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A modification of the Laplace method for the determination of a preliminary orbit of a body moving in the plane of the ecliptic is presented. It is shown that on the basis of three close positions on the celestial sphere, the parabolic orbit can be determined in cases, when the classical Laplace method is not suitable. The numerical estimation of the number of possible solutions is carried out, and their spatial distribution depending on initial conditions is shown. An example of the determination of an orbit for the comet C/2007 N3 (Lulin) is given. [ABSTRACT FROM AUTHOR]

A compiled catalogue of 21 440 stars with magnitudes between 10 and 17 is prepared from original observations made at the end of the 20th century to the beginning of the 21st century. The catalogue contains 227 fields of the celestial sphere centered at ICRF extragalactic radio sources with declinations of −17 to +89°. The field size is 40′ for both right ascension and declination. The internal accuracy of positions for both coordinates is no worse than 0.1″. A comparison of the stellar positions with the UCAC2 and CMC13 catalogues shows that the average external accuracy is approximately 0.05-0.15″. The positions of 10 795 stars with declinations to +50° are given for the epoch and equinox of J2000.0, whereas the positions of other stars are given for the epoch of observation. [ABSTRACT FROM AUTHOR]

We suggest a method for extracting important cosmological information from observational data on galaxy proper motions on the celestial sphere. These data can be used to reconstruct the three-dimensional velocities of galaxies relative to the cosmicmicrowave background (peculiar velocities), and to separate the Hubble and peculiar components of the observed redshifts in a large volume for the first time. As a result, it is possible to determine the Hubble constant accurately and independently using the radial velocities of comparatively close galaxies (up to 50 Mpc), and to determine distances to the galaxies and the mass distribution in the neighborhood of the Local group of galaxies. The proposed task may be solved using the future 'Millimetron' space radio interferometer. [ABSTRACT FROM AUTHOR]

Results of observations of the five candidate GPS sources J0626+8202, J0726+7911, J1044+8054, J1823+7938, and J1935+8130 are presented. GPS sources are extragalactic sources whose spectral peaks are near several GHz. These objects were observed on the RATAN-600 radio telescope from 1999 through 2010 at 1.1, 2.3, 4.8, 7.7, 11.2, and 21.7 GHz. These radio sources were selected from a complete sample ( S ≥ 200 mJy at 1.4 GHz) in the vicinity of the North Celestial Pole (+75° ≤ δ ≤ +88°); four are considered as GPS candidates for the first time here. Their spectral properties, variability and morphology are analyzed, and confirms that these can be classified as GPS sources. These four to five GPS sources probably comprise a complete sample of this class of object in this region of the celestial sphere. [ABSTRACT FROM AUTHOR]

We investigate the energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson-Walker space-time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson-Walker space-time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy-momentum tensor for a conformally invariant field in Robertson-Walker space-time space from the corresponding Rindler counterpart by the conformal transformation. [ABSTRACT FROM AUTHOR]

This chapter focuses on the fundamental origin of lines observed in astrophysical spectra. Some properties of the atomic world are qualitatively explained as an introduction to spectroscopy. General laws and rules are exposed and applied to celestial bodies. [ABSTRACT FROM AUTHOR]

This article deals with the timekeepers of the past, the sundials. Apart from discussing the structure of a few common sundials, we point out the reasons for the variation between sundial time and the time shown by mechanical timekeepers. [ABSTRACT FROM AUTHOR]

The painter Emil Nolde's studio was built in 1927 and, the following year, construction was begun on what was to become the house that he shared with his wife Ada in Seeb??ll. The building was located on a mound in the middle of the marsh, not far from the new border between Germany and Denmark that was made as a result of the vote in 1920. Nolde had designed the building according to the principle that it was to have ???three facades following the passage of the sun???. Like a sunflower, the facades of the building were to reach out and take in the changing light in step with the sun's flight across the sky. There would be ample opportunity for both skylight and sunlight to enter the building as the positioning on a mound raised the building above the surroundings. In Nolde's view, up on the mound, ???the entire celestial sphere was above us; it was greater than a semicircle - strange how even a small elevation in the flat landscape can make the vault of heaven seem larger???. [ABSTRACT FROM AUTHOR]

Based on the available celestial intermediate pole (CIP) coordinate determinations from VLBI observations over the last 25 years, we have constructed a new highly accurate combined series of CIP coordinates. An amplitude-phase analysis of this series has allowed us to improve the previously estimated retrograde free core nutation (RFCN) parameters as functions of time. During this interval, the RFCN period changed several times. It was −418.1 ± 0.2 days before 1992.1 and then −431.6 ± 0.2 days until 1999.0. In 1999, the CIP oscillations damped out almost completely and the processwas restructured. Since 2000, the amplitude of these oscillations has increased and their period has become 450.7± 0.1 days. [ABSTRACT FROM AUTHOR]

The article discusses various issues related to formation of the notion of celestial sphere in the Eastern Han Dynasty of China. The article makes specific reference to the "Book of the Later Han (Houhanshu). The article also takes a comparative study of descriptions of the celestial sphere and various celestial calculations in the treatise "Houhanshu" and "Almagest."

