Level curves of the spin-axis precession rate of the planet as a function of its obliquity and the distance of its satellite. The simplified formula in Eq. (3) is used here with η = 20. Curves in the pink region connect ε = 0° to S₁. Curves in the blue region connect ε = 0° to ε = 0° again. Curves in the green region never go to ε = 0° but they connect to S₁. The mirror level curves exist for ε > 90° with reversed precession motion. The precession rate along the red level is Ω₀ = pη/2. The precession rate along the dark green level is Ω₀ = p; it connects (a, ε) = (0, 0°) to S₁. The dashed blue curve is the ridge line separating the close and far satellite regimes; it has expression . See Fig. 17 of Saillenfest & Lari (2021) for examples with other values of η.