The idea is to modify Newtonian gravity so that it fits measurements of orbits around the sun. For example the precession of Mercury's orbit unlike Newtonian $n$-body simulations.

I'm currently not using this in any serious simulation, but I'm just wondering because it'd simplify approximations a lot.

The modified formula for the force I found about half a year ago after googling was similar to this one: $$F =\frac{Gm_1m_2}{r^2} + \frac{Gm_1m_2B^2}{r^4} = \frac{Gm_1m_2}{r^2} (1+\frac{B^2}{r^2})$$

Similar means that I lost the link which I was unable to relocate and this is the only thing I wrote down elsewhere. $B$ stands for the dot product of velocity and unit vector pointing at the other object if I remember right.

This all sounds rather vague and arbitrary. Thus I'm asking whether anyone knows of something like this and the explanation behind it.