UGC 7388: A galaxy with two tidal loops

We present the results of our spectroscopic and morphological studies of the galaxy UGC 7388 with the 8.1-m Gemini North telescope. Judging by its observed characteristics, UGC 7388 is a giant late-type spiral galaxy seen nearly edge-on. The main body of the galaxy is surrounded by two faint (μ _B ～ 24 ^m /□″ and μ _B ～ 25 _· ^m 5/□″) extended (～ 20–30 kpc) loop-like structures. A large-scale rotation of the brighter loop about the main galaxy has been detected. We discuss the assumption that the tidal disruption of a relatively massive companion is observed in the case of UGC 7388. A detailed study and modeling of the observed structure of this unique galaxy can give important information about the influence of the absorption of massive companions on the galactic disks and about the structure of the dark halo around UGC 7388.     

Inverse problem of central configurations and singular curve in the collinear 4-body problem

In this paper, we consider the inverse problem of central configurations of n-body problem. For a given \({q=(q_1, q_2, \ldots, q_n)\in ({\bf R}^d)^n}\), let S(q) be the admissible set of masses denoted \({ S(q)=\{ m=(m_1,m_2, \ldots, m_n)| m_i \in {\bf R}^+, q}\) is a central configuration for m}. For a given \({m\in S(q)}\), let S _m (q) be the permutational admissible set about m = (m ₁, m ₂, . . . , m _n ) denoted

$S_m(q)=\{m^\prime | m^\prime\in S(q),m^\prime \not=m \, {\rm and} \, m^\prime\,{\rm is\, a\, permutation\, of }\, m \}.$

The main discovery in this paper is the existence of a singular curve \({\bar{\Gamma}_{31}}\) on which S _m (q) is a nonempty set for some m in the collinear four-body problem. \({\bar{\Gamma}_{31}}\) is explicitly constructed by a polynomial in two variables. We proved:

1. (1)
   If \({m\in S(q)}\), then either ^# S _m (q) = 0 or ^# S _m (q) = 1.
    
2. (2)
   ^#S _m (q) = 1 only in the following cases:

   1. (i)
      If s = t, then S _m (q) = {(m ₄, m ₃, m ₂, m ₁)}.
       
   2. (ii)
      If \({(s,t)\in \bar{\Gamma}_{31}\setminus \{(\bar{s},\bar{s})\}}\), then either S _m (q) = {(m ₂, m ₄, m ₁, m ₃)} or S _m (q) = {(m ₃, m ₁, m ₄, m ₂)}.
       
    

     

Systematic error of the Gaia DR1 TGAS parallaxes from data for the red giant clump

Based on the Gaia DR1 TGAS parallaxes and photometry from the Tycho-2, Gaia, 2MASS, andWISE catalogues, we have produced a sample of ~100 000 clump red giants within ~800 pc of the Sun. The systematic variations of the mode of their absolute magnitude as a function of the distance, magnitude, and other parameters have been analyzed. We show that these variations reach 0.7 mag and cannot be explained by variations in the interstellar extinction or intrinsic properties of stars and by selection. The only explanation seems to be a systematic error of the Gaia DR1 TGAS parallax dependent on the square of the observed distance in kpc: 0.18R ² mas. Allowance for this error reduces significantly the systematic dependences of the absolute magnitude mode on all parameters. This error reaches 0.1 mas within 800 pc of the Sun and allows an upper limit for the accuracy of the TGAS parallaxes to be estimated as 0.2 mas. A careful allowance for such errors is needed to use clump red giants as “standard candles.” This eliminates all discrepancies between the theoretical and empirical estimates of the characteristics of these stars and allows us to obtain the first estimates of the modes of their absolute magnitudes from the Gaia parallaxes: mode(M _H ) = ?1.49 ^m ± 0.04 ^m , mode(M _Ks ) = ?1.63 ^m ± 0.03 ^m , mode(M _W1) = ?1.67 ^m ± 0.05 ^m mode(M _W2) = ?1.67 ^m ± 0.05 ^m , mode(M _W3) = ?1.66 ^m ± 0.02 ^m , mode(M _W4) = ?1.73 ^m ± 0.03 ^m , as well as the corresponding estimates of their de-reddened colors.     

