The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

The dark matter distribution in disc galaxies

We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ ₀∼1–4×10⁻²⁴ g cm⁻³) and core radii ( r ₀∼5–15 kpc) scaling as ρ ₀∝ r ₀^−2/3.     

Room-temperature equation of state of Li<Subscript>2</Subscript>VOSiO<Subscript>4</Subscript> up to 8.5 GPa

High-pressure single-crystal X-ray diffraction measurements of lattice parameters of the compound Li₂VOSiO₄, which crystallises with a natisite-type structure, has been carried out to a pressure of 8.54(5) GPa at room temperature. Unit-cell volume data were fitted with a second-order Birch-Murnaghan EoS (BM-EoS), simultaneously refining V ₀ and K ₀ using the data weighted by the uncertainties in V. The bulk modulus is K ₀ = 99(1) GPa, with K′ fixed to 4. Refinements of third order equations-of-state yielded values of K′ that did not differ significantly from 4. The compressibility of the unit-cell is strongly anisotropic with the c axis (K ₀(c) = 49.7 ± 0.5 GPa) approximately four times more compressible than the a axis (K ₀(a) = 195 ± 3 GPa).     

Mid-Holocene emergence of southern Tunisian coasts

We present new sea-level data from the coasts of southern Tunisia, between the Gulf of Gabès and the Libyan border. The work tests, previously, published evidence on Holocene shorelines, and confirmed that a distinct emergence has occurred in this area during this time. The emergence peak lies at least 186 ± 11 cm above present and is inferred from: (1) AMS radiocarbon dates of subtidal vermetids and boring shells collected in growth position, and (2) careful assessment of tidal heights. Maximum emergence took place between about 6000 and 5000 ¹⁴C years BP; it cannot be ascribed to tectonics and is probably related to post-glacial hydro-isostatic effects. It challenges the inference of a 3-m global sea-level rise since 6000 years BP due to residual Antarctic melting.     

A general theory of three-dimensional wave groups Part II: Interaction with a breakwater

The equation obtained in Part I predicts how an exceptionally high wave occurs at any fixed point within a wind wave field. The equation may be applied with a theoretical spectrum or directly with the random time series obtained by an array of wave gauges in the field. From both approaches, it emerges that a very high wave at a breakwater occurs because a well-defined three-dimensional wave group at the apex of its development hits against the breakwater, and that a very high wave at some distance before the breakwater occurs because of the collision of two wave groups: the first one going back after having been reflected, and the second one approaching the breakwater. In order to test the theory, a special breakwater was assembled off the beach at Reggio-Calabria where the significant height of the wind waves typically ranges from 0.20 to 0.40 m. When an exceptionally high wave (H = 9.6 σ) occurred at a point before this breakwater, the records made by a gauge array confirmed all the essential features of the prediction.     

Groundwater flow systems in turbidites of the Northern Apennines (Italy): natural discharge and high speed railway tunnel drainage

Turbidites crop out extensively in the Northern Apennine mountains (Italy). The huge amounts of groundwater drained by tunnels, built for the high speed railway connection between Bologna and Florence, demonstrate the aquifer-like behaviour of these units, up to now considered as aquitards. A conceptual model of groundwater flow systems (GFS) in fractured aquifers of turbidites is proposed, taking into account both system natural state and the perturbation induced by tunnel drainage. Analysis of hydrological data (springs, streams and tunnel discharge), collected over 10 years, was integrated with analysis of hydrochemical and isotopic data and a stream-tunnel tracer test. Hydrologic recession analysis of undisturbed conditions is a key tool in studying turbiditic aquifer hydrogeology, permitting the discrimination of GFS, the estimation of recharge relative to the upstream reach portion and the identification of springs most vulnerable to tunnel drainage impacts. The groundwater budgeting analysis provides evidence that the natural aquifer discharge was stream-focused through GFS, developed downslope or connected to main extensional tectonic lineaments intersecting stream beds; now tunnels drain mainly active recharge groundwater and so cause a relevant stream baseflow deplenishment (approximately two-thirds of the natural value), possibly resulting in adverse effects on local ecosystems.     

A calibration system for superconducting gravimeters

A new method for the calibration of a superconducting gravity meter is described, in which a 273 Kg annular mass is placed around the meter and is moved up and down. The geometry of the apparatus is easy to model and the accuracy in the computation of the gravity variation induced by the mass, 6.7µgal, is limited only by the accuracy in the knowledge of value of the gravitational constant. Measurements done in 91 and 92 for the calibration of the instrument GWR-T015 are described. The calibration factor has been determined with a precision of about 0.3%.     

Dynamical evolution of NEAs: Close encounters, secular perturbations and resonances

We discuss the main mechanisms affecting the dynamical evolution of Near-Earth Asteroids (NEAs) by analyzing the results of three numerical integrations over 1 Myr of the NEA (4179) Toutatis. In the first integration the only perturbing planet is the Earth. So the evolution is dominated by close encounters and looks like a random walk in semimajor axis and a correlated random walk in eccentricity, keeping almost constant the perihelion distance and the Tisserand invariant. In the second integration Jupiter and Saturn are present instead of the Earth, and the 3/1 (mean motion) and v ₆ (secular) resonances substantially change the eccentricity but not the semimajor axis. The third, most realistic, integration including all the three planets together shows a complex interplay of effects, with close encounters switching the orbit between different resonant states and no approximate conservation of the Tisserand invariant. This shows that simplified 3-body or 4-body models cannot be used to predict the typical evolution patterns and time scales of NEAs, and in particular that resonances provide some fast-track dynamical routes from low-eccentricity to very eccentric, planet-crossing orbits.On leave from the Department of Mathematics, University of Pisa, Via Buonarroti 2, 56127 Pisa, Italy, thanks to the G. Colombo fellowships of the European Space Agency.     

Irregular extrasolar systems and dynamical instability

The astrometric search for extrasolar planetary systems can regard, at least in the first stage, only systems with high mass ratio (10^–2) of the largest planets to the central star. The formation of such systems is probably a common occurrence in the galaxy, as indicated by various theoretical arguments; these systems could have evolved in a regular way (near-circular and coplanar orbits, Titius-Bode law, etc.) until the most massive accumulating protoplanet exceeded the critical value of the mass ratio corresponding to dynamical instability. This phenomenon has been extensively investigated in recent years, showing that a three- orN-body system becomes unstable (for relative separations similar to the planetary ones) for >10^–2. Therefore, it seems likely that observations of systems within this range of mass ratio will show the irregular end-products of processes related to the instability (close encounters or ejections), which affected drastically the orbital configuration in the last phase of the planet formation.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.