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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 potential energy 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.

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.