Ch. Froeschle

Secular resonances from 2 to 50 AU

Abstract By means of a new algorithm which generalizes the second-order and fourth-degree secular perturbation theory of Milani and Kneževic (1990, Celest. Mech. 49, 347–411), we find in the a-e-I proper elements space the location of secular resonances between the precession rates of the longitudes of perihelion and node of a minor body and the corresponding eigenfrequencies of the secular perturbations of the four outer planets. Among the most interesting implications of our findings, we can quote: (i) the fact that the g = g6 (or ν6) resonance in the inner asteroid belt lies closer than previously assumed to the densely populated Flora region, providing a plausible dynamical route to inject asteroid fragments into planet-crossing orbits; (ii) the existence of another possible meteorite source near 2.4 AU at moderate inclinations, again through g = g6; (iii) the existence, confirmed by numerical experiments, of a region affected in a chaotic way by the s = s6 (or ν16) resonance at semimajor axis ⋍ 2.2 AU and moderate inclination, where no asteroid is observed; (iv) the possible presence of some low-inclination “rings” between the orbits of the outer planets where no major mean motion or secular resonance lies very near, allowing minor bodies to survive long times without close encounters; (v) the fact that none of the secular resonances considered in this work exists beyond 50 AU, so that these resonances cannot be effective for transporting inward comets belonging to a possible Kuiper flattened disk.

Probable asteroidal origin of the Tunguska Cosmic Body

The complete characterisation of the Tunguska event of 30th June 1908 is still a challenge for astro- physicists. We studied the huge amount of scientic literature to select data directly available from measurements and we introduced parameters calculated by the application of models, and evaluated other possibilities. We then selected a range of meaningful atmospheric trajectories, from which we extracted a set of possible orbits. We obtained 886 orbits, which were used to estimate the probabilities of the possible origin of the Tunguska Cosmic Body (TCB). We found that the probability that the TCB moved on an asteroidal path is higher than it moved on a cometary one, 83% to 17%, respectively.

The three principal secular resonances ?5, ?6, and ?16 in the asteroidal belt

We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. Williams theory (1969) yields the locations of the principal secular resonances ν5, ν6, and ν16 in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances ν16 and ν6, respectively. No theory is available for the secular resonance v5. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances ν5, ν6, and ν16. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed.

The last revolution of new comets: the role of stars and their detectability

Context. This work is a follow-up of a previous study, where we simulated the dynamical evolution of the Oort Cloud over 5 Gyr with special attention to the injection of comets into observable orbits.Aims. We wish to clarify how comet injection operates with two types of perturbers: Galactic tides and passing stars. We illustrate why attempts to identify the stars that might have played an important role in injecting the observed new Oort Cloud comets are as yet unlikely to succeed, and investigate how large an improvement can be expected from the Gaia mission.Methods. We simulate a 5 Gyr time span, concentrating on the injections found during the last 3 Gyr by extracting detailed information about the last revolution of the injected comets. We analyse the contributions of both the Galactic tides and the stars separately, and assess their importance as a function of the semi-major axis of the comets. We also compute the distances and motions of the perturbing stars at the time the comets reach their perihelia and thus estimate their observability.Results. By studying more than 20 000 injected comets, we determine how the likelihood of tidal and stellar injections varies with the semi-major axis. We establish the range of semi-major axis for which a real-time synergy between stellar and tidal perturbations is important. We find how many perturbing stars could be identified using HIPPARCOS and Gaia data, and how the dynamics of injections would change, if only the observable stars were acting.Conclusions. The number of injected comets peaks at a semi-major axis (a) of about 33 000 AU but the comets spread over a wide range around this value. The tides are unable to inject any comets at a 50 000 AU. The real-time synergy is found to extend between a similar to 15 000 AU and a similar to 45 000 AU and to be the main contributor at a similar to 25 000 AU. Stellar perturbations make important contributions at all semi-major axes. On the basis of HIPPARCOS data, only a minority of the stars that may contribute to comet injections are detectable, since most stars have escaped to distances beyond the HIPPARCOS detection limit. For Gaia, on the other hand, a large majority of the perturbing stars will be both identifiable and measurable.

The accuracy of proper orbital elements and the properties of asteroid families: Comparison with the linear theory

Abstract The accuracy and reliability of the proper orbital elements used to define asteroid families are investigated by simulating numerically the dynamical evolution of families assumed to arise from the “explosion” of a parent object. The orbits of the simulated family asteroids have then been integrated in the frame of the elliptic restricted three-body problem Sun-Jupiter-asteroid, for times of the order of the circulation periods of perihelia and nodes. By filtering out short-periodic perturbations, we have monitored the behavior of the proper eccentricities and inclinations, computed according to the linear secular perturbation theory. Significant long-period variations have been found especially for families having nonnegligible eccentricities and/or inclinations (like the Eos family), and strong disturbances due to the proximity of mean motion commensurabilities with Jupiter have been evidenced (for instance, in the case of the Themis family). These phenomena can cause a significant “noise” on the proper eccentricities and inclinations, probably affecting in some cases the derived family memberships. They can also give rise to a spurious anisotropy in the fragment ejection velocity fields computed from the dispersion in proper elements observed in each family, and this could explain the puzzling anisotropies of this kind actually found in real families by D. Brouwer (1951 , Astron. J. 56 , 9–32) and by V. Zappala, P. Farinella, Z. Kneževic, and P. Paolicchi (1984) , Icarus 59 , 261–285).