The article examines the orientation with respect to the sky of ancient temples in Middle Egypt and Sudan. A previous paper compiled facts concerning the location of temples, and from these facts postulated a theory that connected temple siting to celestial phenomena. The current paper describes two separate efforts based on temples in Middle Egypt and Sudan to either refute or confirm this theory. The authors' presentation presents strong evidence of the impact sky-watching had on ancient culture, religion, and architecture.

A numerical and experimental investigation is reported for the flow around a rolling sphere when moving adjacent to a plane wall. The dimensionless rotation rate of the sphere is varied from forward to reversed rolling and the resulting wake modes are found to be strongly dependent on the value of this parameter. Results are reported for the Reynolds number range 100

Analysis of the probable effects of ending the prohibition against sovereign national extraterrestrial territory in the Outer Space Treaty points to large increases in the total territories of a small number of spacefaring states as they compete in a succession of annexations that move from celestial body to celestial body. Rather than result in an increased chance of war between spacefaring states—an argument deployed by defenders of the Outer Space Treaty—extraterrestrial annexations would instead reduce its likelihood, both in the near-term because of the mutual vulnerability of human spacecraft and bases, and over the long-term by making spacefaring states less vulnerable to terrestrial warfare. [ABSTRACT FROM AUTHOR]

In this paper I discuss a cardboard dissected globe made in 1813 by Edward Mogg, a cartographer and map seller, to instruct children in the principles of astronomy. Since little is known about the maker or the specific object, I draw on evidence beyond the sphere itself to construct an account of how the object might have been used. In particular I address conversation as a key part of astronomical education and examine the way in which the cardboard plates of the sphere, the presentation slipcase and the accompanying booklet would have prepared young learners for polite astronomical discourse around large instruments in later life. [Copyright &y& Elsevier]

A method of constructing three-dimensional orbits with a necessary evolution in the system the Sun — (Earth + Moon) is described. The orbit (promising from the viewpoint of solving formulated research problems) of the Millimetron spacecraft is suggested. Feasibility of such an orbit is demonstrated, as well as a possibility to observe with its help the majority of objects on the celestial sphere and to transmit the data to the Earth. [ABSTRACT FROM AUTHOR]

A correlation analysis is made of the spatial distribution of galaxies in the Coma, Bridge, and A1367 clusters, which form the Coma supercluster. The scale of the clustering of galaxies and the variation in their density distribution with the main parameters of the galaxies– luminosity, morphological type, and observed H I deficiency in the 21 cm line– are evaluated. The mass-to-luminosity ratios are computed for the spiral galaxies in the Coma, Bridge, and A1367 clusters. It is suggested that a larger fraction of hypothetical dark matter may be concentrated in the spiral galaxies which predominantly populate the subclusters previously identified by us within these clusters than in the spiral galaxies observed in the peripheral regions of the clusters. [ABSTRACT FROM AUTHOR]

The article focuses on Pierre Crignon (1464?–1540), a sixteenth-century French navigator, explorer, and poet born in Dieppe. The author focuses on the poem "Our Astrolabe Where the Sphere Is Comprised," written for the annual poetry festival in Rouen, France "Puy de palinod." It compares and contrasts qualities of the Blessed Virgin Mary, celestial sphere, and astrolabes. The article also discusses Crignon's friendship with fellow poet and explorer Jean Parameter and Crignon’s account of their voyage to Sumatra, navigational tools used in the early 16th century, and the patronage system used to finance literature and voyages of discovery.

The article presents a study on one of the oldest surviving Euro-American star map made by the American surveyor Simeon de Witt in 1780. De Witt made his planisphere in the perspective that observers were outside the celestial sphere and the constellations appear reversed from those of the planispheres made by Britons John Senex and James Ferguson. The author also imparts his impotence on de Witt's celestial planisphere education and the reason he labeled his work astrolabe.

