Photometry of 433 Eros from 0.65 to 2.2 μm

Lightcurves of 433 Eros are reported for 11 bandpasses ranging from 0.65 to 2.2 μm in wavelength. The relative spectral reflectance, R(λ), was not seen to vary during our observations. Eros has R(1.6 μm) = 1.5 ± 0.1 and R(2.2 μm) = 1.7 ± 0.1, where R(λ) is the spectral reflectance scaled to unity at λ = 0.56 μm. This spectral reflectance is suggestive of a mixture of silicates and material with high infrared reflectance, perhaps a metallic phase such as meteoritic “iron”.     

UBV photometry of asteroid 433 Eros

UBV observations of asteroid 433 Eros were conducted on 17 nights during the winter of 1974/75. The peak-to-peak amplitude of the lightcurve varied from about 0.3 mag to nearly 1.4mmag. The absolute V mag at maximum light, extrapolated to zero phase, is 10.85. Phase coefficients of 0.0233 mag/degree, 0.0009 mag/degree and 0.0004 mag/degree were derived for V, B-V, and U-B, respectively. The zero-phase color of Eros (B?V = 0.88, U?B = 0.50) is representative of an S (silicaceous) compositional type asteroid. The color does not vary with rotation. The photometric behavior of Eros can be modeled by a cylinder with rounded ends having an axial ratio of about 2.3:1. The asteroid is rotating about a short axis with the north pole at λ₀ = 15° and β₀ = 9°.     

Physical properties of asteroid 433 Eros

Newly available photometric, polarimetric, spectroscopic, thermal-radiometric, radar, and occultation results are synthesized in order to derive a coherent model for Eros. The geometric albedo is 0.19±0.01 at the visual wavelength, and the overall dimensions are approximately 13 × 15 × 36km. The rotation is about the short axis, in the direct sense, with a sidereal period of 5^h16^m13^s.4. The pole of rotation lies within a few degrees of ecliptic coordinates λ = 16° and β = + 11°.Eros is uniformly coated with a particulate surface layer several millimeters thick. It has an iron-bearing silicate composition, similar to that of a minority of main-belt asteroids, and probably identifiable with H-type ordinary chondrites.     

Lightcurves and the axis of rotation of 433 Eros

Ten lightcurves and UBV photometry of 433 Eros were obtained between August 1972 and May 1975. The absolute magnitude of the lightcurve maximum is 10.75 and the phase coefficient is 0.025 mag/deg. There may be a small difference in B-V color between the northern and southern hemispheres. The pole of the axis of rotation is directed toward λ₀ = 16°, β₀ = 12°, ecliptic longitude and latitude, respectively, and the rotation is direct with a sidereal period of 0.^d219599 or 5^h16^m13^s4 ± 0.^s2. The dimensions derived from the polarimetric albedo and the lightcurve amplitudes are 12km × 12km × 31km for a smooth cylinder with hemispherical ends.     

Interferometric observations of Saturn and its rings at a wavelength of 3 3.71 cm

Interferometric observations of Saturn and its rings made at the Owens Valley Radio Observatory at a wavelength of 3.71 cm ar fit to models of the Saturn brightness structure. The models have allowed us to estimate the brightness temperatures and optical thicknesses of the A, B, and C rings as well as the brightness temperature of the planetary disk. The most accurate results are the ratios of the ring temperatures to the planet temperature of 0.030 ± 0.012, 0.050 ± 0.010, and 0.040 ± 0.014 for the A, B, and C rings, respectively. The best estimates of the ring optical thicknesses are τ_A = 0.2 ± 0.1, τ_B = 0.9 ± 0.2, and τ_C = 0.1 ± 0.1. The actual brightness temperatures, which are affected by the absolute calibration errors, are T_planet = 178 ± 8, T_A = 5.2 ± 2.0, T_B = 9.1 ± 1.8, and T_C = 7.1 ± 2.6°K. The particle single-scattering albedo that would be most consistent with the observations is slightly less than one, but probably greater than 0.95. The observations are consistent with particles which conservatively scatter the thermal emission from Saturn to the Earth and emit no thermal emission of their own. The 3.71-cm optical depths which we have estimated are very close to the visible wavelength optical depths. This similarity indicates that the ring particles must be at least a few centimeters in size, although we feel that the particles may well be much larger than this in view of the closeness of the visible and microwave optical depths. Particles which are nearly conservative scatterers at our wavelength and at least a few centimeters in size must be composed of a material which is either a very good reflector of microwaves or a very poor absorber of them. At this time, water ice seems to be the most likely candidate since it is a very poor absorber of microwaves and has been detected in the rings spectroscopically.     

