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We generalize Zwanziger's pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless QED and gravity transform under the Poincare group with an additional pair of pairwise celestial representations for each pair of matter particles. We demonstrate that the massless abelian and gravitational exponentiation theorems are consistent with the proposed pairwise Poincare transformation properties. For massless QED we demonstrate that our results are consistent with the effects of the Faddeev-Kulish dressing and the abelian exponentiation theorem for celestial amplitudes found in [2012.04208]. We discuss electric and magnetic charges simultaneously as it is especially natural to do so in this formalism., Clarifying comments added in sections 4 and 5

Infrared divergences in perturbative gravitational scattering amplitudes have been recently argued to be governed by the two-point function of the supertranslation Goldstone mode on the celestial sphere. We show that the form of this celestial two-point function simply derives from an effective action that also controls infrared divergences in the symplectic structure of General Relativity with asymptotically flat boundary conditions. This effective action finds its natural place in a path integral formulation of a celestial conformal field theory, as we illustrate by re-deriving the infrared soft factors in terms of celestial correlators. Our analysis relies on a well-posed action principle close to spatial infinity introduced by Comp\`ere and Dehouck., Comment: 24 pages, one figure

The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2,C) conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the celestial sphere., Comment: 9 pages. v2: replaced to match JHEP

Massless scattering amplitudes in four-dimensional Minkowski spacetime can be Mellin transformed to correlation functions on the celestial sphere at null infinity called celestial amplitudes. We study various properties of massless four-point scalar and gluon celestial amplitudes such as conformal partial wave decomposition, crossing relations and optical theorem. As a byproduct, we derive the analog of the single and double soft limits for all gluon celestial amplitudes., Comment: 13 pages, 1 figure

We demonstrate that a dark silhouette of the black hole illuminated by a thin accretion disk and seen by a distant observer is, in fact, a silhouette of the event horizon hemisphere. The boundary of this silhouette is a contour of the event horizon equatorial circle if a thin accretion disk is placed in the black hole equatorial plane. A luminous matter plunging into black hole from different directions provides the observational opportunity for recovering a total silhouette of the invisible event horizon globe. The event horizon silhouette is projected on the celestial sphere within a position of the black hole shadow. A relative position of the bright part of the accretion disk with respect to the position of event horizon silhouette in the presented first image the black hole in the galaxy M87 corresponds to a rather high value of the black hole spin, $$a\simeq 0.75$$ .

A system of isophotes of the cosmic microwave background (CMB) is constructed for several regions on the celestial sphere using data from the Planck spacecraft. The fractal dimensionality of the isotherms is estimated to be Dc ≈ 1.78 ± 0.03. Our results agree with earlier work based on the ILC charts with WMAP data. Our simulations confirm the previous conclusion that a similar dimensionality is obtained for a gaussian spectrum of initial perturbations.

Five temples of Apollo on Mainland Greece and Ancient Ionia (Asia Minor), namely Delphi, Didyma, Hierapolis, Delos and Rhodes, have been examined regarding their functioning through astronomical orientation. Recent research has shown that the rise, setting, orbit and observation of certain constellations in the celestial sphere, as well as the solar stands, can be directly related to the architecture of the temple, i.e. construction, orientation, and keeping a calendar of the most important Apollonian oracular temple at Delphi. Here this lunar-solar-stellar configuration has been applied to other significant temples of Apollo. It is shown that at Didyma, Hierapolis and Delphi, the celestial pattern, as well as the landscape, local geology and architecture are similar, but different in temples without oracular function (Delos and Rhodes). Measurements were carried out by in situ readings and by Google Map tools.

Onboard the spacecraft Lomonosov is established two fast, fixed, very wide-field cameras SHOK. The main goal of this experiment is the observation of GRB optical emission before, synchronously, and after the gamma-ray emission. The field of view of each of the cameras is placed in the gamma-ray burst detection area of other devices located onboard the “Lomonosov” spacecraft. SHOK provides measurements of optical emissions with a magnitude limit of $\sim 9\mbox{--}10^{m}$ on a single frame with an exposure of 0.2 seconds. The device is designed for continuous sky monitoring at optical wavelengths in the very wide field of view (1000 square degrees each camera), detection and localization of fast time-varying (transient) optical sources on the celestial sphere, including provisional and synchronous time recording of optical emissions from the gamma-ray burst error boxes, detected by the BDRG device and implemented by a control signal (alert trigger) from the BDRG. The Lomonosov spacecraft has two identical devices, SHOK1 and SHOK2. The core of each SHOK device is a fast-speed 11-Megapixel CCD. Each of the SHOK devices represents a monoblock, consisting of a node observations of optical emission, the electronics node, elements of the mechanical construction, and the body.

