Abstract.We study the possibility of the detection of the low amplitude long (P ) period perturbative effect of a distant third companion on the motion of a close binary. We give a new, more accurate analytical formula for this kind of perturbation affecting the moments of the times of minima in eclipsing binaries. The accuracy of this formula is tested by numerical integrations carried out for several initial configurations. We also describe a numerical method based on a non-linear Levenberg-Marquardt algorithm which makes it possible to separate this dynamical effect from the pure geometrical light-time effect in the eclipsing O−C diagram. The capabilities of this new method are demonstrated by the analysis of numerically simulated O−Cs for test systems having physical parameters very similar to Algol and IU Aur. The results show that the above mentioned effect would be detectable in these systems nowadays, observing almost each minima events in a 1-2 year-long interval.

A recently introduced chaos detection method, the relative Lyapunov indicator (RLI) is investigated in the cases of symplectic mappings and of a continuous Hamiltonian system. It is shown that the RLI is an efficient and easy-to-calculate numerical tool in determining the true nature of individual orbits, and in separating ordered and regular regions of the phase space of dynamical systems. An application of the RLI for stability investigations of some recently discovered exoplanetary systems is also presented.

Aims. We study the formation of a hypothetical terrestrial-type body in the equilateral Lagrange points of a giant extrasolar planet. Starting from a swarm of planetesimals in stable tadpole orbits, we simulate its dynamical and collisional evolution under a wide range of different initial conditions and masses for both the Trojan population and its planetary companion. We also analyze the effects of gas drag from the interaction of the planetesimals with the nebular disk. Methods. The formation process is simulated with an N-body code that considers full gravitational interactions between the planetesimals and the giant planet. Gas interaction is modeled with Stokes and Epstein drags, where the drag coefficients are chosen following the results of full hydrodynamic simulations performed with the 2D public hydro-code FARGO. Results. In both gas-free and gas-rich scenarios, we have been able to obtain a single final terrestrial-type body in a stable tadpole orbit around one of the triangular Lagrange points of the system. However, due to gravitational instabilities within the swarm, the accretional process is not very efficient and the mass of the final planet never seems to exceed ∼0.6 Earth masses, even when the total mass of the swarm is five times this value. Finally, we also included an orbital decay of the giant planet due to a type II migration. Although the accretional process shows evidence of a lower efficiency, a small terrestrial planet is still able to form, and follows the giant planet towards the habitable zone of the hosting star.

In the near future, space missions will be launched (e.g. COROT, KEPLER) to detect Earth-like extrasolar planets. The orbital elements of these (still hypothetic) planets will contain some uncertainties that can only be eliminated by careful dynamical investigations of the hosting planetary systems. The proportion of extrasolar planetary systems with one known giant planet is high (∼90 per cent). Therefore, as a first step we have investigated the possible existence of terrestrial planets in these systems. In this paper, the development of a stability catalogue of the habitable zones of exoplanetary systems is reported. This catalogue is formed by a series of stability maps, which can help to establish where Earth-like planets could exist in extrasolar planetary systems having one giant planet. After a description of the dynamical model and the numerical methods, details of the stability maps are discussed. An application of the stability catalogue to 15 known exoplanetary systems is also shown, and a characterization of the stability properties of their habitable zones is given.