In scientific simulations involving multiple particles, the energy is
achieved by specifying not the force between particles, but the energy
potential field around them. The force is then derived from the derivative
of this field. This can stop simulations going off to infinity, because one
can calculate the total energy of the system and then scale the velocities
of the particles appropriately so that the total energy is exactly what it
was at the start of the simulation.


proportional to -1/r. This is the formula to put into the energy calculation
when summing the potential energies.

Obviously there are still errors here - the "scaling" is just a cheat (has
no physical basis), but at least the error is spread through all the
particles, which have slightly different speeds, rather than in only one
particle which shoots off at a totally unrealistic speed.

-Chris

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