Celestial mechanics is one of the most ancient science. It is dedicated to the study of the motion of planets, moons, asteroids, comets and other celestial bodies. It probably started when humans discovered that some special stars differentiate from the others in the sense that they move on the celestial sphere. Currently, it is responsible for successfully guiding spaceships to distant objects in our solar system aiming to explore them. As an introduction to this Focus Issue in Celestial Mechanics, we make here a historical overview of developments in this area and present the articles that comprise this special issue.

13 pages, 8 figures., A statistical analysis of the orientation of Nabatean sacred monuments demonstrates that astronomical orientations were often part of an elaborated plan and possibly a trace of the astral nature of the Nabataean religion. Petra and other monuments in the ancient Nabataean kingdom have proven to be marvellous laboratories for the interaction between landscape features and astronomical events, showing impressive hierophanies on particular monuments related to cultic times and worships. Among other findings, the famous Ad Deir has shown a fascinating ensemble of light and shadow effects, perhaps connected with the bulk of Nabataean mythology, while from the impressive Urn Tomb, a series of suggestive solstitial and equinoctial alignments emanate which might have lately helped its selection as the cathedral of the city. This paper demonstrates that the sky was a substantial element in Nabataean religion and reveals new evidence for cultic worship centred on the celestial sphere.

In this paper, the error analysis has been done for the linear approximate transformation between two tangent planes in celestial sphere in a simple case. The results demonstrate that the error from the linear transformation does not meet the requirement of high-precision astrometry under some conditions, so the linear approximate transformation should be taken seriously.

Multi-frequency same-beam VLBI means that two explorers with a small separation angle are simultaneously observed with the main beam of receiving antennas. In the same-beam VLBI, the differential phase delay between two explorers and two receiving telescopes can be obtained with a small error of several picoseconds. The differential phase delay, as the observable of the same-beam VLBI, gives the separation angular information of the two explorers in the celestial sphere. The two-dimensional relative position on the plane-of-sky can thus be precisely determined with an error of less than 1 m for a distance of 3.8×105 km far away from the earth, by using the differential phase delay obtained with the four Chinese VLBI stations. The relative position of a lunar rover on the lunar surface can be determined with an error of 10 m by using the differential phase delay data and the range data for the lander when the lunar topography near the rover and the lander can be determined with an error of 10 m.

In the first part of this series, we discussed the celestial sphere and Aryabhata’s principle of axial rotation; in this part we shall discuss in detail the concept of sidereal day and then mention Aryabhata’s computations on the duration of sidereal day.

We consider five dimensional deSitter spacetimes with a deficit angle due to the presence of a closed 2-brane and identify one dimension as an extra dimension. From the four dimensional viewpoint we can see that the spacetime has a structure similar to a Kaluza-Klein bubble of nothing, that is, four dimensional spacetime ends at the 2-brane. Since a spatial section of the full deSitter spacetime has the topology of a sphere, the boundary surface surrounds the remaining four dimensional spacetime, and can be considered as the celestial sphere. After the spacetime is created from nothing via an instanton which we describe, some four dimensional observers in it see the celestial sphere falling down, and will be in contact with a 2-brane attached on it., 5pages, 4figures, to be published in GRG

International audience; We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based on the material available for an observer, for example relative positions at a given time of the couple in the ``plane of sky'', namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one hand, the geometric problem is solved using the first Kepler's law from a single observing run and, on the other hand, dynamical parameters are then inferred from the fit of the Kepler's equation. At last, the final stage consists in determining the main physical parameters involved in the secular evolution of the system, that is the spin axis and the J2 parameter of the primary if we assume that it is a quasi-spherical body. As a matter of fact there is no need to make too restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by a non-linear least-squares Levenberg Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto Charon system parameters from observations collected in the literature since 1980.

