Long-term integrations of orbital and rotational parameters of some transiting planets and their host star. Tidal quality parameters Q′ and Q′ _p are initially set to 10 ⁶ but vary with the semimajor axis as Q = Q _p = 1/( nΔ t) where Δ t is a constant tidal time lag. (a) Semimajor axis of OGLE-TR-132b, HD 209458b (solid lines), and eccentricity of HD 209458b (dashed line) as a function of time. The thin dashed line is the usual exponential damping approximation of e with a 4.1 × 10 ⁸ yr relaxation time assuming that only tides raised on the planet are considered and stable tidal equilibrium states exist; (b) rotational periods of HD 209458, HD 209458b (solid lines), and HD 209458's obliquity (dashed line) as a function of time. The initial rotational period of HD 209458b and HD 209458 stellar obliquity are arbitrarily set to half a day and 20° to evaluate the respective timescales of their tidal evolution.