3D stellar reddening map from 2MASS photometry: An improved version

An improved version of the 3D stellar reddening map in a space with a radius of 1200 pc around the Sun and within 600 pc of the Galactic midplane is presented. As in the previous 2010 and 2012 versions of the map, photometry with an accuracy better than 0.05 ^m in the J and Ks bands for more than 70 million stars from the 2MASS catalogue is used in the new version. However, the data reduction technique is considerably more complicated. As before, an analysis of the distribution of stars near the main-sequence turnoff on the (J ? Ks)?Ks diagram, where they form a distribution maximum, provides a basis for the method. The shift of this maximum, i.e., the mode (J ? Ks), along (J ? Ks) and Ks, given the spatial variations of the mean dereddened color (J ? Ks)₀ of these stars, is interpreted as a growth of the reddening with increasing distance. The main distinction of the new method is that instead of the fixed mean absolute magnitude, dereddened color, distance, and reddening for each cell, the individual values of these quantities are calculated for each star by iterations when solving the system of equations relating them. This has allowed one to increase the random accuracy of the map to 0.01 ^m and its spatial resolution to 20 pc in coordinates and distance and to 1° in longitude and latitude. Comparison with other reddening estimates for the same spatial cells and Gaia DR1 TGAS stars shows that the constructed map is one of the best maps for the space under consideration. Its systematic errors have been estimated to be σ(E(J ? Ks)) = 0.025 ^m , or σ(E(B ? V)) = 0.04 ^m . The main purpose of the map is to analyze the characteristics of Galactic structures, clouds, and cloud complexes. For this purpose, the reddening map within each spatial cell has also been computed by analyzing the reddening along each line of sight.     

Searching for Binary Systems Among Nearby Dwarfs Based on Pulkovo Observations and SDSS Data

Our goal is to find previously unknown binary systems among low-mass dwarfs in the solar neighborhood and to test the search technique. The basic ideas are to reveal the images of stars with significant ellipticities and/or asymmetries compared to the background stars on CCD frames and to subsequently determine the spatial parameters of the binary system and the magnitude difference between its components. For its realization we have developed a method based on an image shapelet decomposition. All of the comparatively faint stars with large proper motions (V >13 ^m , μ > 300 mas yr^?1) for which the “duplicate source” flag in the Gaia DR1 catalogue is equal to one have been included in the list of objects for our study. As a result, we have selected 702 stars. To verify our results, we have performed additional observations of 65 stars from this list with the Pulkovo 1-m “Saturn” telescope (2016–2017). We have revealed a total of 138 binary candidates (nine of them from the “Saturn” telescope and SDSS data). Six program stars are known binaries. The images of the primaries of the comparatively wide pairs WDS 14519+5147, WDS 11371+6022, and WDS 15404+2500 are shown to be resolved into components; therefore, we can talk about the detection of triple systems. The angular separation ρ, position angle, and component magnitude difference Δm have been estimated for almost all of the revealed binary systems. For most stars 1.5′′ < ρ < 2.5′′, while Δm <1.5^m.     

Evolutionary studies of the young star clusters: NGC 1960, NGC 2453 and NGC 2384

We report the analysis of the young star clusters NGC 1960, NGC 2453 and NGC 2384 observed in the J (1.12 μm), H (1.65 μm) and K′ (2.2 μm) bands. Estimates of reddening, distance and age as E(B?V)=0.25, d=1380 pc and t=31.6 to 125 Myr for NGC 1960, E(B?V)=0.47, d=3311 pc and t=40 to 200 Myr for NGC 2453 and E(B?V)=0.25, d=3162 pc and t=55 to 125 Myr for NGC 2384 have been obtained. Also, we have extended the color–magnitude diagrams of these clusters to the fainter end and thus extended the luminosity functions to fainter magnitudes. The evolution of the main sequence and luminosity functions of these clusters have been compared with themselves as well as Lyngå 2 and NGC 1582.     

Catalog of red clump candidates in Tycho-2

We present the technique we used to compile a catalog of about 61 000 local stars brighter than K _s = 8.2 ^m which were identified as most likely red clump candidates on the basis of their reduced proper motions in the K _s band. The catalog was compiled from the combined Tycho-2 and 2MASS data for the stars with color indices J-K _s ranging from 0.5 ^m to 0.8 ^m . It includes the equatorial coordinates, the proper motions, the magnitudes B _T , V _T , J, H, and K _s , and the probabilities for the stars to be red clump giants.     