We show that two stationary, asymptotically flat vacuum black holes in 5 dimensions with two commuting axial symmetries are identical if and only if their masses, angular momenta, and their “interval structures” coincide. We also show that the horizon must be topologically either a 3-sphere, a ring, or a Lens-space. Our argument is a generalization of constructions of Morisawa and Ida (based in turn on key work of Maison) who considered the spherical case, combined with basic arguments concerning the nature of the factor manifold of symmetry orbits. [ABSTRACT FROM AUTHOR]

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions. [ABSTRACT FROM AUTHOR]

The basic vector geometry of a stellar interferometer with two telescopes is defined by the right triangle of (i) the baseline vector between the telescopes, of (ii) the delay vector which points to the star, and of (iii) the projected baseline vector in the plane of the wavefront of the stellar light. The plane of this triangle intersects the celestial sphere at the position of the star; the intersection is a circular line segment. The interferometric angular resolution is high (diffraction limited to the ratio of the wavelength over the projected baseline length) in the two directions along this line segment, and low (diffraction limited to the ratio of the wavelength over the telescope diameter) perpendicular to these. The position angle of these characteristic directions in the sky is calculated here, given either local horizontal coordinates, or celestial equatorial coordinates. [ABSTRACT FROM AUTHOR]

A new method of computing the preliminary orbit of a celestial body based on four pairs of angle measurements has been suggested. The method makes use of preliminary orbit previously constructed by the author based on two position vectors and a corresponding time interval, taking into account the main part of the perturbations in the motion of the body under study. Using the example of constructing the orbit of the minor planet 1383 Limburgia, the results obtained using a four-position procedure of the Gaussian type based on the solution of a two-body problem have been compared with those of the new method. The comparison showed the new method to be highly efficient for perturbed motion studies. It is especially advantageous in the case of high-accuracy observation data on small orbital arcs. [ABSTRACT FROM AUTHOR]

Aiming at the generation of a silanone intramolecularly bound to platinum, we prepared pincer-type PSiP silanol Pt(II) complexes. While a stable silanone complex was not isolated, unusual reactivity modes, involving its possible intermediacy, were observed. Treatment of the new PSiH2P-type ligand (o-/Pr2PC6H4)2SiH2 (7) with (Me2S)2Pt(Me)Cl yields the pincer-type hydrosilane complex [{(o- iPr2PC6H4)2SiH}PtCl] (8), which upon Ir(I)-catalyzed hydrolytic oxidation gives the structurally characterized silanol complex [{(o- iPr2PC6H4)2SiOH}PtCl] (3). Complex 3, comprising in its structure the nucleophilic silanol fragment and electrophilic Pt(II)-Cl moiety, exhibits dual reactivity. Its reaction with the non-nucleophilic KB(C6F5)4 in fluorobenzene leads to the ionic complex [{(o- iPr2PC6H4)2SiOH}Pt]+ [(C6F5)4B]- (9), which reacts with CO to yield the structurally characterized [{(o- iPr2PC5H4)2SiOH}PtCO]+ [(C6F5)4B]- (10). Treatment of 3 with non-nucleophilic bases leads to unprecedented rearrangement and coupling, resulting in the structurally characterized, unusual binuclear complex 11. The structure of 11 comprises two different fragments: the original O-Si-Pt(II)-Cl pattern, and the newly formed silanolate Pt(II)-H pattern, which are connected via a disiloxane bridge. Complex 9 undergoes a similar hydrolytic rearrangement in the presence of iPr2NEt to give the mononuclear silanolate Pt(II)-H complex 17. Both these rearrangement-coupling reactions probably involve the inner-sphere generation of an intermediate silanone 14, which undergoes nucleophilic attack by the starting silanol 3 to yield complex 11, or adds a water molecule to yield complex 17. X-ray diffraction studies of 3, 10, and 11 exhibit a very short SiPt bond length (2.27-2.28 Å) in the neutral complexes 3 and 11 that elongates to 2.365 Å in the carbonyl complex 10. A significantly compressed geometry of the silanolate platinum(II)-hydride fragment B of the binuclear complex 11 features a Pt(2)-O(2)-Si(2) angle of 100.4 (3)° and a remarkably short Pt(2)⋯Si(2) [2.884 (3) Å] distance. [ABSTRACT FROM AUTHOR]

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components. [ABSTRACT FROM AUTHOR]

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. [ABSTRACT FROM AUTHOR]

