Reference frames used in the coordinate transformation, with the star given by the orange circle, the planet indicated by the red circle, and its orbital path shown in red. The planet’s reference frame {x_pl, y_pl, z_pl} (in red) contains the orbital plane of the planet x_ply_pl and orbital spin axis along z_pl. The observer’s inertial reference frame {x_obs, y_obs, z_obs} (in blue) is centred on the star, with the observer located at +x_obs and the stellar rotation axis aligned along z_obs. The reference frame {x_⋆, y_⋆, z_⋆} (in black) co-rotates with the star. The spin-orbit angle is Ψ.