[markstock]

Yes, the author uses a globally-adaptive time stepper, which is only efficient for very small N. There are adaptive time step methods that are local, and those are used for large systems.

If you see bodies flung out after close passes, three solutions are available: reduce the time step, use a higher order time integrator, and (the most common method) add regularization. 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.

[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.