The Arp-Burbidge paradox (the enhanced density of distant quasars in the vicinity of some nearby galaxies) can potentially be explained as an effect of gravitational lensing within the existing cosmological paradigm. Distant, rich X-ray clusters, or even superclusters, of galaxies are observed along the lines of sight toward many of the objects on which this “paradox” is based. Such clusters can act as complex, transparent gravitational lenses, which can change the observed surface density of background objects due to the gravitational fields of both the cluster as a whole and of massive member galaxies, as well as of possible intergalactic globular clusters that may contain an appreciable fraction (∼10%) of the dark matter in galaxy clusters. We have verified the statistical basis for the supposedly “paradoxical” observational facts using data from the SDSS catalog, and used the minimal spanning tree method to search for inhomogeneities in the surface distributions of 32 800 quasars in one region of the celestial sphere ( α = 120°–260°, δ = 20°–70°). [ABSTRACT FROM AUTHOR]

Abstract: In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean . The four dimensional cyclographic model of the set of spheres in is an appropriate framework to show that a quadratic triangular Bézier patch in corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the envelope has rational offsets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties. [Copyright &y& Elsevier]

We report new results obtained from multifrequency observations of PSR B0826−34 with the Giant Metre-wave Radio Telescope (GMRT). (1) We find no evidence of weak emission during the typical long null state of this pulsar, simultaneously at 303 and 610 MHz, as well as individually at 157, 325, 610 and 1060 MHz at separate epochs. Our limit of non-detection is at ∼1 per cent or better of the peak of the active state profile, and corresponds to ∼2 mJy at 610 MHz. (2) Significant correlation in the total intensity of the individual pulses between 303 and 610 MHz is reported from the simultaneous dual-frequency observations, which is indicative of the broad-band nature of the emission. We also report correlation between total energy in the main pulse and interpulse region from the high-sensitivity single-frequency observations at 610 and 1060 MHz. (3) Though we find the drift pattern to be very similar in the simultaneous 303- and 610-MHz data, we observe that the drift band separation ( P2) evolves significantly between these two frequencies, and in a manner opposite to the average profile evolution. In addition, we confirm the dependence of P2 on pulse longitude at 303 MHz and find indications for the same at 610 MHz. We also present results for subpulse width (ΔΦs) at different frequencies, and as well as a function of pulse longitude. (4) As a natural outcome of the simultaneous dual-frequency observations, we obtain an accurate dispersion measure value, equal to 52.2(6) pc cm−3, for this pulsar. [ABSTRACT FROM AUTHOR]

Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year Wilkinson Microwave Anisotropy Probe data, through a decomposition of the signal with steerable wavelets on the sphere. In addition to identifying local features of a signal at specific scales, steerable wavelets allow one to determine their local orientation and signed intensity. First, an alignment analysis identifies two mean preferred planes in the sky, both with normal axes close to the CMB dipole axis. The first plane is defined by the directions towards which local CMB features are anomalously aligned. A mean preferred axis is also identified in this plane, located very close to the ecliptic poles axis. The second plane is defined by the directions anomalously avoided by local CMB features. This alignment anomaly provides further insight on recent results. Secondly, a signed-intensity analysis identifies three mean preferred directions in the southern Galactic hemisphere with anomalously high or low temperature of local CMB features: a cold spot essentially identified with a known cold spot, a second cold spot lying very close to the southern end of the CMB dipole axis, and a hotspot lying close to the southern end of the ecliptic poles axis. In both analyses, the anomalies are observed at wavelet scales corresponding to angular sizes around 10° on the celestial sphere, with global significance levels around 1 per cent. Further investigation reveals that the alignment and signed-intensity anomalies are only very partially related. Instrumental noise, foreground emissions and some form of other systematics are strongly rejected as possible origins of the detections. An explanation might still be envisaged in terms of a global violation of the isotropy of the Universe, inducing an intrinsic statistical anisotropy of the CMB. [ABSTRACT FROM AUTHOR]

Abstract: In this paper conformal minimal 2-spheres immersed in a complex projective space are studied by applying Lie theory and moving frames. We give differential equations of Kähler angle and square length of the second fundamental form. By applying these differential equations we give characteristics of conformal minimal 2-spheres of constant Kähler angle and obtain pinching theorems for curvature. We also discuss conformal minimal 2-spheres of constant normal curvature and prove that there does not exist any linearly full minimal 2-sphere immersed in a complex projective space () with non-positive constant normal curvature. We also prove that a linearly full minimal 2-sphere immersed in a complex projective space () with constant normal curvature and constant Kähler angle is of constant curvature. [Copyright &y& Elsevier]

