Example of tidal evolution of the planet HIP 41378 f and a hypothetical former moon. The mass of the moon is chosen to be m/M = 7 × 10⁻⁴. The moon migrates away at constant rate emulating a tidal parameter k₂/Q = 10⁻⁵. The trajectory of the system is shown in black; it goes from the leftmost to the rightmost point in about 1.3 Gyr. The available resonances are shown in pink, with their separatrices in red; they are labelled with the frequencies s_k of the corresponding modes (see Sect. 3). In this example, the resonances have the minimum possible widths according to the planets’ orbital elements in Table 1. In the hatched blue region, the moon is unstable (same as Fig. 1). The top axis shows the moon distance in unit of the planetary radius.