Checking the validity of hierarchical approximation for closer systems. In the first two rows the initial conditions were set to be the same as at the uppermost middle panel of Fig. 5, with the exception of P2 = 1000 (first row) and 2000 days (second row), i.e. a2/a1 ≈ 4.8 and ≈ 7.6, respectively, while the third and last rows have initial conditions similar to the bottom middle panel of Fig. 5, with the exception of P2 = 1000 (third row) and 952.7 days (last row). This latter illustrates the case of a 1:10 mean-motion resonance. The left panels represent a 20-year-long time scale, while the right ones show the TTV behaviour during a century. In the left panel of the last row the blue (quadratic) curve shows the O−C curve calculated by including a quadratic term. See text for details.
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