Photometric observations and modelling of the asteroid 85 Io in conjunction with data from an occultation event during the 1995–96 apparition

The asteroid 85 Io has been observed using CCD and photoelectric photometry on 18 nights during its 1995–96 and 1997 apparitions. We present the observed lightcurves, determined colour indices and modelling of the asteroid spin vector and shape. The colour indices (U-B = 0.35±0.02, B-V = 0.66±0.02, V-R = 0.34±0.02, R-I = 0.36±0.02) are as expected for a C-type asteroid. The allowed spin vector solutions have the pole co-ordinates λ₀ = 285±4°, β₀ = −52±9° or λ₀ = 108±10°, β₀ = −46±10° and λ₀ = 290±10°, β₀ = −16±10° with a retrograde sense of rotation and a sidereal period P_sid = 0^d.286463±0^d.000001. During the 1995–96 apparition the International Occultation Time Association (IOTA) observed an occultation event by 85 Io. The observations and modelling presented here were analysed together with the occultation data to develop improved constraints on the size of the asteroid. The derived value of 164 km is about 5% larger than the IRAS diameter. © 1999 Elsevier Science Ltd. All rights reserved.     

Radio emission from the quiet sun and local sources at wavelengths 5, 10.7, 12, and 95 cm from observations of the January 4, 2011 eclipse in Crimea

The radio radii of the Sun at wavelengths of 5, 10.7, 12, and 95 cm have been determined from eclipse observations as R₅ ?? (1.0 ± 0.015)R _??, R _10,12 = (1.05 ± 0.003)R _??, and R ₉₅ = (1.2 ± 0.02)R _??. The bright-ness temperatures of quiet solar disk areas at these wavelengths have turned out to be Td ₅ = (22 ± 2) × 10³, Td ₁₀ = (44 ± 3) × 10³, Td ₁₂ = (47 ± 3) × 10³, and Td ₉₅ = (1000 ± 30) × 10³ K. There were local sources of radio emission with angular sizes from 1.9 to 2.4 arcmin and brightness temperatures from 80 × 10³ to 1.75 × 10⁶ K above sunspot groups at short wavelengths of 5, 10.7, and 12 cm. The radio flux from the local sources at 95 cm turned out to be below the detection threshold of 1.0 × 10^?22 W m^?2 Hz^?1. Comparison of the values obtained with the results of observations of another eclipse on August 1, 2008, occurred at the epoch of minimum of the 11-year solar cycle has shown that the radio radius of the Sun at 10.7 and 12 cm increased from 1.016 R _?? to 1.05 ± 0.003R _??, the height of the emitting layer at these wavelengths moved from 11 × 10³ km to (30 ± 7) × 10³ K, and the brightness temperature of the quiet Sun rose from (35.8 ± 0.4) × 10³ K to (44 ± 3) × 10³ K at 10.7 cm and from (37.3 ± 0.4) × 10³ K to (47 ± 3) × 10³ K at 12 cm. Consequently, the parameters of the solar atmosphere changed noticeably in 2 years in connection with the beginning of the new solar cycle 24. The almost complete absence of local sources at the longest wavelength of 95 cm suggests that the magnetic fields of the sunspot groups on January 4, 2011, were weak and did not penetrate to the height from where their emission could originate. If this property is inherent in most sunspot groups of cycle 24, then it can be responsible for its low flare activity.     

