Late evolution of the radius of our Sun-like stellar model and orbital parameters of an Earth-mass planet with an initial semimajor axis of 1.0 au. Top panel: stellar radius (red solid line) and orbital semi-major axis (green solid line) vs. time. Second panel: timescale for the damping of the orbital eccentricity τ_e vs. time (red solid line) computed according to Eq. (7) with ß = 1. Third panel: residual eccentricity 〈e² 〉^1/2 vs. time (red solid line) as computed from Eq. (45). Bottom panel: observed minus calculated time of midtransit 〈(O − C)²〉^1/2 vs. time (red solid line) computed according to Eqs. (61) and (77) over a time interval of 10 yr. The green line in the top panel and the plots in the second, third, and bottom panels are truncated at the time of the engulfment of the planet by the red giant star.