Monday 20 July 2020

homework and exercises - Condition for circular orbit


I am a little confused about the condition for circular orbit. Goldstein's Classical Mechanics has the condition for circular orbit as $$f'=0\tag1$$ 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 $$f(r)=-\frac{l^2}{mr^3}\tag2$$ and the one of the equations of motion becomes $$m\ddot r=0\tag3$$ 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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