Artificial equilibrium points for a generalized sail in the circular restricted three-body problem

This paper introduces a new approach to the study of artificial equilibrium points in the circular restricted three-body problem for propulsion systems with continuous and purely radial thrust. The propulsion system is described by means of a general mathematical model that encompasses the behavior of different systems like a solar sail, a magnetic sail and an electric sail. The proposed model is based on the choice of a coefficient related to the propulsion type and a performance parameter that quantifies the system technological complexity. The propulsion system is therefore referred to as generalized sail. The existence of artificial equilibrium points for a generalized sail is investigated. It is shown that three different families of equilibrium points exist, and their characteristic locus is described geometrically by varying the value of the performance parameter. The linear stability of the artificial points is also discussed.     

Evidence for an asteroid–comet continuum from simulations of carbonaceous microxenolith dynamical evolution

Abstract– Micrometeoroids with 100 and 200 μm size dominate the zodiacal cloud dust. Such samples can be studied as micrometeorites, after their passage through the Earth atmosphere, or as microxenoliths, i.e., submillimetric meteorite inclusions. Microxenoliths are samples of the zodiacal cloud dust present in the asteroid Main Belt hundreds of millions years ago. Carbonaceous microxenoliths represent the majority of observed microxenoliths. They have been studied in detail in howardites and H chondrites. We investigate the role of carbonaceous asteroids and Jupiter‐family comets as carbonaceous microxenolith parent bodies. The probability of low velocity collisions of asteroidal and cometary micrometeoroids with selected asteroids is computed, starting from the micrometeoroid steady‐state orbital distributions obtained by dynamical simulations. We selected possible parent bodies of howardites (Vesta) and H chondrites (Hebe, Flora, Eunomia, Koronis, Maria) as target asteroids. Estimates of the asteroidal and cometary micrometeoroid mass between 2 and 4 AU from the Sun are used to compute the micrometeoroid mass influx on each target. The results show that all the target asteroids (except Koronis) receive the same amount (within the uncertainties) of asteroidal and cometary micrometeoroids. Therefore, both these populations should be observed among howardite and H chondrite carbonaceous microxenoliths. However, this is not the case: carbonaceous microxenoliths show differences similar to those existing among different groups of carbonaceous chondrites (e.g., CI, CM, CR) but two sharply distinct populations are not observed. Our results and the observations can be reconciled assuming the existence of a continuum of mineralogical and chemical properties between carbonaceous asteroids and comets.     

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.     

Terrestrial planet formation with strong dynamical friction

We have performed 8 numerical simulations of the final stages of accretion of the terrestrial planets, each starting with over 5× more gravitationally interacting bodies than in any previous simulations. We use a bimodal initial population spanning the region from 0.3 to 4 AU with 25 roughly Mars-mass embryos and an equal mass of material in a population of ∼1000 smaller planetesimals, consistent with models of the oligarchic growth of protoplanetary embryos. Given the large number of small planetesimals in our simulations, we are able to more accurately treat the effects of dynamical friction during the accretion process. We find that dynamical friction can significantly lower the timescales for accretion of the terrestrial planets and leads to systems of terrestrial planets that are much less dynamically excited than in previous simulations with fewer initial bodies. In addition, we study the effects of the orbits of Jupiter and Saturn on the final planetary systems by running 4 of our simulations with the present, eccentric orbits of Jupiter and Saturn (the EJS simulations) and the other 4 using a nearly circular and co-planar Jupiter and Saturn as predicted in the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465] (the CJS simulations). Our EJS simulations provide a better match to our Solar System in terms of the number and average mass of the final planets and the mass-weighted mean semi-major axis of the final planetary systems, although increased dynamical friction can potentially improve the fit of the CJS simulations as well. However, we find that in our EJS simulations, essentially no water-bearing material from the outer asteroid belt ends up in the final terrestrial planets, while a large amount is delivered in the CJS simulations. In addition, the terrestrial planets in the EJS simulations receive a late veneer of material after the last giant impact event that is likely too massive to reconcile with the siderophile abundances in the Earth's mantle, while the late veneer in the CJS simulations is much more consistent with geochemical evidence.     