Five-color photoelectric photometry of asteroid 433 Eros

Five-color photoelectric lightcurves of asteroid 433 Eros were obtained on 9 nights during the 1974/75 apparition. Although color differences due to changing solar phase angle were detected, color differences during a single rotation of Eros are less than 1%. Amplitudes of up to 1^m.44 were measured, and there are indications that three reversals in the relative depths of the two minima occured between late December 1974 and late January 1975. The absolute visual magnitude at primary maximum, corrected to zero phase and to one AU from Earth and Sun, is about V₀(1,0) = 10^m.8.     

Worldwide photometry and lightcurve observations of 16 Psyche during the 1975–1976 apparition

We present 26 lightcurves of 16 Psyche from 1975 and 1976. The synodic period during this apparition was 4^h.1958. Combining photometric data from this opposition with those from previous apparitions allowed us to derive a mean phase coefficient in V of 0.026 ± 0.002 mag/deg and to establish that Psyche's absolute V₀ magnitude and rotational amplitude vary with aspect; at 90° aspect, V₀(1, 0) = 6.27 ± 0.05 and the lightcurve amplitude is 0.30 mag, while at 0° or 180° aspect, V₀(1, 0) = 6.02 ± 0.02 and the amplitude is ?0.03 mag. This behavior is accounted for if, to first order, Psyche's shape is that of a triaxial ellipsoid with axial ratios near 5:4:3. Colors at zero phase are U-B = 0.26 ± 0.01 and B-V = 0.71 ± 0.01. Color phase coefficients are <0.001 mag/deg in U-B and 0.0010 ± 0.0004 mag/deg in B-V.     

Absolute magnitudes and kinematic parameters of the subsystem of RR Lyrae variables

The statistical parallax technique is applied to a sample of 262 RRab Lyrae variables with published photoelectric photometry, metallicities, and radial velocities and with measured absolute proper motions. Hipparcos, PPM, NPM, and the Four-Million Star Catalog (Volchkov et al. 1992) were used as the sources of proper motions; the proper motions from the last three catalogs were reduced to the Hipparcos system. We determine parameters of the velocity distribution for halo [(U ₀, V ₀, W ₀) = (?9±12, ?214 ±10, ? 10, ?16±7) km s ^?1 and (σ _U , σ _V , σ _W ) = (164±11, 105±7, 95±7) km s ^?1] and thick-disk [(U ₀, V ₀, W ₀) = (?16±8, ?41±7, ?18±5) km s ^?1], and [(σ _U , σ _V , σ _W ) = (53±9, 42±8, 26±5) km s ^?1] RR Lyrae, as well as the intensity-averaged absolute magnitude for RR Lyrae of these populations: 〈M _V 〉 = 0.77 ± 0.10 and 〈M _V 〉 = +1.11 ± 0.25 for the halo and thickdisk objects, respectively. The metallicity dependence of the absolute magnitude of RR Lyrae is analyzed (〈M _V 〉 = (0.76 ± 0.12) + (0.26 ± 0.26) · ([Fe/H]+1.6)=1.17+0.26 · [Fe/H]). Our results are in satisfactory agreement with the ?M _V ?(RR)?[Fe/H]relation from Carney et al. (1992) (〈M _V 〉(RR)=1.01+0.15·[Fe/H]) obtained by Baade-Wesselink's method. They provide evidence for a short distance scale: the LMC distance modulus and the distance to the Galactic center are 18.22±0.11 and 7.4±0.5 kpc, respectively. The zero point of the distance scale and the kinematic parameters of the RR Lyrae populations are shown to be virtually independent of the source of absolute proper motions used and of whether they are reduced to the Hipparcos system or not.     

