The impact origin of Eunomia and Themis families

Abstract— Criteria for finding asteroid families (Zappala et al. 1995) are applied to a large (205,770 member) data set of asteroid orbital elements. The cases of the Eunomia and Themis families are considered as examples. This is combined with the cratering criteria for catastrophic disruption of small bodies in the solar system (Leliwa‐Kopystyński et al. 2008). We find that the Eunomia parent body itself was not catastrophically disrupted in the family‐generating impact event; after impact, the current body contains as much as 70% of its primordial mass. However, by contrast with Eunomia, the present mass of 24 Themis is only about 21% of that of its primordial body. Limits are placed on the sizes of the impactors in both examples, and for the case of Eunomia, the radius of the just sub‐critical crater (which may be present on 15 Eunomia) is predicted as <58 km.     

The Maunder Minimum and the Sun as the Possible Source of Particles Creating Increased Abundance of the <Superscript>14</Superscript>C Carbon Isotope

The Maunder Minimum was the time during the second part of the 17th century, nominally from 1645 to 1717 AD, when unusually low numbers of sunspots were observed. On the basis of numerous recorded observations of auroras in the early 18th century, the end of the Minimum could be regarded as around 1700, but details of sunspot observations by Jan Heweliusz (Heweliusz, Machina Coelestis, 1679), John Flamsteed and Philippe de La Hire in 1684 allow us to interpret the Maunder Minimum as the period without a significant cessation of activity. This Minimum was also recognized in ¹⁴C data from trees which grew during the second part of 17th century. The variation in the production rate of radioactive carbon isotope ¹⁴C is due to modulation of the cosmic ray flux producing it by the changing level of solar activity and solar magnetic flux. Stronger magnetic fields in the solar wind make it more difficult for cosmic rays to reach the Earth, causing a drop in the production rate of ¹⁴C. However, more detailed analyses of ¹⁴C data indicate that the highest isotope abundances do not occur at the time of sunspot minima, as would be expected on the basis of modulation of the cosmic ray flux by the solar magnetic field, but two years after the sunspot number maximum. This time difference (or phase delay) can be accounted for if in fact there are both solar and non-solar cosmic ray contributions. Solar flares could also contribute high-energy particles and produce ¹⁴C and are generally not most frequent at the time of the highest sunspot numbers in the cycle.     

Neoproterozoic and Cambrian successions deposited on the East European platform and Cadomian basement area in Poland

Summary A short review of the Neoproterozoic and Cambrian sedimentary and volcanogenic successions in Poland is concerned with depositional and tectonic developments. The successions accumulated in shallow shelf and deeper slope environments. They overlie Palaeoproterozoic crystalline basement of the Baltic Craton and Gondwana-derived Neoproterozoic Cadomian basement. This discrepancy in the nature of the basement is viewed as indicating distinct terranes. During the course of Palaeozoic time, the discrete terranes were assembled along the Teisseyre-Tornquist Lineament and the Trans-European Suture Zone adjacent to the Baltica palaeocontinent.     

Variability of polar motion oscillations with periods from 20 to 150 days in 1979–1991

Variability of short period oscillations of polar motion with periods ranging from 20 to 150 days were investigated in the period 1979–1991. The new computation method of time variable band pass filter spectra and the Wavelet Transform method were applied. These oscillations are elliptical with variable amplitudes. Modulation periods of amplitude variations of these oscillations of about two and three years were found. Correlations of short period oscillations of polar motion and of effective atmospheric angular momentum (EAAM) excitation functions show annual variations and connections of their increases with El Niño phenomena.     

Mixing processes in wide open channels

The work contains analyses of two cases of stream diffusion under conditions of turbulent flow in an open channel. The analysed cases were: a source of rectangular cross-section placed in the channel axis and at the wall. To describe the mixing process the known equation of the turbulent diffusion was used. Verification of the solution for the considered cases was made based on research performed on models.     

Thermomagnetic properties of some Late Mesozoic diabase dikes of South Spitsbergen

Summary Laboratory investigations of thermomagnetic properties of specimens from seven diabase dikes of South Spitsbergen have been performed. Studies of temperature variation of isothermal saturation remanence combined with Hopkinson effect measurements and investigations of low temperature remanence give information on the mineral composition of the magnetic phases present in the magnetic fraction of the diabases. The experiments show that the clean natural remanence of these dikes has been acquired at the time of their, consolidation in the Late Mesozoic, though three of them may have been partially remagnetized at the time of Tertiary orogeny. Since the dikes reveal several normal and reversed directions of clean natural remanence, it is concluded that they were formed at different times in the Late Mesozoic, even though some of them may have been subjected to secondary influences at a later date.     

Nonlinearity of Nonradial Modes in Evolved Stars

We show that in evolved stars, even at relatively low surfaceamplitudes, nonradial modes become strongly nonlinear in thehydrogen shell source, where the Brunt-Väisälä frequency hasits absolute maximum. The measure of nonlinearity is the productof horizontal displacement times the radial wavenumber, . It becomes large already in evolved -Scuti stars.This nonlinearity presents a major problem for interpretations ofamplitude modulation in RR Lyrae stars in terms of nonradial modeexcitation.     

Double Material Segment as the Model of Irregular Bodies

We propose a new, simple model to describe the gravity field of irregular, nonspherical celestial bodies, like small moons or minor asteroids. The simple idea of Duboshin to use a material straight segment for such bodies is extended by combining two perpendicular segments of different lengths and masses. In typical situations, when the longest axis of the body coincides with one segment, the remaining segment must have an imaginary length. The potential remains a real function even if one segment is imaginary. The new model is confronted with the exact form of an ellipsoid's potential and with two alternative simple models for a two-axial and a three-axial ellipsoid.     

Ptolemaic Transformation in Keplerian Problem

We propose the Ptolemaic transformation: a canonical change of variables reducing the Keplerian motion to the form of a perturbed Hamiltonian problem. As a solution of the unperturbed case, the Ptolemaic variables define an intermediary orbit, accurate up to the first power of eccentricity, like in the kinematic model of Claudius Ptolemy. In order to normalize the perturbed Hamiltonian we modify the recurrent Lie series algorithm of HoriuuMersman. The modified algorithm accounts for the loss of a term's order during the evaluation of a Poisson bracket, and thus can be also applied in resonance problems. The normalized Hamiltonian consists of a single Keplerian term; the mean Ptolemaic variables occur to be trivial, linear functions of the Delaunay actions and angles. The generator of the transformation may serve to expand various functions in Poisson series of eccentricity and mean anomaly.     

Energy gap and density in SiO2 polymorphs

A relationship between the energy gap (E _G) and density (ρ) for pure SiO₂ polymorphs is derived from atomic weights and first ionization potentials of free silicon and oxygen atoms. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency v₀ of elementary electron oscillators, in energy units h v₀, is identified with the energy gap of a solid. The numerical relation is expressed as \(E_G = \sqrt {139.24 - 13.8327\rho } \) is in eV. For low-quartz with a density of 2.65 g/cm³ and also for stishovite with a density of 4.28 g/cm³, the energy gap E _G=10.1 eV and 8.9 eV, respectively. From laboratory measurements for low-quartz E _G=10.2 eV. The energy gap-density relation suggests a critical density value of ρ_x ≈ 10.1 g/cm³ for an SiO₂ phase when the energy gap vanishes (E _G=0), which is consistent with estimated densities for a high pressure silica polymorph with the fluorite structure.