The figure illustrates a Keplerian orbit, with Cartesian coordinates (x,y) and p
ID: 2102055 • Letter: T
Question
The figure illustrates a Keplerian orbit, with Cartesian coordinates (x,y) and
plane polar coordinates (r,?).
F = -(G*M*m)/r^2
The parametric equations for the orbit:
r(?) = a ( 1 ? e cos ?)
tan(?/2) = [(1+e)/(1-e)]^(1/2)* tan(?/2)
t(?) = (T/2?) ( ? ? e sin ?)
where ? is the independent, parametric variable; a, e, and T are constants.
I need to prove that the angular moment L is constant using the parametric equations. I know that in order for L to be constant, its derivative (net torque) must be 0, but this isn't really getting me anywhere. I know torque = rxF and L = rmv, but quite frankly I can't seem to figure out how to do this using the parametric equations.
Explanation / Answer
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