Earlier quoted context omitted.
One way of doing that is by each time step delta perform two integrations, one which give you x_1, and another x_2, with different accuracies. The error is estimated by the difference |x_1 - x_2| and you make the error match your tolerance by adjusting the time step. Naturally, this difference becomes big when two objects are close together, since the acceleration will induce a large change of velocity, and a lower t…
I have run into the problem where a constant time step can suddenly result in bodies getting flung out of the simulation because they go very close. Your solution sounds interesting, but isn't it only practical when you have a small number of bodies?
Optimistic fixed time steps are just going to work well almost always and almost everywhere, accumulating errors behind your back at every episode of close approach.