simply switching the p and $\star$ indices. Similarly, the secular evolution of the eccentricity is given by $$\begin{aligned}
\frac{1}{e}\frac{\dd e}{\dd t}=11\frac{a}{GM_{\star}\Mp}
&\Big\{&\Kp&\left[\Omega_e(e)\,x_\mathrm{p}\,
\frac{\op}{n}-\frac{18}{11}N_e(e)\right]  \nonumber\\
&+& \Ks&\left[\Omega_e(e)\,x_\star\,
\frac{\os}{n}-\frac{18}{11}N_e(e)\right]\Big\}\ , \quad
\label{evol_e}\end{aligned}$$ with $$\label{omega_e_e}
\Omega_e(e) =\frac{1+\frac{3}{2}e^2+\frac{1}{8}e^4}{(1-e^2)^{5}}$$ and $$\label{ne_e}
N_e(e)=\frac{1+\frac{15}{4}e^2+\frac{15}{8}e^4+\frac{5}{64}e^6}{(1-e^2)^{13/2}}.$$ The terms proportional to $\Kp$ (resp. $\Ks$) are due to the tides raised by the star (planet) on the planet (star). Finally, the evolution of the rotational state of each object $i$ ($i$ being $p$ or $\star$) is given by: $$\frac{\dd C_\ii\omega_\ii}{\dd t}=-\frac{K_\ii}{n}
 \left[\left(1+x_\ii^2\right)\Omega(e)\frac{\omega_\ii}{n}-2x_\ii\,N(e)
 \right] \ ,
\label{rot_tidal}$$ while the evolution of the obliquity obeys the equation $$\frac{\dd \varepsilon_\ii}{\dd t}=\sin \varepsilon_\ii \frac{K_\ii}{C_\ii \omega_\ii\,n}
  \left[(x_\ii-\eta_\ii)\,\Omega(e) \frac{\omega_\ii}{n}- 2\,N(e) \right] \ , \label{rot_tidal2}$$ where $C_\ii$ is the principal moment of inertia of the deformable body under consideration, $\eta_\ii$ is the ratio of rotational over orbital angular momentum $$\eta_\ii=\frac{\Mp+\Ms}{\Mp\Ms} \frac{C_\ii \omega_\ii}{a^2n \sqrt{1-e^2}},$$ and $$\label{omega_e}
\Omega(e) = \frac{1+3e^2+\frac{3}{8}e^4}{(1-e^2)^{9/2}}.$$ Up to this point, no assumption has been made on the objects themselves. As a result, Eqs.(\[evol\_a\])-(\[rot\_tidal2\]) are fully symmetric in p and $\star$ indices and can be used directly to model binary stars or a planet-satellite system. For typical HD 209458b-like parameters and $\Delta t$-values comparable to that inferred for Jupiter (see §\[sec:q\]), the planetary spin evolves to a 