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Fig. 11

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Some possibilities for the long-term evolution of the GJ 163 planetary system over 1 Myr, including tidal effects with Δtp = 105 s. Time scales are inversely proportional to Δt (Eq. (4)), so 1 Myr of evolution roughly corresponds to 1 Gyr with Δtp = 100 s (Qp ~ 103) or 10 Gyr with Δtp = 10 s (Qp ~ 104). We show the ratio Pc/Pb of the orbital periods of the two inner planets (top) and their eccentricities eb (red) and ec (green) (bottom). We use three different sets of initial conditions: Table 2 (left); Table 2 with ac = 0.060679 and Δtc = 5 × 107 s (middle); Table 4 (right).

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