On the restrited three-body problem when the mass parameter is small

We study some aspects of the restricted three-body problem when the mass parameter is sufficiently small. First, we describe the global flow of the two-body rotating problem, =0, and we use it for the analysis of the collision and parabolic orbits when 0. Also we show that for any fixed value of the Jacobian constant and for any >0, there exists a ₀>0 such that if the mass parameter [0,₀], then the set of bounded orbits which are not contained in the closure of the set of symmetric periodic orbits has Lebesgue measure less than .Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.     

A high resolution mid-infrared image of the Starburst Galaxy M82

We have produced high-resolution images of the nuclear region of M82 with SpectroCam-10, a mid-infrared instrument at the Palomar 5 m telescope. These images were taken at 11.7 m and 9.8 m with a 1m filter bandpass at the diffraction limit of 0.6 arcsec, making them the highest resolution maps yet available of M82. In addition, we have obtained high-resolution (/=2000) maps of the velocity field of the nuclear disk of M82 in the 12.81 m line emission of [NeII]. In these proceedings we present the 11.7 m image, which will appear together with the 9.8 m map and the [Ne II] spectra in a subsequent paper, now in preparation. This image shows very clearly a bridge structure joining the eastern and western clusters.     

The evaluation of the interplanetary diffusion coefficient for energetic particles employing real magnetic field data

A numerical simulation of energetic particle motion in the interplanetary medium is carried out using HEOS-2 magnetometer data in order to computeD(), the pitch angle diffusion coefficient, where is cosine of pitch angle defined with respect to the local field. WhileD() exceeds that given by quasi-linear theory near 90° pitch angle, it is significantly less at higher values of , leading to a parallel transport coefficient in good accord with that given by experimental studies of solar proton propagation. In particular, =0.031 AU at a particle magnetic rigidity of 455 MV, while experimental results range from 0.05 to 0.07 AU (+100%, –50%) in this rigidity region. Furthermore, observed approximately -dependent solar proton pitch angle distributions are consistent with the computed findingD()/(1 – ²)² ~ constant.The validity of various analytical corrections to quasi-linear theory as 0 are also investigated numerically.     

Ejection and collision orbits of the spatial restricted three-body problem

We begin by describing the global flow of the spatial two body rotating problem, =0. The remainder of the work is devoted to study the ejection and collision orbits when >-0. We make use of the blow up techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S²×R. Also we find some particular collision-ejection orbits.     

Sub-arcsec 10 μm imaging of β pictoris and other star disk candidates

We have used the ESO 10 m camera, TIMMI, to image with a very high angular resolution (PFoV: 0.3; FWHM:0.9) several main-sequence star disk candidates. Information on the -Pictoris dust disk has been obtained in a region largely inaccessible to previous observations: 0–80 AU, with a resolution of about 5 AU after deconvolution. Another promising target for 10 m imaging, 51 Ophiuchi, appears point-like.based on data collected at the European Southern Observatory (ESO), La Silla, Chile     

Infrared continuum observations of five-minute oscillations

Infrared continuum observations of the Sun at wavelengths between 10 and 30 show a nonisothermal response of the upper photosphere to compression waves associated with the five-minute oscillations. Observations were made with four broad-band filters with effective transmission wavelengths between 10 and 26 and with a 10 aperture. Further observations at submillimeter wavelengths with a 2 aperture did not resolve oscillatory fluctuations of five-minute period.Comparisons with velocity field data of Howard (1976) suggest that the relaxation time of the photosphere exceeds (300/2) seconds at the height of formation of the 26 continuum (_5000Å 10^-2). The photosphere reponds to 3 mHz oscillatory motion with considerably less compression than expected for simple acoustic modes in an adiabatically responsive atmosphere, confirming the evanescent character of the five-minute oscillations.     

