Level curves of the Hamiltonian function with e = 0 plotted on the sphere. The z-axis is along the spin axis of the planet. The x-axis is along the intersection of the equatorial and ecliptic planes (i.e. the line joining both equinoxes of the planet) and directed towards the ascending node of the star. The equator xy plane and the ecliptic plane are highlighted by the two outer grey circles. A point on the sphere represents the tip of the orbital angular momentum of the satellite, which has coordinates (x, y, z) = (sinI_Q sinδ_Q, −sinI_Q cosδ_Q, cos I_Q). The colour code is the same as in Fig. 1. Panel a: same parameters as Fig. 1. Panel b: parameter region S₁, defined by a∕r_M = 1 and ε = 90°. The magenta curve is made of an infinity of stable equilibria resulting from the merging of P₁ with the separatrix emerging from P₃. Panel c: parameter region S₂, defined by a∕r_M > 0 and ε = 0° (or 180°). The brown curve is made of an infinity of stable equilibria resulting from the merging of P₂ with the separatrix emerging from P₃.