Suppose that the force of attraction between the sun and the earth is(adsbygoogle = window.adsbygoogle || []).push({});

[tex] F = GMm(\frac{1}{r^2} + \frac{\alpha}{r^3}) [/tex]

Where [tex] \alpha [/tex] is a constant. Show that the orbit does not close on itself but can be described as a precessing ellipse. Find an expression for the rate of precession of the ellipse

First, of all what is a precessing ellipse?

I'm working in polar coordinates [tex] r, \theta [/tex]. Assuming that the sun does not move and is fixed at the orgin of the coordinate system, the equation I get is

[tex] u= \frac{1}{r} = \frac{GMm^2}{L^2}(1+e\cos( A^\frac{1}{2} (\theta - \theta_{0}))) [/tex]

Where [tex] A= (1-\frac{GM \alpha m^2}{L^2}) [/tex]

So how do I show the above parametric equation (if it is correct) describes a precessing ellipse?

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# Central Forces

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