Most asteroid discoveries consist of a few astrometric observations over a short time span, and in many cases the amount of information is not enough to compute a full orbit according to the least squares principle. We investigate whether such a Very Short Arc may nonetheless contain signican t orbit information, with predictive value, e.g., allowing to compute useful ephemerides with a well dened uncertainty for some time in the future. For short enough arcs, all the signican t information is contained in an at- tributable, consisting of two angles two angular velocities for a given time; an appar- ent magnitude is also often available. In this case, no information on the geocentric range r and range-rate _ r is available from the observations themselves. However, the values of (r; _ r) are constrained to a compact subset, the admissible region, if we can assume that the discovered object belongs to the Solar System, is not a satellite of the Earth and is not a shooting star (very small and very close). We give a full algebraic description of the admissible region, including geometric properties like the presence of not more than two connected components. The admissible region can be sampled by selecting a nite number of points in the (r; _ r) plane, each corresponding to a full set of six initial conditions (given the four component attributable) for the asteroid orbit. Because the admissible region is a region in the plane, it can be described by a triangulation with the selected points as nodes. We show that triangulations with optimal properties, such as the Delaunay triangulations, can be generated by an eectiv e algorithm; however, the optimal triangulation depends upon the choice of a metric in the (r; _ r) plane. Each node of the triangulation is a Virtual Asteroid, for which it is possible to propagate the orbit and predict ephemerides. Thus for each time there is an image triangulation on the celestial sphere, and it can be used in a way similar to the use of the nominal ephemerides (with their condence regions) in the classical case of a full least square orbit.

We discuss a new method for measuring the coordinates of meteor shower radiants from meteor radar data. The method uses a high accuracy of radar goniometer measurements of one of the angular coordinates for meteor radiants and collective properties of incident meteor showers. It is based on a computer technology of searching for the coordinates of radiants using the intersections of meteor position lines on the celestial sphere and filtering nonrandom combinations of these intersections. The method allows the following: to detect meteor showers with a rate of more than 5 per day of observations and to separate meteor groups from different meteor showers with different radiants and velocities. The method makes it possible to increase the angular resolution from 10° × 10° achieved with a quasi-tomographic technique to 2° × 2°, with a prospect of a further increase in the accuracy through the individual reduction of separated meteor groups. We use the reduction of one-day-long observations during maximum activity of the Geminids meteor shower in 1993 to illustrate the potentialities of the method. We show an example of detecting a weak meteor shower that was active during December 1993.

Since extra-Galactic radio sources are distributed unevenly over the celestial sphere, accumulated experimental data in the domain of spatial frequencies are used. The author was unable to explain discrepancies between experimental and model spectra by errors of calculation or experiment. A possible explanation is the presence of Galactic fluctuations in the cosmic radio background.

We prove experimentally the possibility of direct observations of natural radio echoes on the Sun. The generally simple echo hypothesis on the origin of the time splitting in solar type IIId radio bursts sustained the crucial experimental test. These conclusions are based on both the new positional data and previous information obtained using the UTR-2 antenna system in different years since 1973. In summer 1992, we were able to register for the first time a large number of decameter type IIId bursts with pronounced echo-like components using a radioheliograph at frequencies of 20 and 25 MHz. Elementary (quasi-monochromatic) sources of the short-lived bimodal type IIId bursts were observed especially often on July 6. In this case, the time delay of the second peak, which depends on the heliolongitude of the active region, reached a maximum of about 7 s. All these double-peak bursts were localized in the central region of the solar corona, and, similar to the case of single-pulse “limb” type IIId bursts at a given radio frequency f, the observed elementary sources of these events appeared to be nonstationary. Such a dynamic pulsating source can radically change, at least once, its location in the celestial sphere in the field of view of a two-dimensional radio heliograph during the burst lifetime τΣ. While decaying, an echo-like burst formed rather slowly may abruptly jump from one location to another. As far as its short (3- to 4-s) steep-front precursor is concerned, its visible source behaved usually as an ephemeral sub- or ultrarelativistic object moving at a subluminal velocity over a global-scale trajectory. To all appearances, a twice-pulsing, narrow-band (Δ f/f∼ 0.01) radio burst with an intensity-time profile of type IIId is generally a rather long-term (τΣ ≈ 10-20 s) transient response of the solar atmosphere to the short-term flare of harmonic radio emission generated in the real (probably motionless and compact) source. This complex double-peak profile is due not only to the existence of a reflecting surface deep in the corona near the corresponding plasma level but also, to a considerable extent, to some opaque or semi-transparent structures located at heights of the middle corona. In particular, due to the strong influence of such structures, a coronal primary source of a bimodal burst can be seen on the Earth in some indirect rays before the solar radio echo and has the form of an additional delayed pulse.

