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tokens: of different values of N and α. The 20 main simulations are divided into four sets with different orbital parameters e and Ω * . For each of these four sets, we have performed five simulations with different values of R * . We have performed the O1R39 simulation with N = 500 000 twice to investigate an unexpected effect of the numerical error in the angular momentum (see Section 4.3 ). The age at which the star reaches the desired radius is also included in Table 3 . Table 2. The initial parameters that we did not vary between the main simulations used in this work. The initial parameters that we did vary between simulations can be found in Table 3 . Table 3. The 20 main simulations used in this work and the initial parameters that were varied between them. For the three simulations in bold font, we also performed eight additional test simulations varying N and α (below table). 4.1 Tidal dissipation Before investigating the combined effects of tidal dissipation and mass-loss on the stellar orbit, we isolate the effect of tidal dissipation. We choose a simulation in which the stellar radius R * R Roche (model O0R37, see Table 3 ) so that mass-loss is negligible. In the absence of mass-loss, the change in the orbital parameters is dominated by the effects of tidal dissipation. In Fig. 5 we present the evolution of Ω * , a and e over a period of 5000 d (∼13 orbits). All simulations use the initial conditions of model O0R37 while we varied N (left-hand figure) and α (right-hand figure). It can be seen that for different values of these SPH parameters we find different values of . Figure 5. The long-term evolution through tidal dissipation of Ω * , a and e for model O0R37 with varying values of N and α. Dotted lines show the analytical solution for tidal dissipation (Hut 1981 ) with k / T ≈ 3( k / T ) Rasio . Different values of N and α result in a different radius of the relaxed SPH realization of the star. The analytical solution matching each simulation is therefore calculated with the effective radius of the SPH realization of the star in that simulation. The simulations with N = 100 000 and 200 000 are more computationally expensive and we have therefore decided to run them for only 2000 d. Note that the blue line in both plots is the same simulation. The difference in can be understood by taking the radius of the star into account. Because of the quantization approximations inherent to SPH, a different value of N can result in a slightly different hydrodynamical balance within the star. This difference, or even a different value of α, can result in variation of the radius of the SPH realization of the star after relaxation. Even a small change in R * can account for the differences in because (Hut 1981 ). While we do not include the physical processes that regulate tidal damping in our simulations, the artificial viscosity in SPH can cause dissipation. To interpret the results of our simulation, it is good to know how the time-scale of