Tidal decay and circularization of the orbits of short-period planets

We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of the semi-major axis and eccentricity of the relative orbit. For different types of planets, we compute the variations due to the planetary and stellar tides. We then calculate the critical value of the eccentricity for which the stellar tide becomes dominant over the planetary tide. The timescales for orbital decay and circularization are also discussed and compared