In Symon's book 'Mechanics', he writes that for a body of mass m and angular momentum L in an orbit that does not intersect itself (i.e. a(adsbygoogle = window.adsbygoogle || []).push({}); simplecurve), the period of revolution T is related to the area A of the orbit by

[tex]T=\frac{2Am}{L}[/tex]

Is this exact as he seems to be implying? It seems to me that the correct formula would be obtained by considering the area S of a section of circle, and saying that the area of the orbit is related to the period of revolution by

[tex]A=\int_0^T \frac{dS}{dt}dt = \int_0^T \frac{1}{2}r^2 \frac{d\theta}{dt}dt + \int_0^T \theta r\frac{dr}{dt}dt = \frac{L}{2m}\int_0^T dt + \int_0^T \theta r\frac{dr}{dt}dt = \frac{LT}{2m} + \int_0^T \theta r\frac{dr}{dt}dt[/tex]

Am I missing something?

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# Period of simple orbit in central potential

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