetal force I think I am saying something that doesn't make sense. Since the centripetal force is directed trowrds the center, the satellite should fall with greater speed towards the planet, since both centripetal and gravitational acceleration are directed towards the center.

If I say that the satellite doesn't fall because of the centrifugal force everything would look fine to me. Except for one thing. This force would be real and not fictitious.

To make things even more complex I think that the centripetal force is the force that actually doesn't exist and not the centrifugal one. Why? Because when there's something spinning it always moves away from the center. I can think about a lot of examples where there is the so called centrifugal force, but I can't think of anything when we talk about the centripetal force.

To me this centripetal force moves always away from the center...which is a paradox of course.

This thing is really counterintuitive to me, much more counterintuitive that the theory of relativity, which actually seems pretty logical once you think about it.

I am sure I am wrong about all this. That's why I need your help.

Thanks!