Hall's solution for Mercury's precession

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Hall's solution for Mercury's precession involves modifying the radius exponent in Newton's equation, suggesting that a slight increase in this exponent leads to precession. The discussion references a formula attributed to Bertrand, where the angle between the minimum and maximum radius vector is defined as θ = π / √(n+3), with n representing the exponent in the equations of motion. If n is set to -2, it aligns with Newton's law. The inquiry focuses on the implications of using an exponent slightly less than 2, raising questions about the resulting effects on orbital mechanics. Overall, the conversation highlights the complexities of adjusting the exponent in gravitational equations to understand precession phenomena.
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Hall showed that a slight increase in the radius exponent in Newton's equation would cause precession. What would the result be if the exponent was slightly less than 2.
 
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FWIW:
http://books.google.com/books?id=eQY-AQAAMAAJ&pg=RA1-PA49&cad=2#v=onepage&q&f=false

In which Hall gives a formula, attributed to Bertrand,

\theta = {\pi \over {\sqrt{n+3}}}

where \theta is the angle between minimum and maximum radius vector for an orbit of small eccentricity, and n is the exponent to be used in the equations of motion. He says, "If n = -2 we have the Newtonian law." So I imagine you can figure it out from there.
 
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Thanks for this. I must be thick, but I'm still a bit puzzled.
 
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