Chaotic diffusion of obliquity for different physical parameters. The black trajectory is the same as in Fig. 8. At t = 4 Gyr (vertical bar), parameters are instantly changed and the system is integrated for 1 Gyr more (red part). Panel a: no parameter change. Panel b:the satellite no longer migrates. Panel c: the satellite migrates inwards. Panel d: the planet’s orbital variations are restricted to the 2nd harmonic of ζ. Panel e: the mass of the satellite is halved. Panel f : the mass of the satellite is zero. Panel g: the planet’s orbit is held fixed. Panel h: the planet’s orbit is held fixed and the satellite’s mass is halved. Panel i: the planet’s orbit is held fixed and the satellite’s mass is zero.