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
We present a statistical orbit computation technique for asteroids with transitional observational data, that is, a moderate number of data points spanning a moderate observational time interval. With the help of local least-squares solutions in the phase space of the orbital elements, we map the volume of variation as a function of one or more of the elements. We sample the resulting volume using a Monte Carlo technique and, with proper weights for the sample orbital elements, characterize the six-dimensional orbital-element probability density function. The volume-ofvariation (VOV) technique complements the statistical ranging technique for asteroids with exiguous observational data (short time intervals and/or small numbers of observations) and the least-squares technique for extensive observational data. We show that, asymptotically, results using the new technique agree closely with those from ranging and least squares. We apply the technique to the near-Earth object 2004 HA 39 , the main-belt object 2004 QR and the transneptunian object 2002 CX 224 recently observed at the Nordic Optical Telescope on La Palma, illustrating the potential of the technique in ephemeris prediction. The VOV technique helps us assess the phase transition in orbital-element probability densities, that is, the nonlinear collapse of wide orbital-element distributions to narrow localized ones. For the three objects above, the transition takes place for observational time intervals of the order of 10 h, 5 d and 10 months, respectively, emphasizing the significance of the orbital-arc fraction covered by the observations.
We seek to characterize giant-planet systems by their gravitational scattering properties. We do this to a given system by integrating it numerically along with a large number of hypothetical small bodies that are initially in eccentric habitable zone (HZ)-crossing orbits. Our analysis produces a single number, the escape rate, which represents the rate at which the small-body flux is perturbed away by the giant planets into orbits that no longer pose a threat to terrestrial planets inside the HZ. Obtaining the escape rate this way is similar to computing the largest Liapunov exponent as the exponential rate of divergence of two nearby orbits. For a terrestrial planet inside the HZ, the escape rate value quantifies the "protective" effect that the studied giant-planet system offers. Therefore, escape rates could provide information on whether certain giant-planet configurations produce a more desirable environment for life than the others. We present some computed escape rates on selected planetary systems, focusing on effects of varying the masses and semi-major axes of the giant planets. In the case of our Solar System we find rather surprisingly that Jupiter, in its current orbit, may provide a minimal amount of protection to the Earth.
Abstract. We evaluate asteroid orbital uncertainties from the discovery night onwards using 6D orbit computation tools based on statistical techniques. In particular, we outline a new nonlinear Monte Carlo technique of phase-space sampling that helps us in assessing the nonlinear phase transition from extended orbital-element distributions to well-constrained ones as the observational arc and number of observations grows. We apply the statistical techniques for near-Earth asteroid 2004 AS 1 to examine the time evolution of the orbital uncertainties and to assess the asteroid impact risk immediately after discovery. We start with the technique of statistical ranging for exiguous data, continue with the phase-space sampling technique for moderate data, and conclude with the standard least-squares fit for extensive data.
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