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We study nodal librations of outer particles in the framework of theelliptical restricted three-body problem including general relativity (GR)effects. From an analytical treatment based on secular interactions up toquadrupole level, we derive equations that define the nodal libration region ofan outer test particle, which depends on the physical and orbital parameters ofthe bodies of the system. From this, we analyze how the GR constrains thesemimajor axis of outer test particles that experience nodal librations underthe effects of an inner planet around a single stellar component. Such an upperlimit of the semimajor axis, which is called a2,lim , depends on the mass ofthe star ms, the mass m1, the semimajor axis a1, and the eccentricity e1 of theinner planet, and the eccentricity e2 of the outer test particle. On the onehand, our results show that the greater m1, a1, and e2 and the smaller ms, thegreater the value of a2,lim. On the other hand, for fixed ms, m1, a1, and e2,a2,lim does not strongly depend on e1, except for large values of such anorbital parameter. We remark that N-body experiments of particular scenariosthat include GR show results consistent with the analytical criteria derived inthe present research. Moreover, the study of hypothetical small bodypopulations of real systems composed of a single star and an innerplanetary-mass companion show that the GR effects can play a very importantrole in their global dynamics.

Constraints to the semimajor axis of outer particles with nodal librations by general relativity effects