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We explore the long-term stability of Earth Trojans by using a chaos indicator, the Frequency Map Analysis. We find that there is an extended stability region at low eccentricity and for inclinations lower than about even if the most stable orbits are found at . This region is not limited in libration amplitude, contrary to what found for Trojan orbits around outer planets. We also investigate how the stability properties are affected by the tidal force of the Earth–Moon system and by the Yarkovsky force. The tidal field of the Earth–Moon system reduces the stability of the Earth Trojans at high inclinations while the Yarkovsky force, at least for bodies larger than 10 m in diameter, does not seem to strongly influence the long-term stability. Earth Trojan orbits with the lowest diffusion rate survive on timescales of the order of  years but their evolution is chaotic. Their behaviour is similar to that of Mars Trojans even if Earth Trojans appear to have shorter lifetimes.

Isotopic dating indicates that chondrules were produced a few million years after the solar nebula formed. This timing is incompatible with dynamical lifetimes of small particles in the nebula and short time scales for the formation of planetesimals. Temporal and dynamical constraints can be reconciled if chondrules were produced by heating of debris from disrupted first-generation planetesimals. Jovian resonances can excite planetesimal eccentricities enough to cause collisional disruption and melting of dust by bow shocks in the nebular gas. The ages of chondrules may indicate the times of Jupiter's formation and dissipation of gas from the asteroidal region.

The new profiles of the space missions aimed at asteroids and comets, moving from fly-bys to rendezvous and orbiting, call for new spaceflight dynamics tools capable of propagating orbits in an accurate way around these small irregular objects. Moreover, interesting celestial mechanics and planetary science problems, requiring the same sophisticated tools, have been raised by the first images of asteroids (Ida/Dactyl, Gaspra and Mathilde) taken by the Galileo and NEAR probes, and by the discovery that several near-Earth asteroids are probably binary. We have now developed two independent codes which can integrate numerically the orbits of test particles around irregularly shaped primary bodies. One is based on a representation of the central body in terms of “mascons” (discrete spherical masses), while the other one models the central body as a polyhedron with a variable number of triangular faces. To check the reliability and performances of these two codes we have performed a series of tests and compared their results. First we have used the two algorithms to calculate the gravitational potential around non-spherical bodies, and have checked that the results are similar to each other and to those of other, more common, approaches; the polyhedron model appears to be somewhat more accurate in representing the potential very close to the body’s surface. Then we have run a series of orbit propagation tests, integrating several different trajectories of a test particle around a sample ellipsoid. Again the two codes give results in fair agreement with each other. By comparing these numerical results to those predicted by classical perturbation formulae, we have noted that when the orbit of the test particle gets close to the surface of the primary, the analytical approximations break down and the corresponding predictions do not match the results of the numerical integrations. This is confirmed by the fact that the agreement gets better and better for orbits farther away from the primary. Finally, we have found that in terms of CPU time requirements, the performances of the two codes are quite similar, and that the optimal choice probably depends on the specific problem under study.

THE recent discoveries 1–4 of massive planetary companions orbiting several solar-type stars pose a conundrum. Conventional models 5,6 for the formation of giant planets (such as Jupiter and Saturn) place such objects at distances of several astronomical units from the parent star, whereas all but one of the new objects are on orbits well inside 1 AU; these planets must therefore have originated at larger distances and subsequently migrated inwards. One suggested migration mechanism invokes tidal interactions between the planet and the evolving circumstellar disk 7 . Such a mechanism results in planets with small, essentially circular orbits, which appears to be the case for many of the new planets. But two of the objects have substantial orbital eccentricities, which are difficult to reconcile with a tidal-linkage model. Here we describe an alternative model for planetary migration that can account for these large orbital eccentricities. If a system of three or more giant planets form about a star, their orbits may become unstable as they gain mass by accreting gas from the circumstellar disk; subsequent gravitational encounters among these planets can eject one from the system while placing the others into highly eccentric orbits both closer and farther from the star.

Context: In the early evolution of a planetary system, a pair of planets may be captured in a mean motion resonance while still embedded in their nesting circumstellar disk. Aims: The goal is to estimate the direction and amount of shift in the semimajor axis of the resonance location due to the disk gravity as a function of the gas density and mass of the planets. The stability of the resonance lock when the disk dissipates is also tested. Methods: The orbital evolution of a large number of systems is numerically integrated within a three-body problem in which the disk potential is computed as a series of expansion. This is a good approximation, at least over a limited amount of time. Results: Two different resonances are studied: the 2:1 and the 3:2. In both cases the shift is inwards, even if by a different amount, when the planets are massive and carve a gap in the disk. For super--Earths, the shift is instead outwards. Different disk densities, Sigma, are considered and the resonance shift depends almost linearly on Sigma. The gas dissipation leads to destabilization of a significant number of resonant systems, in particular if it is fast. Conclusions: The presence of a massive circumstellar disk may significantly affect the resonant behavior of a pair of planets by shifting the resonant location and by decreasing the size of the stability region. The disk dissipation may explain some systems found close to a resonance but not locked in it.