Gamow was one of the pioneers who studied the possible variability of fundamental physical constants. Some versions of modern Grand Unification theories do predict such variability. The paper is concerned with three of the constants: the fine-structure constant α, the ratio of the proton massm p to the electron massm e, and the ratio of the neutron massm n tom e. It is shown on the basis of the quasar spectra analysis, that all the three constants revealed no statistically significant variation over the last 90% of the life time of the Universe. At the 2δ significance level, the following upper bounds are obtained for the epoch corresponding to the cosmological redshiftsz∼2–3: Δα/α

An analysis of sporadic meteor flux distributions over the celestial sphere is given. Symmetry of the radiant distribution relative to the plane crossing the ecliptic pole and the Earth's apex and antapex was identified.

We have carried out double-station TV meteor observations between 1990 and 1994. The orbits of 326 meteors have been determined from doubly observed meteors, and radiant distributions are studied. The mean magnitude of the observed meteors was as faint as +4.7, since I.I. (Image Intensifier) and Video cameras were used. Radiants were widely distributed over the celestial sphere. The velocity distribution showed some similarity with the distribution predicted by the theoretical radiant distribution from comets rather than that from asteroids. In all 13 showers including both major and minor meteor showers were detected from radiant distributions of the observed meteors; from the orbital elements and meteor velocities as well as from the radiant directions.

This article contains the tomographic problem's solution of the radiants distribution study by the meteor radar data. It was received the distribution of meteors velocities for the parts of celestial sphere with angular dimensions 10° × 10° and 1° × 1°. Was shown that the angular dimensions of most of radiants are equal 1° – 3° and larger part of the sporadic background looks like a totality of microstreams.

0°. Among Ptolemy's works are two whose mathematical bases historians of science have interpreted in very much the same way. The works are The Planispherium and the cartographic sections of The Geography, and in both cases the interpretation has been in terms of pointwise projection of a portion of the surface of the sphere onto a portion of the plane. In the case of The Planispherium the sphere is the celestial sphere and the mapping appears to be stereographic projection of the portion of the celestial sphere to the north of "the greatest always-invisible circle"1 on the interior of a circular part of the plane. For example, Neugebauer 1975 (857-858) writes "it [The Planispherium] deals with the representation of the celestial sphere . . . known today as stereographic projection", Toomer 1978 (219) writes "the whole necessary theory of stereographic projection is set out in Ptolemy's Planispherium,'" and Pedersen 1974 writes "In the Planispherium ... Ptolemy describes how the celestial sphere can be projected in a different way, namely by stereographic (central) projection from the southern pole of the heavens onto the plane of the equator." In the case of The Geography however the sphere is the terrestrial globe and, in addition to Marinus's much-criticized representation of its surface, Ptolemy gives three other representations of the inhabited portion of the earth (the oikoumene in the language of Greek geographers) onto plane regions of varying shapes. Here again, the best of the recent literature on the topic has set forth Ptolemy's representations in terms of pointwise maps or projections of the sphere into the plane. Some examples are the analyses of F. Hopfner in the appendices to Mžik & Hopfner 1938 and the summary in Neugebauer 1975 (879-890).

It is easy to compute the diurnal arc or day length. We show that the same simplicity exists for the “solar arc” on an inclined surface, i.e. the theoretical interval during which it sees the sun. By transposing the daily extraterrestrial irradiance onto the celestial sphere, we demonstrate the concept of image, sunshine modes, transitions from one mode to another and annual sequence of modes which are, in a sense, the generalization of astronomical seasons for inclined surfaces. The modes are the elements of a group, or the focus of the theory. We give the foundation of a simple and exhaustive theory on the subject for any surface the following explicit formulae: image, mode, declination of transition between two modes, sunrise and sunset, solar arc or extraterrestrial sunshine, and daily irradiance. This subject has been previously broached in some infrequently referenced papers as well as in more recent papers by Revfeim (1976, 1978, 1982), Swift (1976), and Sato (1984). However, due to their lack of structure, those contributions to a geometrical theory have been largely neglected and the empirical point of view still prevails.

Radiation transfer problem in the slowing-down region is solved for a spherical geometry. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the sphere for two cases: (i) in the presence of internal source, (ii) if the radiation is incident on the sphere. Numerical results are obtained by using the Pade approximant technique.

