[hermitcrab]

>Regularization (often called "softening") removes the singularity by adding a constant to the squared distance. So 1 over zero becomes one over a small-ish and finite number.

IIRC that is what I did in the end. It is fudge, but it works.

[markstock]

It is a fudge if you really are trying to simulate true point masses. Mathematically, it's solving for the force between fuzzy blobs of mass.

[mkoubaa]

You are never simulating pure anything. All computational models are wrong. Some are useful