We compared the effectiveness of a new continuous positive airway pressure (CPAP) device (neonatal helmet CPAP) with a conventional nasal CPAP system in preterm neonates needing continuous distending pressure. Randomized, physiological, cross-over study in a tertiary referral, neonatal intensive care unit in a university teaching hospital. Twenty very low birth weight infants with a postnatal age greater than 24 h who were receiving nasal CPAP for apnea and/or mild respiratory distress were enrolled. CPAP delivered by neonatal helmet CPAP and nasal CPAP in random order for two subsequent 90-min periods. Were continuously measured the Neonatal Infant Pain Scale (NIPS) score, oxygen requirements, respiratory rate, heart rate, oxygen saturation, transcutaneous PO(2) (tcPO(2)) and PCO(2) (tcPCO(2)), blood pressure, and desaturations. NIPS scores were significantly lower when the infants were on the neonatal helmet CPAP than when they were on nasal CPAP (0.26+/-0.07 vs. 0.63+/-0.12). The other studied parameters did not differ between the two CPAP modes. The number of desaturations was reduced during the neonatal helmet CPAP treatment (18 vs. 32), although this difference was not significant. In this short-term physiological study the neonatal helmet CPAP appears to be as good as the golden standard for managing preterm infants needing continuous distending pressure, with enhanced tolerability. Further evaluation in a randomized clinical trial is needed to confirm these findings.

Planet--Planet scattering is an efficient and robust dynamical mechanism for producing eccentric exoplanets. Coupled to tidal interactions with the central star, it can also explain close--in giant planets on circularized and potentially misaligned orbits. We explore scattering events occurring close to the star and test if they can reproduce the main features of the observed orbital distribution of giant exoplanets on tight orbits.In our modeling we exploit a numerical integration code based on the Hermite algorithm and including the effects of general relativity, dynamical tides and two--body collisions.We find that P--P scattering events occurring in systems with three giant planets initially moving on circular orbits close to their star produce a population of planets similar to the presently observed one, including eccentric and misaligned close--in planets. The contribution of tides and general relativity is relevant in determining the final outcome of the chaotic phase. Even if two--body collisions dominate the chaotic evolution of three planets in crossing orbits close to their star, the final distribution shows a significant number of planets on eccentric orbits. The highly misaligned close--in giant planets are instead produced by systems where the initial semi--major axis of the inner planet was around 0.2 au or beyond.

While a large fraction of the stars are in multiple systems, our understanding of the processes leading to the formation of these systems is still inadequate. Given the large theoretical uncertainties, observation plays a basic role. Here we discuss the contribution of high contrast imaging, and more specifically of the SPHERE instrument at the ESO Very Large Telescope, in this area. SPHERE nicely complements other techniques - in particular those exploiting Gaia and ALMA - in detecting and characterising systems near the peak of the distribution with separation and allows to capture snapshots of binary formation within disks that are invaluable for the understanding of disk fragmentation.

Planet--planet scattering is a major dynamical mechanism able to significantly alter the architecture of a planetary system. In addition to that, it may also affect the formation and retention of a debris disk by the system. A violent chaotic evolution of the planets can easily clear leftover planetesimal belts preventing the ignition of a substantial collisional cascade that can give origin to a debris disk. On the other end, a mild evolution with limited steps in eccentricity and semimajor axis can trigger the formation of a debris disk by stirring an initially quiet planetesimal belt. The variety of possible effects that planet--planet scattering can have on the formation of debris disks is analysed and the statistical probability of the different outcomes is evaluated. This leads to the prediction that systems which underwent an episode of chaotic evolution might have a lower probability of harboring a debris disk.

The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their dynamical behaviour is investigated with the frequency map analysis as chaos indicator. Following the guidance of this analysis, it is found that for two-planet systems the dependence of the Hill limit on the planet mass, usually made explicit through the Hill's radius parametrization, does not appear to be fully adequate. In addition, frequent cases of stable chaos are found in the proximity of the Hill limit. For three-planet systems, the usual approach adopted in numerical explorations of their stability, where the planets are initially separated by multiples of the mutual Hill radius, appears too reducing. A detailed sampling of the parameter space reveals that systems with more packed inner planets are stable well within previous estimates of the stability limit. This suggests that a two-dimensional approach is needed to outline when three-planet systems are dynamically stable.