The probability of pulsars and supernovae being found close to each other on the celestial sphere by chance is calculated. It is found that this corresponds to the number of pulsars found close to supernovae in recent investigations. Thus, we conclude that, given also the inaccuracy of distances involved, the apparent spatial coincidence of pulsars and supernovae does not generally imply generic associations.

New data are given on the structure of the region around the nucleus of the Seyfert galaxy NGC 1275 and the nucleus itself. Direct plates obtained with the 6-m telescope with red and blue glass filters were used. The scale of the images on the negatives was 17.5 mm/sup -1/. The galaxy NGC 1275 has a double nucleus. The position angle of the line joining the components of the nucleus is approx. =5/sup 0/. The distance between the components, projected onto the celestial sphere, is 1.50 + or 0.60 (or 500 + or - 20 pc). Each of the components is

A new reduction method usingx, y, z-coordinates is derived for astrolabe observations. By this method, the latitude and the longitude of the station are computed without the need of a priori knowledge of the station position. This method is a significant development in data reduction of astrolabe and other almucantar observations due to its mathematical exactness, simplicity, and the ease of handling the associated statistics.

γ-ray astronomy is the study of the most energetic photons originating in our Galaxy and beyond, and therefore, provides the most direct means of studying the largest transfers of energy occurring in astrophysical processes. The first certain detection of celestialγ-rays came from a satellite experiment flown on OSO-III (Kraushaaret al., 1972); more recently two second generation spark chamberγ-ray telescopes, flown on the SAS-2 (Fichtelet al., 1975) and COS-B (Bennettet al., 1974) satellites, are now obtaining more detailed results on the high energy celestial radiation causingγ-ray astronomy to move from the discovery phase to the exploratory phase. The most striking feature of the celestial sphere when viewed in the frequency range ofγ-rays is the emission from the galactic plane, which is particularly intense in the galactic longitudinal region from 300° to 50°. The longitudinal and latitudinal distributions are generally correlated with galactic structural features and when studied in detail suggest a non-uniform distribution of cosmic rays in the galaxy. Several pointγ-ray sources have now been observed, including four radio pulsars. This last result is particularly striking since only one radio pulsar has been seen at either optical or X-ray frequencies. Nuclearγ-ray lines have been seen from the Sun during a large solar flare and future satellite experiments are planned to search forγ-ray lines from supernovae and their remnants. A general apparently diffuse flux ofγ-rays has also been seen whose energy spectrum has interesting implications; however, in view of the possible contribution of point sources and the observation of galactic features such as Gould's belt, its interpretation must awaitγ-ray experiments with finer spatial and energy resolution, as well as greater sensitivity. Instruments with much greater sensitivity and improved energy and angular resolution are now available and will greatly enhance our understanding of high energy processes in astrophysics, especially in view of the high penetrating power ofγ-rays, which for example permit them to reach the solar system from the far side of the galaxy essentially unattenuated.

The ultraviolet stellar spectrophotometer S59 of the Utrecht Astronomical Institute uses the stabilization properties of the ESRO TD-1A satellite. This spacecraft scans the sky along eliptic meridians with an orbital precession of one degree per day, thus covering the whole celestial sphere in half a year. This property is combined with a tracking system which points the spectrophotometer during four minutes at stars of sufficient brightness. During this time interval the ultraviolet stellar spectrum is scanned with a resolution of 1.7 A in three bands of about 100 A, around 2110, 2545 and 2825 A. The optical, mechanical and electronic properties of the instrument and its tracking system are described in some detail, as well as the optical and technical performance in laboratory tests and in orbit. Some results obtained during the first half year of operation are briefly described.

A comparison of the radio luminosities of isolated single and double galaxies has shown that spiral galaxies which are members of pairs have a radio luminosity which exceeds that of single galaxies by 2.5 times on the average. The power of the radio emission of members of pairs depends on the projection onto the celestial sphere of the linear distance between the components of the pairs. For example, members of pairs with projection of the distance between them less than 10 kpc have a radio luminosity greater by 2-2.5 times than members of pairs for which the distance between them is greater than 50 kpc. Members of interacting pairs are more powerful emitters in the radio range. It is also shown that spiral galaxies that are members of triplets have radio luminosities that are apparently not interior to members of pairs.

