for finite eccentricity values. The main argument claimed for using such a simple tidal model is the large uncertainty on the tidal dissipation processes in astrophysical objects. In particular, as detailed by @Gre09, the linearity of the response to the tidal forcing based on the viscoelastic model may not hold in a real object for the large spectrum of exciting frequencies encountered when computing high order terms in the eccentricity. Although the large uncertainty in the dissipative processes certainly precludes an exact determination of the tidal evolution, it can by no means justify calculations which are neglecting dominant terms at finite $e$.

Indeed, from a dimensional point of view and prior to any particular tidal model, the strong impact of high order terms in the eccentricity is simply due to the fact that the tidal torque ($\mathbf{N}$) is proportional to $(\omega-\dot{\theta})/r^{6}$ ($\theta$ being the true anomaly) and that over a keplerian orbit, the average work done by the torque is of the form $$<\mathbf{N}\cdot\mathbf{\dot{\theta}}>\,\propto\,<\frac{\dot{\theta}^2}{r^6}>=\frac{n^2}{a^6}\cdot\frac{1+14e^2+\frac{105}{4}e^4+\frac{35}{4}e^6+\frac{35}{128}e^8}{(1-e^2)^{15/2}},$$ which is a rapidly increasing function of $e$ (see Appendix \[appendix\] for the details of the calculation). This means that, although the mean distance between the planet and the star increases with $e$, the distance at 