On Estimating the Dissipative Factor of the Martian Interior

An attempt is made to construct a trial Q_μ(l) distribution in the silicate mantle of Mars. With the allowance for the fact that on the P–T plane the Earth’s geotherm is close to the distribution of areotherms, it was concluded that Q_μ(l) should be distributed in the Martian interior topologically close to the Q_μ(l) distribution in the Earth. The initial distribution was specified by the four-layer piecewise-constant distribution from the QML9 model. An important step was to select the power index in the frequency dependence of Q_μ. Based on the laboratory data and on the experience of studying this problem for the Earth, n was specified in the interval 0.1–0.3. It was found that with the conversion of the initial distribution to the orbital period of Phobos around Mars, which is the only constraint for the problem derived from the observations, this distribution agrees reasonably well with the observational data at n = 0.1.     

One-meter Schmidt telescope of the Byurakan Astrophysical Observatory: New capabilities

In 2013–2015 the Laboratory of spectroscopy and photometry of extragalactic objects (LS-PEO) of the Special Astrophysical Observatory together with Armenian specialists upgraded the 1-m Schmidt telescope of the Byurakan Astrophysical Observatory of the National Academy of Sciences of Armenia. We completely redesigned the control system of the telescope: we replaced the actuating mechanisms, developed telescope control software, and made the guiding system. We reworked and prepared a 4k × 4k Apogee (USA) liquid-cooled CCD with RON ~ 11.1 e^?, a pixel size of 0.″868, and field of view of about 1□°, and in October 2015 mounted it in the focus of the telescope. The detector is equipped with a turret bearing 20 intermediate-band filters (FWHM = 250 Å) uniformly covering the 4000–9000 Å wavelength range, five broadband filters (u, g, r, i, z SDSS), and three narrow-band filters (5000 Å, 6560 Å and 6760 Å, FWHM = 100 Å). During the first year of test operation of the 1-m telescope we performed pilot observations within the framework of three programs: search for young stellar objects, AGNevolution, and stellar composition of galaxy disks.We confirmed the possibility of efficiently selecting of young objects using observations performed in narrow-band Hα and [SII] filters and the intermediate-band 7500 Å filter. Three-hours long exposures with SDSS g-, r-, and i-band filters allow us to reach the surface brightness level of 28^m/□″ when investigating the stellar content of galaxy disks for a sample of nine galaxies. We used observations performed with the 1-m telescope in five broadband (SDSS u, g, r, i, and z) and 15 intermediate-band filters (4000–7500 Å) to construct a sample of quasar candidates with 0.5 < z < 5 (330 objects) in about one-sq. degree SA68 field complete down to R_AB = 23^m. Spectroscopic observations of 29 objects (19.^m5 < R < 22^m) carried out at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences confirmed the quasar nature of 28 objects.     

A New Solar Spectrum from 656 to 3088 nm

The solar spectrum is a key parameter for different scientific disciplines such as solar physics, climate research, and atmospheric physics. The SOLar SPECtrometer (SOLSPEC) instrument of the Solar Monitoring Observatory (SOLAR) payload onboard the International Space Station (ISS) has been built to measure the solar spectral irradiance (SSI) from 165 to 3088 nm with high accuracy. To cover the full wavelength range, three double-monochromators with concave gratings are used. We present here a thorough analysis of the data from the third channel/double-monochromator, which covers the spectral range between 656 and 3088 nm. A new reference solar spectrum is therefore obtained in this mainly infrared wavelength range (656 to 3088 nm); it uses an absolute preflight calibration performed with the blackbody of the Physikalisch-Technische Bundesanstalt (PTB). An improved correction of temperature effects is also applied to the measurements using in-flight housekeeping temperature data of the instrument. The new solar spectrum (SOLAR–IR) is in good agreement with the ATmospheric Laboratory for Applications and Science (ATLAS?3) reference solar spectrum from 656 nm to about 1600 nm. However, above 1600 nm, it agrees better with solar reconstruction models than with spacecraft measurements. The new SOLAR/SOLSPEC measurement of solar spectral irradiance at about 1600 nm, corresponding to the minimum opacity of the solar photosphere, is 248.08 ± 4.98 mW?m^?2?nm^?1 (1?\(\sigma\)), which is higher than recent ground-based evaluations.     

Determination of the combination of cosmological parameters Ω<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript><Superscript><Emphasis Type="Italic">α</Emphasis></Superscript><Emphasis Type="Italic">σ</Emphasis><Subscript>8</Subscript>

We have obtained new constraints on the cosmological parameters Ω _m and σ ₈ from the peculiar velocities of flat edge-on spiral galaxies from the RFGC catalog. Based on these results presented graphically, we have found the quantitative condition (Ω _m /0.3)^0.37 σ ₈ = 0.92 ± 0.05. The estimates of Ω _m and σ ₈, along with their combinations Ω _m ^α σ ₈ for various α, are compared with the estimates by other authors.     