Abstract: Some ways to obtain upper and lower bounds for measures of noncompactness of retractions onto spheres in infinite-dimensional normed spaces are discussed. Moreover, relations with 0-epi maps are revealed and the extension of condensing maps on spheres is discussed. As an application, some results of Birkhoff–Kellog type and Nussbaum''s fixed point theorem on spheres are obtained. [Copyright &y& Elsevier]

Abstract  Gluck has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K 5-minor freeness guarantees the stress freeness. More generally, we prove that every K r+2-minor free graph is generically r-stress free for 1≤r≤4. (This assertion is false for r≥6.) Some further extensions are discussed. [ABSTRACT FROM AUTHOR]

The two-dimensional (2D) phases of fatty-acid monolayers (hexadecanoic, octadecanoic, eicosanoic, and docosanoic acids) have been studied at the interface of a nematic liquid crystal (LC) and water. When observed between crossed polarizers, the LC responds to monolayer structure owing to mesoscopic alignment of the LC by the adsorbed molecules. Similar to Langmuir monolayers at the air/water interface, the adsorbed monolayer at the nematic/water interface displays distinct thermodynamic phases. Observed are a 2D gas, isotropic liquid, and two condensed mesophases, each with a characteristic anchoring of the LC zenithal tilt and azimuth. By varying the monolayer temperature and surface concentration we observe reversible first-order phase transitions from vapor to liquid and from liquid to condensed. A temperature-dependent transition between two condensed phases appears to be a reversible swiveling transition in the tilt azimuth of the monolayer. Similar to monolayers at the air/water interface, the temperature of the gas/liquid/condensed triple-point temperature increased by about 10 °C for a two methylene group increase in chain length. However, the absolute value of the triple-point temperatures are depressed by about 40 °C compared to those of analogous monolayers at the air/water interface. We also observe a direct influence by the LC layer on the mesoscopic and macroscopic structure of the monolayer by analyzing the shapes and internal textures of gas domains in coexistence with a 2D liquid. An effective anisotropic line tension arises from elastic forces owing to deformation of the nematic director across phase boundaries. This results in the deformation of the domain from circular to elongated, with a distinct singularity. The LC elastic energy also gives rise to transition zones displaying mesoscopic realignment of the director tilt or azimuth between adjacent regions with a sudden change in anchoring. [ABSTRACT FROM AUTHOR]

The article focuses on the medieval text by Abu 'l-Husayn 'Abd al-Rahman al-Sufi concerning celestial charts. Al-Sufi presents two equivalent projections of each constellation. Some passages from John Flamsteed and Leonard Heuler's works that are related to celestial charts and charting are considered.

We present explicit examples to show that the "compatibility criterion" (recently obtained by us toward providing equilibrium configurations compatible with the structure of general relativity) which states that for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), where M is the total mass and R is the radius of the configuration] of any static configuration cannot exceed the compactness ratio, uh, of the homogeneous density sphere (i.e., u ≤ uh) is capable of providing a necessary and sufficient condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the M–R relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion such that each member of this sequence satisfies the extreme case of causality condition v = c = 1 at the center. The maximum stable value of u ≃ 0.3389 (which occurs for the model corresponding to the maximum value of mass in the mass–radius relation) and the corresponding central value of the local adiabatic index, (Γ1)0 ≃ 2.5911, of this model are found fully consistent with those of the corresponding absolute values, umax ≤ 0.3406 and (Γ1)0 ≤ 2.5946, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the "trial function," ξ = reν/4, as well as the mass–central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favor of the statement regarding compatibility criterion mentioned above. Together with other results, this study also confirms the previous claim that just the choice of the "trial function," ξ = reν/4, is capable of providing the necessary and sufficient condition for dynamical stability of a mass on the basis of variational method. Obviously, the upper bound on the compactness ratio of neutron stars, u ≅ 0.3389, which belongs to two-density model studied here, turns out to be much stronger than the corresponding "absolute" upper bound mentioned in the literature. [ABSTRACT FROM AUTHOR]

