coplanar ($\ep=0$) state with the equilibrium rotation rate value (setting $ \dd \op / \dd t = 0$) $$\omega_{\mathrm{eq}}=\frac{N(e)}{\Omega(e)}\frac{2x}{1+x^2}\,n= \frac{N(e)}{\Omega(e)}\,n\,,
\label{rot_eq}$$ within a time scale $\tau=C_\mathrm{p}\,n^2/\Kp \sim 10^5$ yr. Since the age of the known transiting systems ranges from a few Myr to Gyr, we can safely assume that the planet is now in this state of pseudo synchronization. The evolution of the orbital parameters of the planet-star systems is thus fully defined by the system of differential equations, to be solved consistently, given by Eqs.(\[evol\_a\]) and (\[evol\_e\]) for $a$ and $e$, Eqs.(\[rot\_tidal\]) and (\[rot\_tidal2\]) for the stellar rotation and $\ep=0$, $\op=\omega_{\mathrm{eq}}$. The rate of tidal dissipation within the [*planet*]{} in this state of pseudo synchronization reads [@Hut81; @LCC07] $$\dot{E}_{\mathrm{tides}}=
2\Kp\left[N_a(e)-\frac{N^2(e)}{\Omega(e)} \right] \ ;\ \ (\op=\omega_{\mathrm{eq}})\ .
\label{tidal_energy}$$ The dissipated heat is deposited over the whole planet’s interior.

One can see from Eq.(\[appendtidalnrj2\]) in Appendix \[appendix\] that Eq.(\[tidal\_energy\]) is a special case of energy dissipation for a body in pseudo synchronous rotation as expected for fluid objects ($\ep=0$, $\op=\omega_{\mathrm{eq}}$). For a rocky planet, the external gravitational potential created by its permanent quadrupole moment can cause its locking into synchronous rotation ($\op=n$) and the dissipation rate reads in that case $$\begin{aligned}