Multicolor Photometry and Spectroscopy of the Yellow Supergiant with Dust Envelope HD 179821 = V1427 Aquilae

We present the results of multicolor (UBV JHKLM) photometry (2009–2017) and low-resolution spectroscopy (2016–2017) of the semi-regular variable V1427 Aql = HD 179821, a yellow supergiant with gas-dust envelope. The star displays low-amplitude (ΔV<0 _. ^m 2) semi-periodic brightness variations superimposed on a long-term trend. The light curve shape and timescale change from cycle to cycle. There are temperature variations characteristic for pulsations; brightness oscillations with no significant change of color are also observed. The UBV data for the 2009–2011 interval are well reproduced by a superposition of two periodic components with P = 170^d and 141^d (or P = 217^d—the one year alias of P = 141^d). The variation became less regular after 2011, the timescale increased and exceeded 250^d. Unusual photometric behavior was seen in 2015 when the star brightness increased by 0 _. ^m 25 in the V filter in 130 days and reached the maximum value ever observed in the course of our monitoring since 1990. In 2009–2016 the annual average brightness monotonically increased in V, J, K, whereas it decreased in U and B. The annual average U ? B, B ? V, and J ? K colors grew, the star was getting redder. The cooling and expanding of the star photosphere along with the increasing of luminosity may explain the long-term trend in brightness and colors. Based on our photometric data we suppose that the photosphere temperature decreased by ~400 K in the 2008–2016 interval, the radius increased by ~24%, and the luminosity grew by ~19%. We review the change of annual average photometric data for almost 30 years of observations. Low-resolution spectra in the λ4000?9000 Å wavelength range obtained in 2016–2017 indicate significant changes in the spectrum of V1427 Aql as compared with the 1994–2008 interval, i.e., the Ba II and near-infraredCa II triplet absorptions have gotten stronger while the OI λ7771-4 triplet blend has weakened that points out the decrease of temperature in the region where the absorptions are formed. The evolutionary stage of the star is discussed. We also compare V1427 Aql with post-AGB stars and yellow hypergiants.     

Results of Complex Observations of Asteroid (596) Scheila at the Sanglokh International Astronomical Observatory

Results of astrometric and BVRI photometric observations of the active asteroid (596) Scheila are presented. The observations were carried out at the Zeiss-1000 telescope of the Sanglokh International Astronomical Observatory of the Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan on June 16?17 and from July 30 to August 1, 2017. The coordinates of the object and its orbit were determined; and the apparent brightness in four filters, the absolute brightness in the V and R filters, and the color indices were obtained. The light curves suggest that no substantial changes in the asteroid’s brightness occurred during the observations. The absolute brightness of the asteroid in the V and R filters was (9.1 ± 0.05)^m and (8.8 ± 0.03)^m, respectively. The mean value of the asteroid diameter was (119 ± 2) km. The mean values of the color indices (B?V = (0.72 ± 0.05)^m, V?R = (0.29 ± 0.03)^m, and R?I = (0.31 ± 0.03)^m) agree well with the values for asteroids of the P- and D-types and its averages. The rotation period of the asteroid estimated from photometric observations was 16.1 ± 0.2 h. The analysis of the data has shown that the asteroid continues to exhibit the same values of absolute brightness and other characteristics as those before the collision with a small body in December 2010, though the latter resulted in the outburst event and cometary activity of the asteroid. Most likely, the collision of asteroid (596) Scheila with a small body did not lead to catastrophic changes in the surface of the asteroid or to its compete break-up.     

Measurement of Extreme Ultraviolet Solar Radiation in Different Wavelength Intervals Onboard the <Emphasis Type="Italic">CORONAS</Emphasis> Satellites: Instruments and Main Results

The paper presents a brief review of the instruments developed for measurement of ionizing extreme UV solar radiation at wavelengths of less than 130 nm onboard the CORONAS-I and CORONAS-F satellites and summarizes the observation data. The main goal of the study was to obtain information concerning variations of fluxes of solar radiation and solar flares at various wavelengths in the extreme ultraviolet. SUFR radiometers based on the thermoluminescent method were mounted onboard both CORONAS satellites (CORONAS-I and CORONAS-F). They performed measurements at λ < 130 nm. Spectral measurements in the 30.4-nm line were made by the photoelectronic spectrometer VUSS tested on CORONAS-I. Spectral measurements in the waveband including the H L_α line (121.6 nm) were conducted by the VUSS-L instrument (a Lyman alpha spectrophotometer) onboard the CORONAS-F satellite. The basic characteristics of the instruments, which were supposed to be used in a system of space weather monitoring on patrol satellites of the hydrometeorological service of Russia, are presented. The main data on the solar radiation flux at λ < 130 nm for minimum and maximum solar activity are given for quiet conditions and during solar flares.     

