Dependence of |$\Delta d_{\mathrm {SN}}$| on the total mass |$M_{\mathrm {plu}}$| of Plutinos, with |$e=0.25$| and |$A_{\mathrm {max}}=120^{\circ }$| in the three-arc model. The squares indicate the results from numerical computations, and the solid line denotes the prediction from equation (11). This figure illustrates good agreement between these two approaches. As in Fig. 6, |$\Delta d_{\mathrm {SN}}$| refers to the epoch of |$T=100$|⁠.