Extinction and scattering by several types of silicate sphere of radius 0.05–1.0μm,for the wavelength range 0.21–50μm

The exact calculation of scattering and absorption by various sub-micron sized silicate spheres is presented here, using accurately determined optical constants in the wavelength range from 50 m to 0.21 m. The extinction features near 10 m and 20 m for various samples are discussed. It is found that the ratio of peak extinction at 20 m to that at 10 m is constant for small particles up tor=0.4 m, but is less for particles of radius 1 m. The ratio of maximum extinction in the ultraviolet to that at 10 m decreases with increasing particle size.     

Laboratory simulation of infrared astrophysical features

Laboratory infrared emission and absorption spectra have been taken of terrestrial silicates, meteorites and lunar soils in the form of micrometer and sub-micrometer grains. The emission spectra were taken in a way that imitates telescopic observations. The purpose was to see which materials best simulate the 10 m astrophysical feature.The emission spectra of dunite, fayalite and Allende give a good fit to the 10 m broadband emission feature of comets Bennett and Kohoutek. A study of the effect of grain size on the presence of the 10 m emission feature of dunite shows that for particles larger than 37 m no feature is seen.The emission spectrum of the Murray meteorite, a Type 2 carbonaceous chondrite, is quite similar to the intermediate resolution spectrum of comet Kohoutek in the 10 m region. Hydrous silicates or amorphous magnesium silicates in combination with high-temperature condensates, such as olivine or anorthite, would yield spectra that match the intermediate resolution spectrum of comet Kohoutek in the 10 m region. Glassy olivine and glassy anorthite in approximately equal proportions would also give a spectrum that is a good fit to the cometary 10 m feature.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6 8 September, 1978.     

Stability of and motion aboutL 4 at three-to-one commensurability

The stability ofL ₄ and the motion aboutL ₄ in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio has the value =0.013516.... The two time scale method is used (1) to show thatL ₄ is an unstable equilibrium point when =₃, (2) to determine for what initial conditions periodic orbits occur when ₃, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions aboutL ₄ when ₃.     

On periodic flybys of the moon

This paper considers the plane circular restricted three-body problem for small . Symmetric periodic solutions of the second species (passing near the body of mass ) and their distance from the center of the body of mass are studied by constructing perturbations of arc-solutions (solutions with consecutive collisions) existing for =0. Orbits which also pass near the body of mass 1- are studied in detail. The results are applied to finding periodic orbits in the Earth-Moon system and in the Sun-Jupiter system.Russian version: Preprint No. 91 (1978) of Inst. Appl. Math.; present English translation was made by L. M. Perko and W. C. Schulz (February 1979).     

The distribution of infrared sources in the galactic plane

A study of the galactic structure has been made by deriving the brightness distribution of the galactic plane at 2.2 m and 4.2 m near infrared region using infrared objects detected by ground-based sky surveys. The infrared brightness distribution shows distinct peaks at every 8–12° galactic longitude and indicates a periodic structure. The one-to-one positional correlation observed between the periodic structure in 2.2 m infrared brightness and the 2.6 mm CO emission line suggests that the near-infrared sources are strongly associated with dense clouds of molecular hydrogen distributed in the galactic plane.     

The velocity correlation function in cosmic-ray diffusion theory

The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than B _x ² /B ₀ ² . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients ²/t=2D and /t=D /, and that all higher-order coefficients are identically zero.     

An analysis of full-disk observations of facular contrast in the blue and red

Full-disk images from the Cartesian Full-Disk Telescope no. 2 (CFDT2) were used to study the center-to-limb (CLV) variation of facular contrast in two colors. The CFDT2 images, which have 2.5 arc sec pixels, were obtained during the summer months of 1993, 1994 and 1995. In order to minimize the bias in finding faint facular features in continuum images, we have used coaligned images obtained in the Ca K-line to identify faculae. Faculae were sorted into 20 annular bins of equal width. To reduce the effects of seeing, faculae were not identified closer to the limb than =0.2. The facular pixel contrasts were fitted to various trial functions. The contrast in the blue filter (470.6 nm) rose from 0.122% at disk center to 12.2% at =0.2. The contrast in the red filter (672.3 nm) rose from 0.13% at disk center to 8.16% at =0.2. We have also analyzed the facular contrasts multiplied by their -value to obtain an estimate of facular flux tube contrasts. These flux tube contrasts increased roughly linearly from =0.95 to 0.25. The blue flux tube contrast reached a maximum of 2.48% near =0.25. The red flux tube contrast reached a maximum of 1.59% at =0.2. These contrast values are not corrected for the filling factor. The blue curve leveled off slightly betwen =0.25 and 0.2 while the red curve showed no deviation from its linear trend. These results may provide some support for the hot wall model of facular flux tubes.     