Catalog of equatorial coordinates and <Emphasis Type="Italic">B</Emphasis>-magnitudes of stars of the Kitab part of the FON project

The processing of the plates of the Kitab part of the FON project has been completed. In total, 1963 plates were processed. The catalog of equatorial coordinates α, δ, and B-magnitudes for 13 413268 stars and galaxies up to B ≤ 17.5 ^m for the epoch 1984.97 is compiled. The Epson Expression 10000XL scanner with a 1200 dpi scanning mode and a plate size of 30 × 30 cm or 13000 × 13000 pel was used to digitize astronegatives. Coordinates of stars and galaxies are obtained in the Tycho-2 catalog system and B-magnitudes are obtained in the photovoltaic system. The catalog internal accuracy for all objects is σ_α,δ = 0.23" and σ _B = 0.15 ^m (for stars in the range B = 5 ^m …14 ^m , errors are σ_α,δ = 0.085" and σ _B = 0.054 ^m ) for equatorial coordinates and stellar B-magnitudes, respectively. Convergence between the calculated and reference positions is σ_α,δ = 0.042", and convergence between photoelectric B-magnitudes is σ _B = 0.16 ^m . Coordinate errors with respect to the UCAC-4 catalog are σ_α,δ = 0.26" (9892697 or 73.75% of stars and galaxies were identified).     

Unveiling the atmospheres of giant exoplanets with an EChO-class mission

More than a thousand exoplanets have been discovered over the last decade. Perhaps more excitingly, probing their atmospheres has become possible. With current data we have glimpsed the diversity of exoplanet atmospheres that will be revealed over the coming decade. However, numerous questions concerning their chemical composition, thermal structure, and atmospheric dynamics remain to be answered. More observations of higher quality are needed. In the next years, the selection of a space-based mission dedicated to the spectroscopic characterization of exoplanets would revolutionize our understanding of the physics of planetary atmospheres. Such a mission was proposed to the ESA cosmic vision program in 2014. Our paper is therefore based on the planned capabilities of the Exoplanet Characterization Observatory (EChO), but it should equally apply to any future mission with similar characteristics. With its large spectral coverage (0.4 ? 16 μm), high spectral resolution (λ/Δλ > 300 below 5 μm and λ/Δλ > 30 above 5 μm) and 1.5m mirror, a future mission such as EChO will provide spectrally resolved transit lightcurves, secondary eclipses lightcurves, and full phase curves of numerous exoplanets with an unprecedented signal-to-noise ratio. In this paper, we review some of today’s main scientific questions about gas giant exoplanets atmospheres, for which a future mission such as EChO will bring a decisive contribution.     

A Comprehensive Study of 94 Open Clusters Based on the Data from IPHAS,GAIA DR2, and Other Sky Surveys

We determine the color excesses, photometric distances, ages, astrometric parallaxes and proper motions for 94 open clusters in the northern part of the Milky Way. We estimate the color excesses and photometric distances based on the data from IPHAS photometric survey of the northern Galactic plane using individual total-to-selective extinction ratios R_r = A_r/E_r?i for each cluster computed via the color-difference method based on IPHAS r, i, and Hα-band, 2MASS J-, H-, and K_s-band, WISE W1-band, and Pan-STARRS i-, z-, and y-band data. The inferred R_r values vary significantly from cluster to cluster spanning the R_r = 3.1–5.2 interval with a mean and standard deviation equal to 〈R_r〉 = 3.99 and σR_r = 0.34, respectively.We identified cluster members using (1) absolute proper motions determined from individual-epoch positions of stars retrieved from IPHAS, 2MASS,URAT1, ALLWISE,UCAC5, and Gaia DR1 catalogs and positions of stars on individual Palomar Sky Survey plates reconstructed based on the data provided in USNO-B1.0 catalog and (2) absolute proper motions provided in Gaia DR2 catalog, and computed the averageGaia DR2 trigonometric parallaxes and propermotions of the clusters. Themean formal error of the inferred astrometric parallaxes of clusters is of about 7 μas, however, a comparison of astrometric and photometric parallaxes of our cluster sample implies that Gaia DR2 parallaxes are, on the average, systematically underestimated by 45 ± 9 μas. This result agrees with estimates obtained by other authors using other objects. At the same time, we find our photometric distance scale to be correct within the quoted errors (the inferred correction factor is equal to unity to within a standard error of 0.025).     

