On the stability of possible Trojan planets in the habitable zone: an application to the systems HD 147513 and HD 210277

Abstract

In this paper, we study the dynamical stability of fictitious terrestrial planets in the 1:1 mean-motion resonance with a gas giant moving in the habitable zone (HZ). We investigate the stability of Trojan planets both in a general study and for two specific known extrasolar planetary systems (HD 147513 and HD 210277). In the general study, we determine the stability of the Lagrangian point L4. The numerical simulations have been carried out using the spatial elliptic-restricted three-body problem, where we placed the test particles (TPs) exactly at L4, which is located 60° ahead of the gas giant at the same distance to the star. In the stability study, we have concentrated on the dependences between the eccentricity and the inclination of the Trojan planet. Going a step further, we have investigated two specific systems where the known gas giant moves in the HZ. The two specific extrasolar systems are investigated by using the general study to define the region in eccentricity and inclination where, in principle, stable motion is possible. To find out whether the existence of a Trojan planet is possible, in addition we have calculated the stable area in the semimajor axis (aTP) and the argument of perihelion (ωTP) for an actual planetary mass (2 M⊕). Thus, we can conclude that the region around the Lagrangian points L4 and L5 allows stable motion in the system HD 147513, because the gas giant of this system has an eccentricity of 0.26, which lies well within the stable region. The known planet in the system HD 210277 has a much higher eccentricity and thus it cannot harbour any terrestrial planets in the Lagrangian points.