Orbital evolution of two near-earth asteroids: Nereus and 1989 ML

Abstract In 2002, the Institute of Space and Astronautical Science (ISAS) of Japan will send the MUSES-C spacecraft to an asteroid to get the surface material of the asteroid, and return them to the Earth in 2006. The target asteroid is (4660) Nereus, and the backup target is 1989 ML. In this paper, we studied the orbital evolution of these asteroids. We found that both of these asteroids show chaotic motions. In particular the motion of Nereus is quite chaotic, so we cannot determine its orbital evolution for more than 200 years. However, we also found that these asteroids have been moving around the Sun in asteroid-like orbits for at least 5,000 years.

Numerical experiments in the 3/1 andv 6 overlapping resonance region

Numerical experiments of fictitious small bodies with initial eccentricities e=0.1 have been performed in the overlapping region of the 3/1mean motion resonance and of the v 6 secular resonance 2.48 ≤ a ≤ 2.52AU for different values of the initial inclination 16° ≤ i ≤ 20°. An analysis for the v 6 secular resonance shows that the topology is different from the one found outside the overlapping region: the critical argument for the v 6 resonance in the overlapping region rotates in opposite direction as compared to the pure v 6 region. In the 3/1 resonance region the secular resonance v 5 is dominant, and some secondary secular resonances as v 6 — v 16 and v 5 + v 6 are present.

Dynamics of Small Earth-Approachers on Low-Eccentricity Orbits and Implications for Their Origins

The population of Near-Earth Asteroids (NEAs) appears to be overabundant at sizes smaller than 50 m, compared to a power-law extrapolation from kilometer-sized objects. Several of these small NEAs are also concentrated on low-eccentricity orbits, where a few larger Earthcrossers are observed, and are called Small Earth-Approachers (SEAs). Their source region as well as the dynamical mechanisms involved in their transport close to the Earth on low-eccentricity orbits have not yet been determined. In this paper, we present our numerical and statistical study of the production and dynamical evolution of these SEAs. We first show that three main sources of Earthcrossers which are, according to recent simulations, the 3/1 and v6 resonances in the main belt, and the Mars-crosser population, are not able to produce as many bodies on SEAs-like orbits compared to other Earth-crossing orbits as has been inferred from observations. From these sources, SEAslike orbits are reached through the interplay of two required mechanisms: secular resonances and planetary close approaches. However, the time spent on these orbits remains smaller than 1 Myr as confirmed by the study of the evolutions of 11 observed SEAs which also reveal the action of various mechanisms such as close approaches to planets and/or secular resonances. Therefore, our results present some mechanisms which can be responsible for their production but none that would preserve the lifetime of the SEAs sufficiently to enhance their abundance relative to other Earth-crossing orbits at the level observed. The overabundance of the SEA population, if real, remains a problem and could be related to the influence of collisional disruption and tidal splitting of Earthcrossers, as well as to observational biases that might account for a discrepancy between theory and observation.

Distribution of long-period comets: comparison between simulations and observations

Aims. This paper is devoted to a comparison between observations and simulations of the so-called Oort spike formed by the “new” observable long-period comets. Methods. The synthetic distributions of observable comets come from the propagation of a huge sample of objects during the age of the solar system that were initially in a proto-Oort cloud, which was flattened around the ecliptic and had perihelia in the region of Uranus and Neptune. For the known new long-period comets, two samples were used, one that is assumed to be complete, and the comets of the other exclusively come from the Warsaw catalog of comets. The original orbital energy of the comets in this catalog is more reliable. Results. Considering comets with a perihelion distance smaller than 4 AU, for which one of our samples of known comets can be assumed to be complete, the comparison shows small but significant differences in the orbital energy distribution and in the proportion of retrograde comets. When we extend the limiting perihelion distance to 10 AU, the observed samples are obviously strongly incomplete. The synthetic distribution showsthat the number of observable comets per year and per perihelion distance unit is ∝ q 1.09 for q q 2.13 for 6 q q > 6 AU comes from comets that were already within the Jupiter-Saturn barrier ( q Conclusions. To explain the small but significant differences between our synthetic sample and the known comets for a perihelion distance smaller than 4 AU, different hypotheses are proposed: a still erroneous value of the original orbital energy in the observed sample, a higher density of low-mass stars in the actual solar neighborhood, a ninth planet, and obviously the initial population of objects from which the synthetic distributions are derived.

Delivery of Meteorites from the v 6 Secular Resonance Region Near 2 AU

Numerical integrations in the frame of Sun-Mars-Jupiter-Saturn model over 1Myr have been performed in order to investigate the orbital evolution of asteroid fragments produced in the innermost asteroid belt (2.07–2.13AU). Fragments injected in the vicinity of the V6 secular resonance enhance their eccentricities and become Mars-crossers. Close encounters to Mars will then lead to a random walk in semi- major axes. Two different mechanisms may occur to produce Earth-crossers. In the first case, the fragment enters the 4/1 mean motion resonance and becomes an Earth-crosser within at least 2.6 * 105 years. In the second case, which involves only the secular resonance V6 the shortest timescale for deriving meteorites is of the order of 5.6 * 105years.