The search for the Figure of the Earth is rooted in the age-old wonder about the world we live in. The ancient mythical notions have developed, under the tutelage of Greek systematic thought, into specific questions of the shape and size of the Earth. The history of these questions, now spanning more than two millenia, shows a continuous refinement in formulation, as each bona fide answer prompted refined measurements which, in turn, started a new round of problems. The change in concept of what one was looking for was, and still is, closely connected with the technical capability and its potential for further development. This change in concept is traced here from ancient times to the present throungh some of its milestones: Anaximander's partly invisible celestial sphere and Pythagoras' spherical Earth; Eratosthenes' exemplary combination of astronomy and land surveying for the dual purpose of determining the size of the spherical Earth and making a map of the habitable world; the identical dual purpose followed by the Academie Royale des Sciences in the 17th century, but on a more sophisticated technical level; the challenge to the spherical concept by Newton's gravitational theory and the absorption of that theory into a wider concept of the Figure of the Earth; the acknowledgment of the irregular geoid by Gauss, Bessel, and Helmert, and the changed significance of the ellipsoid; Heiskanen's and Vening Meinesz' ‘Basic Hypothesis of Geodesy’ concerning the hydrostatic equilibrium of the Earth, and O'Keefe's contradiction on the basis of satelite data; the dream of global surveys come true through satellite geodesy and the accompanying inclusion of the outer gravity field of the Earth into the concept of its Figure; and lastly, the present and projected capability of high precision measurement and the widening of the concept of the Figure of the Earth from 3-dimensional rigidity to 4-dimensional time-dependence.

This work is devoted to describing new statistical and geometrical procedures for dating ancient star catalogues considering numerical data contained in these catalogues and the known real configurations of stars on the celestial sphere. The method was tested on several star catalogues whose dates are well known (Tycho Brahe, etc.) and on several artificially generated star catalogues. Then the same method was applied to the Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift its dating to the Arabian epoch: 600–1300 AD.

The reliability of identifications of narrow absorption lines with small red shifts is analyzed statistically on the basis of literature data on spectra with high spectral resolution for 38 quasi-stellar objects. The identifications were made using a reference spectrum including the most pronounced lines of the interstellar medium. Particular attention is devoted to the case of quasi-stellar objects in the region + or - 10 deg from the supergalactic equator or coincident in position on the celestial sphere with high-latitude high-velocity hydrogen clouds, and also situated at small angular distances from nearby galaxies. It is shown that in the majority of cases identifications with the line pairs of Ca II and Na I are random.

Huchra and Geller proposed a new method for identifying groups of galaxies. One begins by choosing an arbitrary galaxy from a list restricted by a certain apparent magnitude and with complete data on the radial velocities. In the neighborhood of this galaxy one then seeks neighbors in accordance with the following criteria: the radial velocities and apparent magnitudes of the first and second galaxy, the angular separation, the projection of the linear distance between the two galaxies onto the celestial sphere, and Hubble's constant. Neighbors that satisfy these criteria are assumed to be members of a group. One then considers the neighborhoods of the members of a group already chosen in this manner and finds new neighbors by the same method. This process is continued until all members of the group have been found. The aim of this note is to find physically more justified criteria for identifying groups of galaxies in the hope of eliminating or at least significantly ameliorating the noted shortcomings while retaining the main advantages of Huchra and Geller's method.

A cosmic-ray counter telescope (OKAYAMA telescope) has been operated at several zenith angles at sea level. Several millions of clean single events have been analysed. About thirty candidates of (4/3)e charged leptons were found at around 40° zenith angles. The distribution of the arrival directions of these candidates in the celestial sphere was found to be anisotropic.

Observations of 85 gamma bursts by the KONUS instruments on the Venera 11 and Venera 12 spacecraft in the period September 1978 to May 1979 inclusive have provided proof of a galactic localization of the gamma-burst sources based on an analysis of the logN-logS plot and the revealed anisotropy in the angular distribution of sources over the celestial sphere. Evaluation of the energy released in the sources yields 1040–1041 erg. There apparently exist several types of gamma bursts differing in time profile, duration and shape of their energy spectrum. In some cases, extensive evolution of the energy spectrum is observed during a burst. The discovery of a flaring X-ray pulsar in Dorado has provided the first observational evidence for a connection of gamma bursts with neutron stars. Repeated short bursts from this source have revealed for the first time the recurrent features of this phenomenon. Repeated bursts have been detected from one more source in the short burst class. The data obtained thus far impose a number of restrictions on the applicability of many theoretical suggestions concerning the nature of the gamma bursts. The most plausible model for the gamma-burst source appears to be a binary with a neutron star with strongly non-stationary accretion involving, possibly, non-stationary thermonuclear fusion of matter falling onto the surface of a degenerate star.

