A Systematic Study of the Stability of Symmetric Periodic Orbits in the Planar, Circular, Restricted Three-Body Problem

We investigate symmetric periodic orbits in the framework of the planar, circular, restricted, three-body problem. Having fixed the mass of the primary equal to that of Jupiter, we determine the linear stability of a number of periodic orbits for different values of the eccentricity. A systematic study of internal resonances, with frequency p/q with 2p 9, 1 q 5 and 4/3 p/q 5, offers an overall picture of the stability character of inner orbits. For each resonance we compute the stability of the two possible periodic orbits. A similar analysis is performed for some external periodic orbits.Furthermore, we let the mass of the primary vary and we study the linear stability of the main resonances as a function of the eccentricity and of the mass of the primary. These results lead to interesting conclusions about the stability of exosolar planetary systems. In particular, we study the stability of Earth-like planets in the planetary systems HD168746, GI86, 47UMa,b and HD10697.     

First Byurakan Spectral Sky Survey. Blue stellar objects. VIII. zone +65° ≤ δ ≤, + 69°

The eighth list of blue stellar objects in the second part of the First Byurakan Spectral Sky Survey (FBS) is presented. The objects are located in the zone +65° +69° and 5 ^h 15^m 18 ^h 05^m.The list contains data on 98 blue stellar objects detected, of which 73 are previously unknown. A preliminary classification of the objects is given. The exact coordinates of the centers and the limiting magnitudes of the plates for this zone have been determined using the charts of the Palomar Sky Survey.Translated from Astrofizika, Vol. 37, No. 2, pp. 197–206, April–June, 1994.This work has been performed with financial support of the ESO C&EE fund (A-02-043).     

The first byurakan Spectral Sky Survey. Blue stellar objects. X. The zone+73°≤σ≤+80°

We present the tenth list of blue stellar objects of the second part of the First Byurakan Spectral Sky Survey (FBS). The list contains 100 objects in the region+73°+80° and3 ^h 30 ^m 18 ^h 30 ^m encompassing an area of 355 square degrees. The objects have stellar V magnitude within the limits 12.0–18.5 and B-V colors between–0.77 and+0.37. Of these 100 objects, 80 were discovered for the first time. We give the equatorial coordinates, stellar V magnitude, color index CI, and preliminary classification of the objects on the basis of low-disperion prismatic spectra. For 29 objects we give approximate types, among which 4 are candidates for quasars, 2 for Seyfert galaxies, 1 for superassociation galaxy IC 381, 18 for white dwarfs, and 4 for cataclysmic variables.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

The photometric solution of cc com by use of the

The contact binary system CC Com (=12^h09^m33^s.8, =+22°4339, (1950);V _max=11.31, (B-V)_max=1.24) is a W UMa-type system with the shortest known period. The photometric solution of CC Com is presented using the Wilson and Devinney method. The results show that the CC Com belongs to the late-type eclipsing binary with the spectral type K5V and K6V, low temperatureT ₁=4300 K,T ₂=4265 K, the mass ratioq=0.5873±0.0021, and the inclinationi=87°.719±1°.44. The best regions of the gravity darkening exponents , the bolomotric albedov, and the limb-darkening coefficients are tested. It is found that 0.1250.065, 0.1v0.5, =0.5 are better regions for CC Com. The third body ofl ₃ is not found to be significant. The results are combined with the spectroscopic results of Rucinski to provide an estimate of the absolute parameters.     

First Byurakan Spectral Sky Survey. Blue stellar objects. VII. Zone +61° ≤δ ≤, +65°

The seventh list of blue stellar objects in the second part of the First Byurakan Spectral Sky Survey (FBS) is presented. The objects are located in the zone + 61° + 65° and 5 ^h 30^m 18 ^h 40 ^m .The list contains data on 119 blue stellar objects detected, of which 73 are previously unknown. A preliminary classification of the objects is given. The limiting magnitude of the FBS plates are determined using the photometric calibration of the charts of the Palomar Sky Survey.Translated fromAstrofizika, Vol. 37, No. 1, pp. 43–55, January–March, 1994.     

Integrals of motion in the elliptic three-dimensional restricted three-body problem

Three integrals of motion have been found in the three-dimensional elliptic restricted three-body problem for small eccentricitye of the relative orbit of the primaries and small distancer and eccentricitye of the orbit of the third body around a primary. The integrals are given in the form of formal series in the mass-ratio , the eccentricitiese, e and the coordinates and velocities. These integrals depend periodically on the time.     

