Abstract.We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments. The systems Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of whether they could host terrestrial-like planets in their habitable zones (HZ). First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems. Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system, from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years. For each of the five systems the 2-dimensional grid of initial conditions contained 80 eccentricity points for the Jovian planet and up to 160 semimajor axis points for the fictitious planet. The computations were carried out using a Lie-series integration method with an adaptive step size control. This integration method achieves machine precision accuracy in a highly efficient and robust way, requiring no special adjustments when the orbits have large eccentricities. The stability of orbits was examined with a determination of the Rényi entropy, estimated from recurrence plots, and with a more straightforward method based on the maximum eccentricity achieved by the planet over the 1 million year integration. Additionally, the eccentricity is an indication of the habitability of a terrestrial planet in the HZ; any value of e > 0.2 produces a significant temperature difference on a planet's surface between apoapse and periapse. The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are: for Gl 777 A nearly the entire HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time, while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ. Studies such as this one are of primary interest to future space missions dedicated to finding habitable terrestrial planets in other stellar systems. Assessing the likelihood of other habitable planets, and more generally the possibility of other life, is the central question of astrobiology today. Our investigation indicates that, from the dynamical point of view, habitable terrestrial planets seem to be compatible with many of the currently discovered extrasolar systems. they could host additional terrestrial-like planets in their habitable zones (=HZ).Since the discovery of the first extrasolar planetary system about 10 years ago (Mayor & Queloz 1995), a major point of dynamical investigations has been the determination of stable regions in extrasolar planetary systems, where additional planets on stable orbits could exist. Today we know about 105 planetary systems with 120 planets, where 13 systems have more than one planet (both confirmed and unconfirmed cases).Article published by EDP Sciences and available at

The triple asteroidal system (87) Sylvia is composed of a 280‐km primary and two small moonlets named Romulus and Remus (Marchis et al. 2005b). Sylvia is located in the main asteroid belt, with semi‐major axis of about 3.49 au, eccentricity of 0.08 and 11° of orbital inclination. The satellites are in nearly equatorial circular orbits around the primary, with orbital radius of about 1360 km (Romulus) and 710 km (Remus). In this work, we study the stability of the satellites Romulus and Remus. In order to identify the effects and the contribution of each perturber, we performed numerical simulations considering a set of different systems. The results from the three‐body problem, Sylvia–Romulus–Remus, show no significant variation of their orbital elements. However, the inclinations of the satellites present a long‐period evolution with amplitude of about 20° when the Sun is included in the system. Such amplitude is amplified to more than 50° when Jupiter is included. These evolutions are very similar for both satellites. An analysis of these results shows that Romulus and Remus are librating in a secular resonance and their longitude of the nodes are locked to each other. Further simulations show that the amplitude of oscillation of the satellites' inclination can reach higher values depending on the initial values of their longitude of pericentre. In those cases, the satellites get caught in an evection resonance with Jupiter, their eccentricities grow and they eventually collide with Sylvia. However, the orbital evolutions of the satellites became completely stable when the oblateness of Sylvia is included in the simulations. The value of Sylvia's J2 is about 0.17, which is very high. However, even just 0.1 per cent of this value is enough to keep the satellite's orbital elements with no significant variation.

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We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of di †erent capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elementsÈinclination (i), longitude of the node ()), argument of pericenter (u), and time of pericenter passage (q)Èare Ðrst taken to be zero. Then we investigate the cases with u \ 90¡, 180¡, and 270¡. We also present a sample of results for) \ 90¡, considering the cases i \ 60¡, 120¡, 150¡, and 180¡. Special attention is given to the inÑuence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0¡ to 180¡ in steps of 10¡. The success of the Ðnal stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60¡È70¡ and 160¡. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

In terms of stability around the primary, it is widely known that the semimajor axis of the retrograde satellites is much larger than the corresponding semimajor axis of the prograde satellites. Usually this conclusion is obtained numerically, since precise analytical derivation is far from being easy, especially, in the case of two or more disturbers. Following the seminal idea that what is unstable in the restricted three-body problem is also unstable in the general N-body problem, we present a simplified model which allows us to derive interesting resonant configurations. These configurations are responsible for cumulative perturbations which can give birth to strong instability that may cause the ejection of the satellite. Then we obtain, analytically, approximate bounds of the stability of prograde and retrograde satellites. Although we recover quite well previous results of other authors, we comment very briefly some weakness of these bounds.