to estimate the quality factor in the case of the jovian planets as long as semi-diurnal tides dominate. As the planet tends toward synchronization, the dissipative effects of the semi diurnal tides ($\sigma=2|\op-~n|$) vanish with their frequency. Then, the most dissipative tides are the eccentric annual tides ($\sigma=n$) and $$\label{QforExo}
Q_{\mathrm{p}}'^{-1}\approx \frac{2}{3}k_2\Delta t\, n.$$ Apart from these two limit cases, no tidal frequency dominates, and the dissipation is the response of the body to the rich spectrum of exciting tidal frequencies. Thus no simple relation exists between $Q'$ and $\Delta t$ in the general case.

Although it is tempting to use Eq.(\[QforExo\]) to rewrite the tidal equation and to keep $Q'$ constant instead of $\Delta t$ as done by, for example, @ML02, @DLM04 and @BO09, one must keep in mind that this procedure is not equivalent either to the constant phase lag (i.e. constant $Q$) or time lag model. Indeed the frequency dependence of the phase lag is given by $\epsilon(\sigma)=\sigma/(nQ)$ and is still proportional to the tidal frequency over an orbit as in the constant time lag model, but with a slope that is changing during the evolution.

In §\[sec:2ndOrder\] and §\[sec:comp\], we compare the constant time lag model 