Optical Identifications of IRAS Point Sources Based on Low-Dispersion FBS Spectra. Stars. V

A fifth list of point sources from the IRAS Point Source Catalog (PSC) that are optically identified with stars of late spectral types is given. The list contains data on 75 objects. The identifications were based on the Digital Sky Survey (DSS), the First Byurakan Survey, blue and red maps of the Palomar Observatory Sky Survey, and infrared fluxes at the wavelengths 12, 25, 60, and 100 m in the regions of +73° +80° and 03^h30^m 18^h30^m and of +80° +90° and 00^h00^m 20^h00^m. Of the 99 objects, which are given in the IRAS PSC as unidentified sources of infrared emission, 24 are associated with known stars in existing catalogs while 75 sources proved to be unknown in the optical range. The optical coordinates, their departures from the IR coordinates, the V stellar magnitudes, the color indices CI, and the preliminary spectral subtypes have been determined. The objects have optical magnitudes in the range of 6 ^m .5-17 ^m .2. Finder charts from the DSS are given for the 69 new objects.     

Three-dimensional,periodic, ‘halo’ orbits

A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L₁, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing .     

Radial pulsation of less-massive yellow supergiants

The conclusions of the present paper broadly are: (a) The galactic concentration of doubles by comparing the distributions in galactic latitudes 0°<20° and >40° is nearly twice as large as the galactic concentration of stars in general. (b) The astrographic catalogues are not complete in the fainter magnitudes. (c) The large value of the ratioT:O _k (observed to optical number of pairs) from Kreiken's formula shows that almost all stars in the group 0<d5 and quite a few in the other two groups, viz., 5<d10 and 10<d15 might be shown true binaries. Consequently, Aitken's working definition of a true binary should be extended if it were to include all true binaries. (d) The doubles are probably stars of Population I. (e) The logarithm to the base 10 of the cumulative counts can be represented by an empirical relationA+B(m–1.5)+C(m–1.5)².Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846)     

Optical Identifications of IRAS Point Sources. Galaxies. VII

A seventh list of objects from the BIG (Byurakan-IRAS galaxies) sample is given: 95 galaxies identified with 63 point sources from the IRAS Point Source Catalog. The identifications were based on the Digital Sky Survey (DSS), the First Byurakan Survey, blue and red maps from the Palomar Observatory Sky Survey, and infrared fluxes at 12, 25, 60, and 100 m in the region of +65° 69° and 14^h00^m 18^h05^m with an area of 96 deg². For the identified galaxies the optical coordinates, their departures from the IR coordinates, the stellar V magnitudes, morphological types, angular sizes, and position angles were determined. The objects have optical magnitudes in the range of 13 ^m .8-21 ^m .5 and angular sizes in the range of 4-38. Finder charts from the DSS are given for these objects.     

Linearized limb-darkening coefficients for use in analysis of eclipsing binary light curves

Linear limb-darkening coefficientsu required in the analysis of eclipsing binary curves, are tabulated for a wide range of effective temperature (50 000° to 4000°), wavelength (0.2 2.2 ), and gravitiesg (2.0logg5.0). The computation is based on the comprehensive range of model atmospheres of Carbon and Gingerich (1969).The results are compared with the theoretical values of Hosokawa (1957), Kopal (1959) and Grygaret al. (1972), and examined in relation to empirically determined values ofu from analyses of eclipsing binary light curves. An improved agreement between theory and observation for the calculated limb-darkening coefficients of the present work is noted.     

Symmetries and Bifurcations in the Sitnikov Problem

We present some qualitative and numerical results of the Sitnikov problem, a special case of the three-body problem, which offers a great variety of motions as the non-integrable systems typically do. We study the symmetries of the problem and we use them as well as the stroboscopic Poincarée map (at the pericenter of the primaries) to calculate the symmetry lines and their dynamics when the parameter changes, obtaining information about the families of periodic orbits and their bifurcations in four revolutions of the primaries. We introduce the semimap to obtain the fundamental lines l ₁. The origin produces new families of periodic orbits, and we show the bifurcation diagrams in a wide interval of the eccentricity (0 0.97). A pattern of bifurcations was found.This revised version was published online in October 2005 with corrections to the Cover Date.     

