Hall's solution for Mercury's precession

1. Jan 10, 2014

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.

2. Jan 11, 2014

tfr000

FWIW:

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.

Last edited: Jan 11, 2014
3. Jan 11, 2014

Shaw

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

A An aqueos solution of $M^+X^-$ from Kubo's problems book Jan 6, 2018