Galactic rotation curve and spiral density wave parameters from 73 masers

Based on kinematic data on masers with known trigonometric parallaxes and measurements of the velocities of HI clouds at tangential points in the inner Galaxy, we have refined the parameters of the Allen-Santillan model Galactic potential and constructed the Galactic rotation curve in a wide range of Galactocentric distances, from 0 to 20 kpc. The circular rotation velocity of the Sun for the adopted Galactocentric distance R ₀ = 8 kpc is V ₀ = 239 ± 16 km s^?1. We have obtained the series of residual tangential, ΔV _θ , and radial, V _R , velocities for 73 masers. Based on these series, we have determined the parameters of the Galactic spiral density wave satisfying the linear Lin-Shu model using the method of periodogram analysis that we proposed previously. The tangential and radial perturbation amplitudes are f _θ = 7.0±1.2 km s^?1 and f _R = 7.8±0.7 km s^?1, respectively, the perturbation wave length is λ = 2.3±0.4 kpc, and the pitch angle of the spiral pattern in a two-armed model is i = ?5.2° ±0.7°. The phase of the Sun ζ _⊙ in the spiral density wave is ?50° ± 15° and ?160° ± 15° from the residual tangential and radial velocities, respectively.     

Pole coordinates of the asteroids 9 metis, 22 kalliope,and 44 Nysa

By means of new photoelectric observations made in 1974 an attempt to determine the poles of asteroids 9 and 44 was made. Following a method based upon the magnitude-aspect and amplitude-aspect relations, the coordinates of the poles for 9 and 44 were found to be, respectively, λ₀ = 191° ± 5°, β₀ = 56° ± 6° and λ₀ = 100° ± 10°, β₀ = 50° ± 10°. The previously published pole for asteroid 22, λ₀ = 215° ± 10°, β₀ = 45° ± 15°, was confirmed. From its phase relation we determined the phase coefficient of 44 Nysa, a very high albedo object (p_v = 0.377). The very low phase coefficient obtained (β_v = 0.018 mag/deg) agrees very well with an inverse relation between geometrical albedo and phase coefficient. The results are summarized in a table.     

Rotation of the nucleus of comet p/Arend-Rigaux

Time-resolved charge-coupled device photometry of Comet p/Arend-Rigaux shows a cyclic variation in cometary brightness consistent with the periods T₁ = 574 ± 5 min (9.58 ± 0.08 hr) and T₂ = 407 ± 5 min (6.78 ± 0.08 hr). The variation has a 30% range and is confined to the inner coma. The relative photometric stability of the outer coma indicates that the variations in the inner coma are associated with the nucleus and probably result from its rotation at, or at a multiple of, one of the above periods.     

Galactic kinematics from a sample of young massive stars

Based on published sources, we have created a kinematic database on 220 massive (> 10 M _⊙) young Galactic star systems located within ≤3 kpc of the Sun. Out of them, ≈100 objects are spectroscopic binary and multiple star systems whose components are massive OB stars; the remaining objects are massive Hipparcos B stars with parallax errors of no more than 10%. Based on the entire sample, we have constructed the Galactic rotation curve, determined the circular rotation velocity of the solar neighborhood around the Galactic center at R ₀ = 8kpc, V ₀ = 259±16 km s^?1, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations f _R = ?10.8 ± 1.2 km s^?1 and f _θ = 7.9 ± 1.3 km s^?1, respectively; the pitch angle for a two-armed spiral pattern i = ?6.0° ± 0.4°, with the wavelength of the spiral density wave near the Sun being λ = 2.6 ± 0.2 kpc; and the radial phase of the Sun in χ _⊙ = ?120° ± 4°. We show that such peculiarities of the Gould Belt as the local expansion of the system, the velocity ellipsoid vertex deviation, and the significant additional rotation can be explained in terms of the density wave theory. All these effects decrease noticeably once the influence of the spiral density wave on the velocities of nearby stars has been taken into account. The influence of Gould Belt stars on the Galactic parameter estimates has also been revealed. Eliminating them from the kinematic equations has led to the following new values of the spiral density wave parameters: f _θ = 2.9 ± 2.1 km s^?1 and χ _⊙ = ?104° ± 6°.     

