Locations and widths of secular spin–orbit resonances for the exoplanet HIP 41378 f for different parameters of a hypothetical moon. The moon is placed on its Laplace equilibrium plane at a fixed distance from the planet (see labels). The three resonances reachable appear in blue, red, and green. They correspond to the resonances labeled s₃, s₆, and s₁ by Saillenfest et al. (2023). The hatched blue zone is the E₁ region where the classic Laplace plane of the moon is unstable. The magenta circle highlights the fully relaxed state of the planet (ω = n_p and θ ≈ 0). Panel c additionnaly shows the black trajectory from Fig. 2: the system evolves from right to left; the moon is lost in the E₁ region, then the planet fully relaxes due to tidal dissipation.