The paper reviews the current status of observational research into the highly puzzling problem of cosmic gamma-ray bursts. Up to now there is no convincing temporal or spatial correlation with any known celestial processes or objects. The typical burst source strength is somewhere between 10 to the 26th power ergs and 10 to the 52nd power ergs. A list of 39 confirmed and 9 unconfirmed cosmic gamma-ray bursts observed by satellite is given, showing times of occurrence and in some cases, the size in erg per square centimeter. Several approaches to the problem of source object identification are discussed: (1) accumulation of observation statistics with their present poor resolution and research for correlative phenomena, (2) mapping out celestial source distributions with moderate resolution in order to search for galactic or other anisotropies in direction or to look for repeating source regions, and (3) very high-accuracy localization of the source directions of one or several bursts in order to pinpoint a tiny fraction of the celestial sphere for correlative radio, optical and X-ray studies. Planned future instrumentation for deep space probes and multiple-balloon studies is described.

Interest in scientific cosmogony is a recent, and still a very tender growth. Anthropologists and geologists tell us that man has existed on earth for something like 300,000 years ; we must go this far back to meet our ape-like ancestry. Between them and us some 10,000 generations of men have walked the Earth, most of whom have probably given some thought, in varying degrees, to the significance of their existence and the plan of the universe. But of these 10,000 generations of men, the first 9990 unhesitatingly regarded the earth as the centre, and terrestrial life as the central fact, of the universe. As was suited to its majesty and dignity as the abode of man, the earth stood still while the celestial sphere spun round it, covering in the earth much as a telescope-dome covers in the telescope. And this dome was spangled with stars, which had been thoughtfully added so as not to leave the central earth unillumined at night. Ten generations at most have been able to consider the problem of their existence in anything like its proper astronomical perspective. The total age of the earth far exceeds the 300,000 years or so of man's existence. The evidence of geology and of radio-activity in rocks in particular, shows that it must be something like 2,000 million years, which is several thousand times the age of the human race. Old Mother Earth must regard man as a very recent apparition indeed ; he has just appeared to burrow into her, burn her forests, put her waterfalls into pipes, and generally mar the beauty of her features. If he has done so much in the first few moments of his existence, she may well wonder what is in store for her in the long future ages in which he is destined to labour on her surface. For in all probability the life in front of the human race must enormously exceed the short life behind it. A million million years hence, so far as we can foresee, the sun will probably be much as now, and the earth will be revolving round it much as now. The year will be a little longer, and the climate quite a lot colder, while the rich accumulated stores of coal, oil and forest will have long been burnt

For navigation, desert ants apply piloting and dead-reckoning strategies based on terrestrial and celestial visual cues, respectively. Visual spatial memories, rather than general concepts derived from landmark constellations, are most probably used to define points on earth by nearby landmarks. The visual field of a specialized dorsal part of the ant's retina is mapped on to the celestial sphere to consider the possibility that similar mechanisms are used to define directions on earth by exploiting skylight patterns present at infinity.

The γ-ray burst detector Konus1, on the Venera 11 and Venera 12 spacecraft, detected on 5 and 6 March, 1979 two bursts of hard X rays originating from the same source. These events are quite unusual and of considerable interest. The burst of 5 March was very intense, particularly in the initial phase. This event was also observed by several other spacecraft2. The second burst on 6 March was considerably weaker. The observations reported here permitted us to obtain a detailed time structure of the bursts, to measure their energy spectra and to locate the source on the celestial sphere.

Many objections have recently been raised—above all, in America—to the decisions of the International Conference that met in May 1896, at Paris, with the object of choosing a uniform system of fundamental stars and astronomical constants for the four great ephemerides of Berlin, London, Paris and Washington. The matter is of the greatest importance, in as much as it refers to the bases of precise astronomy, together with a general tendency of all science to a method of international discussion that, leaving free and autonomous all personal and local initiatives, bring workers in such agreement as is necessary for nullifying discrepancies and contradictions. Of such tendency we have the most comforting manifestations in the International Geodetical Association, in the Commission (also international) for unifying weights and measures, and in the similar meetings of scientific men of every nation for the electrical measurements, for meteorological services, for the photography of the heavens. Astronomy is, perhaps, among all physical sciences the one destined by its historical tradition, no less than by its present and future necessities, to second—nay, to promote and develop—the cosmopolitan tendency. The grand spectacle of the face of the heavens, ever before the eyes of all; the difference of phenomena according to the horizons, which carries with it the need of co-operation between the observers diversely situated with regard to the celestial sphere; in fine, the high and significant moral education that comes to astronomers from the continual contrast between the immensity of the heavens and the miserable narrowness of the limits traced out conventionally on the globe between one country and another; here are the causes through which a spirit superior to any narrow nationalism was soon breathed into our souls. Tycho Brahe, the proud Danish patrician, the founder of practical astronomy in the Renaissance, sings sternly—

