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We analyse the secular dynamics of planets on S-type coplanar orbits in tightbinary systems, based on first- and second-order analytical models, and comparetheir predictions with full N-body simulations. The perturbation parameteradopted for the development of these models depends on the masses of the starsand on the semimajor axis ratio between the planet and the binary.  We show that each model has both advantages and limitations. While thefirst-order analytical model is algebraically simple and easy to implement, itis only applicable in regions of the parameter space where the perturbationsare sufficiently small. The second-order model, although more complex, has alarger range of validity and must be taken into account for dynamical studiesof some real exoplanetary systems such as $\gamma$-Cephei and HD 41004A.However, in some extreme cases, neither of these analytical models yieldsquantitatively correct results, requiring either higher-order theories ordirect numerical simulations.  Finally, we determine the limits of applicability of each analytical model inthe parameter space of the system, giving an important visual aid to decodewhich secular theory should be adopted for any given planetary system in aclose binary.

Secular Dynamics of S-type Planetary Orbits in Binary Star Systems: Applicability Domains of First- and Second-Order Theories