I am a little confused about the condition for circular orbit. Goldstein's Classical Mechanics has the condition for circular orbit as f′=0 where f′ is the effective force. I understand that the reason for this requirement is that the corresponding V′is at an extremum. However, setting f′=0 yields f(r)=−l2mr3 and the one of the equations of motion becomes m¨r=0 This can't be right as it is saying that the net force on the object is zero, and yet the object is supposedly in a circular orbit. Am I interpreting equation (3) wrong?
Answer
In the coordinate frame where the satellite is at rest, there is also a centrifugal force which balances the central force.
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