Fourier techniques for an analysis of eclipsing binary light curves: III

The aim of the present paper will be to present a new approach to the light changes of eclipsing binary systems. The light changes have been expanded into the Fourier-Bessel and Dini series. The coefficients of these expansions which are the Hankel transforms of the order of the loss of light (1–l) have been expressed in terms of the eclipse elements. These discrete Hankel transformsH (j _m ) andH ( _m ) valid for only the positive real zerosj _m and _m of the functionsJ and [xJ(x)+J (x)] have been generalized for any positive value of andy. Thus, these general expressions for the Hankel transforms of the light curves which are valid for all types of eclipses, for any arbitrary degree of the adopted limb-darkening law and, moreover, for any positive value of the free parameters andy, may be used for the solution of the elements of eclipsing binary systems.     

Comparison of analytical and numerical calculations of the first class periodic orbits

The analytic construction of the direct periodic orbits in the circular 3-body problem is given in explicit form to the linear terms in . It is shown to be in good agreement with the numerically found orbits for large values of .     

The identification of the 3μ spectral feature in galactic infrared sources

We show that a 3 extinction feature in galactic infrared sources cannot be due to water-ice grains. Infrared spectra with a resolution of /=0.015 are in remarkably close agreement with the 2.5–4 extinction properties calculated for bacterial grains.     

Second species solutions with an 0(μν), 1/3<ν<1, near-moon passage

This paper uses Guillaume's extension of the Breakwell-Perko matching theory for the restricted three-body problem with small mass ratio >0 to establish the existence and asymptotic approximation of one-parameter families of second species periodic solutions with one near-moon passage of , during a half-period. The deflection angle at such a near moon passage, 0(^1–v), approaches zero as the mass ratio approaches zero.This work was supported by the National Science Foundation under Grant GP42739.     

On the infrared opacity of sunspots

In the umbral atmosphere the depth dependence of the opacity due to the vibration rotation bands of various abundant molecules in the wavelength region 1 m to 10 m has been calculated. In the higher layers of the umbral atmosphere, the molecular opacity seems to dominate the opacity due to the negative hydrogen ion.     

Charge-coupled device imaging spectroscopy of Mars. 1. Instrumentation and data reduction/analysis procedures

This paper describes the collection, reduction, and analysis of 0.4–1.0 m Mars imaging spectroscopy data obtained during the 1988 and 1990 oppositions from Mauna Kea Observatory and provides a general outline for the acquisition and analysis of similar imaging spectroscopy data sets. The U.H. 2.24-m Wide Field Grism CCD Spectrograph was used to collect 13 three-dimensional image cubes covering 90% of the planet south of 50°N in the 0.4–0.8 m region (/=245 at 0.6 m) and covering 55% of the planet south of 50°N in the 0.5–1.0 m region (/=293 at 0.75 m). Spectra extracted from these image cubes reveal the detailed character of the martian near-UV to visible spectrum. Images at red wavelengths reveal the classical albedo markings at 100–500 km spatial resolution while images at blue wavelengths show little surface feature contrast and are dominated by condensate clouds/hazes and polar ice. Many of the data acquisition, reduction, and analysis steps discussed here are new or unique to imaging spectroscopy data sets. These techniques exploit the information contained within the spatial domain of data such as these, thus allowing more traditional point-spectral analysis techniques to be expanded into an imaging format.     

Движение малых частиц в окрестностях протосолнца переменной светимости

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