Reference frames adopted to define the true anomaly f and the rotational coordinates of the star φ and the planet ψ to express the Lagrangian of our star-planet system (see text for details). The relative separation of the barycenters of the two bodies isr = OO′. The rotational coordinate of the star is defined as the angle between the x-axis, the directionof which is fixed in an inertial space, and the principal axis of inertia of the star with respect to which the angle α in Eq. (6) is measured. A similar definition is adopted for the rotational coordinate of the planet considering ψ as the angle between the axis x′ parallel to x and the principal axis of inertia of the planet passing through its permanent quadrupole bulge (see text).