the periapsis strongly [*decreases*]{}, and most of the work due to the tidal forces occurs at this point of the orbit. One can see that for $e>0.32$ the high order terms dominate the constant and $e^2$ terms. This is a physical evidence that shows that for moderate to large eccentricity, most of the tidal effects are contained in the high order terms that can therefore not be neglected independently of any tidal model.

In this section we quantify more comprehensively this statement. We will demonstrate analytically that:

-   in the context of the Hut model, a truncation of the tidal equations at the order $e^2$ can lead not only to quantitatively wrong but to [*qualititatively*]{} wrong tidal evolution histories, with sequences drastically differing from the ones obtained with the complete solution.

-   the rate of tidal dissipation can be severely underestimated by the quasi circular approximation ($e\ll1$).

Furthermore, $Q$-constant models consider only low order terms in obliquity ($\varepsilon_\ii$), and thus cannot address the problem of obliquity tides and energy dissipation produced by this mechanism. A detailed discussion on this subject is presented in @LCC07 and @BO09 and will not be reproduced here.

Expanding vs shrinking orbits
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On one hand, 