Impact ejecta in upper Eocene deposits at Massignano,Italy

Abstract— Previous workers have shown that an impact ejecta layer at Massignano, Italy contains a positive Ir anomaly, flattened spheroids (pancake spherules), Ni‐rich spinel crystals, and shocked quartz with multiple sets of planar deformation features. Because of sample sizes and work by different investigators, it was not clear if the shocked quartz is associated with the Ir anomaly and pancake spherules or if it belongs to a separate impact event. To address this problem, we carried out a high‐resolution stratigraphic study of this ejecta layer. The ejecta layer was sampled continuously at 1 cm intervals in two adjacent columns. The carbonate was removed with dilute HCl, and the non‐carbonate fraction was gently sieved. Pancake spherules were recovered from the 250–500 μm size fraction and counted. At the peak abundance, the number of pancake spherules in the 250–500 μm size fraction is about 6–7/g of sample. The pancake spherules removed from the 250–500 μm size fraction are mostly translucent to opaque pale green, but some have a grey color or dark opaque patches due to a coating of Ni‐ and Cr‐rich spinel crystals. Energy‐dispersive X‐ray analysis and X‐ray diffraction data indicate that the green spherules are composed of iron‐rich smectite, probably nontronite. Black opaque spinel stringers (dark spinel‐rich pancake spherules), usually <200 μm across, can be seen in a polished section of a block that includes the ejecta layer. None of the dark spinel‐rich pancake spherules were recovered from the sieved non‐carbonate fraction due to their fragile nature, but we believe that they are from the same impact event as the green pancake spherules. The <250 μm size fractions from both columns were disaggregated using ultrasonics and re‐sieved. The 63–125 μm size fractions were then searched for shocked quartz using a petrographic microscope. At the peak‐abundance level, the number of shocked quartz grains in the 63–125 μm size fraction is about 7/g of sample. Some of the shocked quartz grains have a “toasted” appearance. These grains have a brownish color and contain a patchy distribution of faint, densely spaced planar deformation features (PDFs). Polymineralic fragments containing one or two shocked quartz grains with one or two sets of PDFs were observed. They appear to have an organic matrix and are probably fragments of agglutinated foraminiferal tests. We searched for, but did not find, coesite or shocked zircons. We found that the peak abundance of the shocked quartz is within a centimeter of the peak abundance of the green pancake spherules. We conclude that the pancake spherules are diagenetically altered clinopyroxene‐bearing spherules and that the shocked quartz, green (and presumably the dark spinel‐rich) pancake spherules, and Ir anomaly all belong to the same impact event. This conclusion is consistent with previous suggestions that the cpx spherule layer may be from the 100 km‐diameter Popigai impact crater in northern Siberia.     

Unveiling the Launching Region of YSO Jets with AMBER

The interplay between accretion and ejection in the environment of young stellar objects (YSOs) is believed to be a crucial element in the star formation process. Since most of the properties of the models are set up in the first few AUs from the source (below the so-called Alfvèn surface), to validate and constrain the models observationally we need very high angular resolution. With HST (resolution ∼ 0.'1, i.e. about 14 AU in Taurus)we have been able to access the external border of the acceleration region, for jets in the Taurus-Auriga cloud. Here we see an onion-like kinematic structure in the first 200 AU of the flow, and indications for rotation around the symmetry axis for the resolved low/moderate velocity component. We have now planned observations with AMBER on the VLTI to investigate at 1 mas resolution (in J) the core of the central engine, down to 0.1 AU from the source. Here we describe a joint project by several Institutes in the AMBER consortium dedicated to the study of the morphology and detailed kinematics of a few selected targets. On one hand we will use the large UV coverage of the ATs to explore at medium spectral resolution the structure of the flow. On the other hand the large collection area of the UTs combined with the high resolution mode (R=10000) of AMBER will allow us to search for interesting kinematic features, among which signatures of rotation around the axis, that would constitute an important validation of the proposed models for the jet launching. This revised version was published online in July 2006 with corrections to the Cover Date.     

Proper elements for highly inclined asteroidal orbits

Based on Williams' work and rewritten in action angle variables, a method for the calculation of proper elements is here presented. The averaging over the long periodic terms is performed by the semi numerical method developed by Henrard (1990); no series expansion in eccentricity or inclination of the asteroid is used which allows calculating proper elements for highly inclined orbits. Conversely, the theory is truncated at the first degree in the eccentricity and the inclination of the perturbing planets. A few tests about accuracy and consistency are presented.