2023MNRAS.525.2125Z

We study nodal librations of outer particles in the framework of the elliptical restricted three-body problem including general relativity (GR) effects. From an analytical treatment based on secular interactions up to quadrupole level, we derive equations that define the nodal libration region of an outer test particle, which depends on the physical and orbital parameters of the bodies of the system. From this, we analyse how the GR constrains the semimajor axis of outer test particles that experience nodal librations under the effects of an inner planet around a single stellar component. Such an upper limit of the semimajor axis, which is called a_2,lim, depends on the mass of the star m_s, the mass m₁, the semimajor axis a₁, and the eccentricity e₁ of the inner planet, and the eccentricity e₂ of the outer test particle. On the one hand, our results show that the greater m₁, a₁, and e₂ and the smaller m_s, the greater the value of a_2,lim. On the other hand, for fixed m_s, m₁, a₁, and e₂, a_2,lim does not strongly depend on e₁, except for large values of such an orbital parameter. We remark that N-body experiments of particular scenarios that include GR show results consistent with the analytical criteria derived in this research. Moreover, the study of hypothetical small body populations of real systems composed of a single star and an inner planetary-mass companion show that the GR effects can play a very important role in their global dynamics.