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noospace
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Homework Statement
Consider the following parametrization of an orbit in polar form,
[itex] \ell u = 1 + e \cos[(\phi -\phi_0)\Gamma][/itex]
where u = 1/r.
I'm trying to find the shift in the angular position of the periapsis after one complete orbit.
The Attempt at a Solution
Choose axes so that the point of first closest approach is [itex]\phi_0[/itex].
[itex] u'(\phi) = - \Gamma e \sin[(\phi -\phi_0)\Gamma][/itex]
Setting [itex]u'(0) =0[/itex] we obtain
[itex] (\phi -\phi_0)\Gamma = n \pi[/itex] where n is an integer.
So after one complete orbit I guess the shift is [itex]\Delta \phi = \phi - \phi_0 = \frac{\pi}{\Gamma}[/itex], or should that be [itex]\frac{2pi}{\Gamma}[/itex]?
Thanks.