Estimation of the galactic spiral pattern speed from Cepheids

To study the peculiarities of the Galactic spiral density wave, we have analyzed the space velocities of Galactic Cepheids with propermotions from the Hipparcos catalog and line-of-sight velocities from various sources. First, based on the entire sample of 185 stars and taking R ₀ = 8 kpc, we have found the components of the peculiar solar velocity (u _⊙, v _⊙) = (7.6, 11.6) ± (0.8, 1.1) km s^?1, the angular velocity of Galactic rotation Ω₀ = 27.5 ± 0.5 km s^?1 kpc^?1 and its derivatives Ω′₀ = ?4.12 ± 0.10 km s^?1 kpc^?2 and Ω″₀ = 0.85 ± 0.07 km s^?1 kpc^?3, the amplitudes of the velocity perturbations in the spiral density wave f _R = ?6.8 ± 0.7 and f _θ = 3.3 ± 0.5 km s^?1, the pitch angle of a two-armed spiral pattern (m = 2) i = ?4.6° ± 0.1° (which corresponds to a wavelength λ = 2.0 ± 0.1 kpc), and the phase of the Sun in the spiral density wave χ_⊙ = ?193° ± 5°. The phase χ_⊙ has been found to change noticeably with the mean age of the sample. Having analyzed these phase shifts, we have determined the mean value of the angular velocity difference Ω _p ? Ω, which depends significantly on the calibrations used to estimate the individual ages of Cepheids. When estimating the ages of Cepheids based on Efremov’s calibration, we have found |Ω _p ? Ω₀| = 10 ± 1_stat ± 3_syst km s^?1 kpc^?1. The ratio of the radial component of the gravitational force produced by the spiral arms to the total gravitational force of the Galaxy has been estimated to be f _r0 = 0.04 ± 0.01.     

Non-linear stability of L 4 in the restricted problem when the primaries are finite straight segments under resonances

The non-linear stability of L ₄ in the restricted three-body problem when both primaries are finite straight segments in the presence of third and fourth order resonances has been investigated. Markeev’s theorem (Markeev in Libration Points in Celestial Mechanics and Astrodynamics, 1978) is used to examine the non-linear stability for the resonance cases 2:1 and 3:1. It is found that the non-linear stability of L ₄ depends on the lengths of the segments in both resonance cases. It is also found that the range of stability increases when compared with the classical restricted problem. The results have been applied in the following asteroids systems: (i) 216 Kleopatra–951 Gaspara, (ii) 9 Metis–433 Eros, (iii) 22 Kalliope–243 Ida.     

Trigonometric parallaxes and a kinematically adjusted distance sale for OB associations

By directly comparing the photometric distances of Blaha and Humphreys (1989) (BH) to OB associations and field stars with the corresponding Hipparcos trigonometric parallaxes, we show that the BH distance scale is overestimated, on average, by 10–20%. This result is independently corroborated by applying the rigorous statistical-parallax method and its simplified analog (finding a kinematically adjusted rotation-curve solution from radial velocities and proper motions) to a sample of OB associations. These two methods lead us to conclude that the BH distance scale for OB associations should be shrunk, on average, by 11±6 and 24±10%, respectively. Kinematical parameters have been determined for the system of OB associations: u ₀ = 8.2 ± 1.3 km s^?1, v ₀ = 11.9 ± 1.1 km s^?1, w ₀ = 9.5 ± 0.9 km s^?1, σ _u = 8.2 ± 1.1 km s^?1, σ _v = 5.8 ± 0.8 km s^?1, σ _w = 5.0 ± 0.8 km s^?1, Ω₀ = 29.1 ± 1.0 km s^?1 kpc^?1, Ω₀′ = ?4.57 ± 0.20 km s^?1 kpc^?2, and Ω₀″ = 1.32 ± 0.14 km s^?1 kpc^?3. The distance scale for OB associations reduced by 20% matches the short Cepheid distance scale (Berdnikov and Efremov 1985; Sitnik and Mel’nik 1996). Our results are a further argument for the short distance scale in the Universe.     

