Illustration of the impact of the equilibrium planetary and stellar tides on the orbital evolution of a system represented through the timescales of migration and circularisation τ_e = (e/ė). The system evolves around the stellar model of Kepler 91 presented in Sect. 5. The initial mass of the planet is set at 0.88 Jupiter’s mass, its initial semi major axis is set at 0.10 AU, its initial eccentricity to 0.2 and k_2,p∆t_p is set at 10⁻² s. The upper panel illustrates the different timescales, the dashed lines correspond to the circularisation timescales while the solid lines represent the migration timescales. Each modified component of these timescales (planetary, stellar and their total) are represented namely in green, red and black. The lower panel correspond to the associated migration of the planet, the engulfment of the planet occurs at t_engulfment = 4.897 Gyr. Finally the shaded areas correspond to the different evolutionary phases of the star, in yellow the MS, in orange, the sub-Giant phase, and in red the RGB phase.