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tokens: the main object, respectively, and Na 1, Na 2, Ne 1, and Ne 2 are factors that take place in eccentric orbits and are defined by 5.2 General relativistic effect The important effect derived from General Relativity theory (GRT) on the dynamic of planetary systems is the precession of ω ( Einstein 1916 ). In our case, we considered that only the main object contributes with relevant corrections. As we worked in the reference frame of the star, the associated correction in the acceleration of the embryo is with c the speed of light. Eq. ( 19 ) was proposed by Anderson et al. (1975) , who worked under the parameterize post-Newtonian theories. The authors obtained a relative correction associated with two parameters β and γ , which are equal to unity in the GRT case. This expression has been used in several works that included relativistic corrections (e.g., Quinn et al. 1991 ; Shahid-Saless Yeomans 1994 ; Varadi et al. 2003 ; Benitez Gallardo 2008 ; Zanardi et al. 2018 ). The timescale associated with the precession of the longitude of periastron is given by 5.3 Test simulations We made a set of N -body simulations in order to test the agreement between the external forces that we incorporated in the M ERCURY code and the timescale associated with them. To test the precession of ω , we developed two simulations: one that included the tidal distortion term, and another that included the GR correction. In Fig. 5 we show the apsidal precession timescale of a planet with 1 M ⊕ orbiting a 1 Myr substellar object of 0.08 M ⊙ with initial values a = 0.01 au and e = 0.1 for the two simulations we made. Our results show that the apsidal precession of 360° is completed in 14 750 and 3060 yr, respectively, which agrees with the time predicted by the timescales associated with each correction term in Eqs. ( 20 ) and ( 8 ). These timescale values depend on the physical parameters of the protoplanetary embryos and the substellar object, as well as on the initial orbital elements. For instance, if the protoplanets are smaller than Earth in mass and radius, then the relativistic effect is more relevant than the tidal distortion regarding the precession of ω . Fig. 5 Apsidal precession due to tidal distortion (solid red line) and GR effects (dotted blue line) in a system composed of a 1 M ⊕ planet around a 0.08 M ⊙ BD with initial a = 0.01 au and e = 0.1. In this example, the argument of periastron completes an orbit in ~14 750 yr when is affected by GR and in ~3060 yr when is affected by tidal distortion. Fig. 6 Evolution of e , a , and the pseudo-synchronization period of a 1 M ⊕ around a 0.04 M ⊙ BD. Solid lines indicates the results considering the initial orbital elements from Bolmont et al. (2011) . The dashed lines indicate the evolution of r corot ( middle panel ) and the rotational period of the BD, P ⋆ ( bottom panel ). To test the analytic expressions for the tidal dissipation with the timescales of e and a decay, we developed a N -body simulation