that they are point mass objects and the only force acting between them is Newtonian gravitation, i.e. tidal dissipation is neglected. This will be our second physical model. In all cases we consider point (constant) mass objects orbiting in a conservative system; therefore, relativistic effects are ignored.

To ensure that the code used in this study was appropriate for the task, a significant amount of testing was performed and its numerical integrations have been validated against publicly available results obtained by other authors using other algorithms and physical models. Following Varadi, Runnegar & Ghil (2003), we also estimated the actual integration errors by computing the same orbits with the same physical model but with two different step sizes (or, more properly, blocks of them). In the predictor-corrector algorithm embedded into the Hermite scheme, the overall “step size” is controlled by an input amount called the time-step convergence parameter for total force polynomials, $\eta$, which is a dimensionless accuracy parameter (Aarseth 2003). For values of $\eta$ in the range 10$^{-5}$-10$^{-7}$, the results (and the integration errors) are similar but the error in the total energy is minimal for $\eta$ = 1$\times10^{-6}$. Then, relative errors in the total energy are as low 