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The discovery of planets in binaries is one the most interesting outcomes ofplanetary research. With the growing number of discoveries has also grown theinterest on describing their formation, long-term evolution and potentialhabitability. In this work we revisit the dynamics of planets in S-type binarysystems. For that purpose we develop explicit formulas for the secularizedoctupolar Hamiltonian, coupled with general relativistic corrections andnon-conservative interactions. We implemented those formulas in an open-sourcepackage \texttt{SecDev3B}, that can be used to reproduce our results or testimproved versions of the models. In order to test it, we study the long-termdynamical evolution of S-type binary planets during the pre-main-sequence phaseof stellar evolution. During that phase, stellar radius significantly changesin timescales similar to secular timescales. We hypothesize that whenclose-encounters between the planet and its host star happens (e.g. viaLidov-Kozai effect), particularities in the secular formalism plus changes instellar radius may alter significantly the dynamical evolution. We study thewell-known binary planet HD 80606b and found that an octupolar expansion of theconservative Hamiltonian is required to properly predict its dynamicalevolution. We also apply the dynamical model, enriched with results coming fromstellar evolutionary models, to demonstrate that in S-type systems aroundlow-mass stars, with relative high inclinations ($\itot\ge 60^\circ$), moderateeccentricities ($0.2\le e\le 0.4$) and planets located around 1 AU, theevolution of stellar radius during the first few hundreds of Myr, alterssignificantly the timescales of dynamical evolution.

Revisiting the dynamics of planets in binaries: evolutionary timescales and the effect of early stellar evolution