Photometric and spectroscopic study of the supergiant with an infrared excess V1027 Cygni

We present the results of our UBV and JHKLM photometry for the semiregular pulsating variable V1027 Cyg, a supergiant with an infrared excess, over the period from 1997 to 2015 (UBV) and in 2009–2015 (JHKLM). Together with the new data, we analyze the photometric observations of V1027 Cyg that we have obtained and published previously. Our search for a periodicity in the UBV brightness variations has led to several periods from P = 212^d to 320^d in different time intervals. We have found the period P = 237^d based on our infrared photometry. The variability amplitude, the lightcurve shape, and themagnitude of V1027 Cyg atmaximum light change noticeably from cycle to cycle. The deepest minimum was observed in 2011, when the amplitudes of brightness variations in the star reached the following values: ΔU = 1 _. ^m 28, ΔB = 1 _. ^m 10, ΔV = 1 _. ^m 05, ΔJ = 0 _. ^m 30, ΔH = 0 _. ^m 35, ΔK = 0 _. ^m 32, ΔL = 0 _. ^m 26, and ΔM = 0 _. ^m 10. An ambiguous correlation of the B ? V and U ? B colors with the brightness has been revealed. For example, a noticeable bluing of the star was observed during the deep 1992, 2008, and 2011 minima, while the variations with smaller amplitudes show an increase in B ? V at the photometric minima. The spectral energy distribution for V1027 Cyg from our photometry in the range 0.36 (U)–5.0 (M) μm corresponds to spectral types from G8I to K3I at different phases of the pulsation cycle. Low-resolution spectra of V1027 Cyg in the range λ4400–9200 ?A were taken during 16 nights over the period 1995–2015. At the 1995 and 2011 photometric minima the star’s spectrum exhibited molecular TiO bands whose intensity corresponded to spectral types M0–M1, while the photometric data point to a considerably earlier spectral type. We hypothesize that the TiO bands are formed in the upper layers of the extended stellar atmosphere. We have measured the equivalent widths of the strongest absorption lines, in particular, the infrared Ca II triplet in the spectrum of V1027 Cyg. The calcium triplet (Ca T) with W _λ(Ca T) = 20.3 ± 1.8 ?A as a luminosity indicator for supergiants places V1027 Cyg in the region of the brightest G–K supergiants. V1027 Cyg has been identified with the infrared source IRAS 20004+2955 and is currently believed to be a candidate for post-AGB stars. The evolutionary status of the star and its difference from other post-AGB objects are discussed.     

Interstellar polarization: New approximation

A new, physically valid, approximation of the wavelength dependences of the degree of linear interstellar polarization P _λ observed in a wavelength range from 0.2 to 4 μm is suggested. The data obtained from the ground-based observations and the HPOL and WUPPE space missions on P _λ of 104 stars located in a galactic latitude range B from ?20° to +20° are used. This approximation provides better agreement with the observational P _λ data than the models by Serkowski (1973) and Whittet et al. (1992) proposed before.     

Forbidden Zones for Circular Regular Orbits of the Moons in Solar System,R3BP

Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analysing such a system of equations, we considered the case of small-body motion of negligible mass m ₃ around the second of two giant-bodies m ₁, m ₂ (which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. In the current development, we have derived a key parameter η that determines the character of quasi-circular motion of the small third body m ₃ relative to the second body m ₂ (planet). Namely, by making several approximations in the equations of motion of the three-body problem, such the system could be reduced to the key governing Riccati-type ordinary differential equations. Under assumptions of R3BP (restricted three-body problem), we additionally note that Riccati-type ODEs above should have the invariant form if the key governing (dimensionless) parameter η remains in the range 10^?2 Open image in new window 10^?3. Such an amazing fact let us evaluate the forbidden zones for Moon’s orbits in the inner solar system or the zones of distances (between Moon and Planet) for which the motion of small body could be predicted to be unstable according to basic features of the solutions of Riccati-type.