The efficiency of using the coded aperture on the ‘Gamma-1’ telescope to solve a variety of astrophysical problems has been considered. The coded aperture technique is shown to be at a disadvantage in relation to the conventional one so far as discriminating a source from the background is concerned. However, for powerful sources the coded aperture technique has an advantage from the viewpoint of accuracy of source location on the celestial sphere, the resolution of closely spaced sources and the determination of the sizes of sources.

MANY theories of the origin of comets predict that there are ∼ 1011 comets in the Solar System; most of them, unfortunately, at such a distance that they can never be observed. Some theories go even further and predict that, in addition to these comets in the Oort cloud, the remains of a primaeval comet belt may still exist at a distance of ∼ 50 AU. This idea has been investigated by Hamid et al.1, who show (from an analysis of observed perturbations on Halley's comet) that the total mass of the comet belt must be ≲ 1 Earth mass. Even this relatively small mass would be enough for ∼ 1010 comets—a significant fraction of the total of the whole Oort cloud. It has been noted that comets contain a relatively large fraction of‘heavy’elements, and it has been suggested2 that the total galactic population of comets may be large enough to affect significantly the chemical evolution of the Galaxy by acting as a ‘sink’ for the heavy elements.

SINCE the γ-ray burst was discovered in 1973, approximately 50 events have been observed using artificial satellites1,2. In addition, several bursts of smaller size have been found using balloon-borne detectors3–6 with large sensitive areas. No burst has yet been located on the celestial sphere, with an adequate precision to associate it with an astronomical object. To determine the precise position of a γ-ray burst which had not been predicted to occur, the detector must have a wide field of view and the capability of precise location of the source. A rotating cross-modulation-collimator (RCMC) proposed7 as a device to fulfill these apparently conflicting requirements was used in the series of balloon observations reported here. A small γ-ray burst was found during ∼ 150 h of observations and its celestial position was determined with a precision of ∼ 0.3°.

DETECTION of gamma-ray bursts of cosmic origin by detectors onboard Vela, OGO, IMP-6 and OSO-7 satellites1–3 was one of the major surprises of observational astronomy recently. The bursts were observed over the energy range 7 keV to 1.5 MeV and were found to have time durations ranging from less than a second to about 80 s with integrated flux density between a few times 10−6 and 3 × 10−4 erg cm−2 for different events. From the 20 events that have been detected so far (from data accumulated over 5 yr) it seems that these events are distributed almost isotropically on the celestial sphere and occur at frequencies of about four to five each year, at the level of sensitivity of Vela satellites. In view of the absence of definitive positive associations with well known transient phenomena1,4 such as supernovae, galactic radio noise spikes, rapid atmospheric fluorescence increases, Cygnus X-3 radio flares or even with gravitational radiation events, continuous patrol for detecting these events through as many independent techniques as possible is very important to understand the nature of their origin.

IN order to search for possible point sources of cosmic rays, an alt-azimuth Geiger–Muller counter telescope of narrow angular resolution (5° × 5°) was made, and kept nearly horizontal (zenith distance Z = 80°) so that the effective cosmic-ray particles were free from complicated geomagnetic deflexion. After scanning over the celestial sphere, especially large intensities were observed at two positions as noticed in our earlier paper1.

IN a recent communication1 an outline was given of investigations of the variable galactic noise received from the constellation of Cygnus, first noticed by Hey, Parsons and Phillips2. The characteristics of the radiation were described, and evidence was given of its origin in a discrete source. A search has since been made over about one quarter of the celestial sphere for other such sources. The region investigated is roughly enclosed by the co-ordinates : The frequency used was 100 Mc./s., with an overall sensitivity of 10−24 watts m.−2 (c./s.)-1, and the technique and equipment employed were as previously described1,3.