In our work we concentrate on investigating Trojan-like habitable planets ( Type 4 see introduction). As dynamical model, we used on one hand the planar elliptic restricted three-body problem (ER3BP) - shown in Catalogue 2D - and on the other hand inclined Trojan planets - shown in Catalogue 3D. We used the ER3BP because one can neglect the mass of the Trojan planets since the stability character of the equilateral Lagrangian points and the extension of the stability zone does not change significantly with a small third mass, which is shown in Marchal (1990) and Schwarz et al. (2005). Therefore, we did not use the available Nbody integrators, but wrote our own code on the basis of a Bulirsch-Stoer integrator, where we do not have to integrate the orbits of the primaries. For the analysis of the stability we used the method of the maximum eccentricity and the Lyapunov characteristic indicators (LCI). For the maximum eccentricity (emax) we checked the largest eccentricity of the TP during its motion. For larger eccentricities it becomes more probable that the orbits of the test particles are more chaotic (having close encounters or even collisions). We determined the size of the stability region around L4, because it is known that both Lagrangian equilibrium points are symmetric in the ER3BP. The eccentricity of the Trojan was the same as for the GG, ω of the Trojan was always set to ωTrojan = ωGG + 60°, + the respective variation in ω. Therefore we varried the semimajor axis (a) and the synodic longitude (λ) of the fictitious Trojan planet. This obtained maps of dynamical stability depending mainly on the initial eccentricty of the gas giant (GG) and the Trojan planet and the mass ratio (μ) of the primary bodies (star and GG) which we changed. The extension of the stability region around the Lagrangian points depends also on secondary resonances. This was also examined in case of Jupiter’s Trojan asteroids shown in the paper of Robutel & Gabern (2006). References Marchal, C.: 1990, The three-Body Problem, Elsevier, 49. Robutel P., Gabern F., 2006, MNRAS, 372, 1463. Schwarz, R., Pilat-Lohinger, E. Dvorak, R., Érdi, B., Sándor, Zs.: 2005, AsBio, 5, 579.