We present a method to numerically estimate the densities of a discretely sampled data based on a binary space partitioning tree. We start with a root node containing all the particles and then recursively divide each node into two nodes each containing roughly equal number of particles, until each of the nodes contains only one particle. The volume of such a leaf node provides an estimate of the local density and its shape provides an estimate of the variance. We implement an entropy-based node splitting criterion that results in a significant improvement in the estimation of densities compared to earlier work. The method is completely metric free and can be applied to arbitrary number of dimensions. We use this method to determine the appropriate metric at each point in space and then use kernel-based methods for calculating the density. The kernel-smoothed estimates were found to be more accurate and have lower dispersion. We apply this method to determine the phase-space densities of dark matter haloes obtained from cosmological N-body simulations. We find that contrary to earlier studies, the volume distribution function v( f) of phase-space density f does not have a constant slope but rather a small hump at high phase-space densities. We demonstrate that a model in which a halo is made up by a superposition of Hernquist spheres is not capable in explaining the shape of v( f) versus f relation, whereas a model which takes into account the contribution of the main halo separately roughly reproduces the behaviour as seen in simulations. The use of the presented method is not limited to calculation of phase-space densities, but can be used as a general purpose data-mining tool and due to its speed and accuracy it is ideally suited for analysis of large multidimensional data sets. [ABSTRACT FROM AUTHOR]

Abstract: The effect of impactor obliquity and shape on crater evolution for a typical celestial impact event is examined in this numerical study. An important overall finding is that for a given obliquity angle, crater volume is not independent of impactor shape. The most varied behavior occurs at large obliquity angles, where the crater crest becomes highly elliptical and the ejecta pattern exhibits characteristic butterfly wings. Impacts at large obliquity angles can also produce craters with roughly equivalent dimensions from a wide range of impactor shapes and volumes. Conventional energy scaling can be applied to these results at moderate obliquities if the energy based on the vertical component of the velocity is used. For example, for a given impactor shape the crater volume scales with this energy and the depth with the cube root of this energy. However, at large obliquities, these relationships are invalid. Applying these results to the meteor crater at Odessa [Littlefield DL, Bauman PT, Molineux A. Analysis of formation of the Odessa Crater. Int J Impact Eng, accepted for publication.], some interesting conjectures can be made. First, the small depth-to-diameter ratio of that particular crater suggests that the impact occurred at a large obliquity angle, with a trajectory extending from the southwest to the northeast. Second, the circular entrance hole and the absence of additional impact craters along this trajectory suggest that the meteor may have been either disk-like or highly elliptical in shape. [Copyright &y& Elsevier]

A relatively simple technique is outlined to estimate the location of the solar apex and the mean velocity of the Sun with respect to the brightest 313 stars (V > 3.55). The apex and mean velocity are found from a visual examination of plots of stellar radial velocity versus right ascension, and radial velocity versus galactic longitude. The technique appears to be appropriate for undergraduate college astronomy classes and can be adapted to courses of various levels. [ABSTRACT FROM AUTHOR]

A statistical study of motions of images of distant extragalactic sources, such as quasars on the celestial sphere, due to the action of weak gravitational microlensing is presented. It was assumed that the parallax of the lens was 10 milliarcseconds (mas), the mass of the lens was 1 M ⊙, and the proper motion was µ = 30 mas. The initial point for the motion of the lens (a star in our Galaxy) was taken to be the boundary of a region with a radius of ϑ = 100 mas and its center coincident with the distant source. The simulations for each trajectory were carried out in steps, with the time step being 0.1 year. The number of sources “launched” over the computational period was 5000. The appearance of the trajectories for the source images is presented; 57% of the total number of sources that participated in the simulations showed motions of 0.7–1.0 mas. [ABSTRACT FROM AUTHOR]

We describe a method for producing high-resolution maps of the radiant distribution of meteor activity over the celestial sphere using single-station radio-meteor observations. The method uses a convolution technique and we show how a suitable convolution function can be chosen to enhance the apparent activity of meteor shower radiants. We apply this method to data produced by the Canadian Meteor Orbit Radar system near London, Ontario and show that the daily motion of the radiant can be measured within a fraction of a degree per day. The system has detected a number of weak showers that have not been previously catalogued. We show how the sensitivity of the system can be improved by combining observations from several days. [ABSTRACT FROM AUTHOR]

Spectral studies of one of the brightest Herbig-Haro objects, HH12, using a multiaperture (multi-pupil) spectrograph are reported. We identify nine knots (densification nodes) in intensity diagrams. Hα emission mainly predominates in this object, except in two of the knots (C and M) which have a lower excitation level, given their high [SII] line intensity. The average electron temperature across the object is 6700 K. It is shown that the radial velocity of the object as a whole is low, i.e., its motion is mostly in the celestial plane. The excitation source for HH12 is also discussed. [ABSTRACT FROM AUTHOR]