Enhancement of solar heavy nuclei at high energies in the 4 July 1974 event

Relative abundances of energetic nuclei in the 4 July 1974 solar event are presented. The results show a marked enhancement of abundances that systematically increase with nuclear charge numbers in the range of the observation, 6 Z 26 for energies above 15 MeV nucl.^–1 While such enhancements are commonly seen below 10 MeV nucl^–1, most observations at higher energies are found to be consistent with solar system abundances. The energy spectrum of oxygen is observed to be significantly steeper than most other solar events studied in this energy region. It is proposed that these observations are characteristic of particle populations at energies 1 MeV nucl^–1, and that the anomalous features observed here may be the result of the high energy extension of such a population that is commonly masked by other processes or populations that might occur in larger solar events.     

On the pulsation amplitude of cepheid variables

On the basis of more abundant data a relation logPV/logR for cepheid variables (Fernie, 1965) is constructed. A linear relation between logP V and logR for classical cepheids is found, which perhaps has a break at R=10R . On the logR/logP diagram thes-cepheids (Efremov, 1968) show a distinct sequence. Alls-cepheids present a relative variation of the radii R/R0.075. The existence of non-s-cepheids with R/R0.075 raises a point about the evolutionary place of these stars (see Efremov, 1968). One could suppose that cepheids with logP>1.1 pulsate in the first overtone.     

Relativistic supermassive stars

A plausible scenario for the formation of a stable supermassive star in the relativistic regime has been discussed. The onset of the negativity of the `distribution function' in the stable sequences of the star clusters [the stability of star clusters is assured by using the variational method (Chandrasekhar, 1964a,b) for equivalent gas spheres] described by Tolman's type VII solution with vanishing surface density has been regarded as an indication of the conversion of the cluster structure into a supermassive star. For the critical values of the `adiabatic index', (4/3) < _crit (5/3) (forwhich a supermassive star represent neutrally stable system), the mass, and the size of this object comes out to be 6.87 × 10⁷ M M 1.7 × 10⁹M, and 2.74× 10¹⁴ cm a 1.43× 10¹⁵cm respectively, for the central temperature,T₀ = 6× 10⁷°K, which is sufficient for the release ofnuclear energy. The total energy released during their evolution rangesfrom 2.46× 10⁶⁰ - 3.18× 10⁶² erg, which is sufficient to power these objects at least for a period of 10⁶ - 10⁷years. These figures agrees quite well with those cited for Quasi Stellar Objects (QSOs) in the literature.     

Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

Synthetic integrated fluxes and colours for elliptical galaxies

Photometric intergrated colours (UBVRI+UV selected bands) of elliptical galaxies are theoretically evaluated, accounting for stellar populations of different metal abundance (0.00001Z0.04). The contribution of different evolutionary phases (from M.S. up to Post-A.G.B.) to the integrated fluxes in the various photometric bands is computed. An explanation for the UV-excess in elliptical galaxies and of its dependence on the metallicity (Mg₂) and mass is also suggested.     

The polarization of coronal emission lines

By means of a photographic polarimeter, we attempted to measure both the amount and direction of linear polarization of all emission lines between 3400 and 9000 Å in the inner corona (1.034 r/r ₀ 1.085). Only the green and red coronal lines have been analyzed in detail. Neither of these lines shows polarization exceeding the probable error of 1.0% for 5303 and 1.8% for 6374. None of the other 17 coronal lines observed during the 7 March, 1970 solar eclipse show any obvious (>5%) polarization.Presently at the Sacramento Peak Observatory.     

Formation of short-period orbits of minor bodies of the Mars family

It is shown that the orbits of minor bodies of the Mars family can be formed as a result of single close encounters with the inner planets (Venus -Mars) of minor bodies moving along orbits with the aphelion distanceq' 4.26 AU. The Laplace method of the unperturbed two-body problem was applied.     

Low-Degree Low-Order Solar p Modes As Seen By GOLF On board SOHO

Data recovered from the GOLF experiment on board the ESA/NASA SOHO spacecraft have been used to analyze the low-order low-degree solar velocity acoustic-mode spectrum below =1.5 mHz (i.e., 1n9,l2). Various techniques (periodogram, RLAvCS, homomorphic-deconvolution and RLSCSA) have been used and compared to avoid possible biases due to a given analysis method. In this work, the acoustic resonance modes sensitive to the solar central region are studied. Comparing results from the different analysis techniques, 10 modes below 1.5 mHz have been identified.