Hall's solution for Mercury's precession

[Shaw]

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.

 

[tfr000]

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.

 

[Shaw]

Thanks for this. I must be thick, but I'm still a bit puzzled.