parameter.

The $N$-body simulation of point-mass systems with a large number of particles poses several technical problems beside the necessary computing power. The difficulty comes from the wide range of the timescale. The critical separation of two particles at which we apply the KS regularization is about $1/N$. The timestep for particles involved is of the order of $1/(100N^{1.5})$. On the other hand, the timescale of the evolution of the system is of the order of $N$. Thus, the timesteps of particles that are integrated in KS formalism is $1/100N^{2.5}$ of the system time, which, for $N\sim 10^5$, about as small as the limit of double precision numbers. Note that this estimate is valid for a soft binary. A hard binary would require timesteps smaller by several orders of magnitude than described above. Of course, a clever treatment can overcome this kind of difficulties, but the amount of programming work and the complexity of the resulting code would be considerable. The simplest solution would be to use the longer number format ($e.g.$, the quadruple precision). This would have been a viable solution in ’70s, when mainframe machines could handle quadruple precision arithmetic reasonably fast. Unfortunately, most of present RISC computers 