Long-term perturbations in four-body systems with mutual highly inclined orbits

Hierarchical Three Body systems with mutual highly inclined orbits have been well-known since the 1960s. Lidov-Kozai cycles arise within them where the inner orbit eccentricity acquires extreme values. In particular, we focus our research on the motion of exoplanets and exomoons on different Three Body stellar scenarios. Our goal is to study how the LK cycles are perturbed by a fourth body (which we called perturbed LK). We analyze the evolution of the eccentricity and inclination of the inner orbit in two cases: the first involves an exoplanet and the second involves an exomoon. Due to the possible stable configurations of a four-body system, we treat two subcases as well: the Totally Hierarchical Configuration and the 2 + 2 configuration. According to that derived from the particular scenarios of study discussed in the present research, the LK perturbed in exomoon orbits around exoplanets seem to exhibit, in general, way less alterations than the exoplanet orbit around its star.