The pole orientation of asteroid 433 Eros determined by photometric astrometry

Refinements to the pole-determination method photometric astrometry (PA) were completed in 1983 (R. C. Taylor and E. F. Tedesco, 1983, Icarus54, 13–22). A goal is to redo the pole analysis for every asteroid whose pole had been determined from earlier versions of PA: Previous PA poles are reviewed in this paper. Asteroid 433 Eros is in that collection and has redone. The result are prograde rotation; a sidereal period of 0.219588 ± 0.000005 day; and a north pole at 22° longitude, +9° latitude. The uncertainty of the pole is 10°. The pole position of Eros determined by C.D. Vesely (1971, In Physical Studies of Minor Planets (T. Gehrels, Ed.), pp. 133–140, NASA SP-267) and Dunlap (1976, Icarus28, 69–78), using earlier versions of photometric astrometry, were within 21 and 7°, respectively, of the present result.     

Spectrophotometry of Saturn and its rings from 60 to 180 microns

We observed Saturn at far-infrared and submillimeter wavelengths during the Earth's March 1980 passage through the plane of Saturn's rings. Comparison with earlier spectroscopic observations by D. B. Ward [Icarus32, 437–442 (1977)], obtained at a time when the tilt angle of the rings was 21.8°, permits separation of the disk and ring contributions to the flux observed in this wavelength range. We present two main results: (1) The observed emission of the disk between 60 and 180 μm corresponds to a brightness temperature of 104 ± 2°K; (2) the brightness temperature of the rings drops approximately 20°K between 60 and 80 μm. Our data, in conjunction with the data obtained by other observers between 1 μm and 1 mm, permit us to derive an improved estimate for the total Saturnian surface brightness of (4.84 ± 0.32) × 10^?4W cm^?2 corresponding to an effective temperature of 96.1 ± 1.6°K. The ratio of radiated to incident power, P_R/P_I, is (1.46 ± 0.08)/(1 - A), where A is the Bond albedo. For A = 0.337 ± 0.029, P_R/P_I = 2.20 ± 0.15 and Saturn's intrinsic luminosity is L_S = (2.9 ± 0.5) × 10^?10L_⊙.     

Corrections for the Lutz-Kelker bias for Galactic masers

Based on published data, we have collected information about Galactic maser sources with measured distances. In particular, 44 Galactic maser sources located in star-forming regions have trigonometric parallaxes, proper motions, and radial velocities. In addition, ten more radio sources with incomplete information are known, but their parallaxes have been measured with a high accuracy. For all 54 sources, we have calculated the corrections for the well-known Lutz-Kelker bias. Based on a sample of 44 sources, we have refined the parameters of the Galactic rotation curve. Thus, at R ₀ = 8kpc, the peculiar velocity components for the Sun are (U _⊙, V _⊙, W _⊙) = (7.5, 17.6, 8.4) ± (1.2, 1.2, 1.2) km s^?1 and the angular velocity components are ω ₀ = ?28.7 ± 0.5 km s^?1 kpc^?1, ω ₀′ = +4.17 ± 0.10 km s^?1 kpc^?2, and ω₀″ = ?0.87 ± 0.06 km s^?1 kpc^?3. The corresponding Oort constants are A = 16.7 ± 0.6 km s^?1 kpc^?1 and B = ?12.0 ± 1.0 km s^?1 kpc^?1; the circular rotation velocity of the solar neighborhood around the Galactic center is V ₀ = 230 ± 16 km s^?1. We have found that the corrections for the Lutz-Kelker bias affect the determination of the angular velocity ω ₀ most strongly; their effect on the remaining parameters is statistically insignificant. Within themodel of a two-armed spiral pattern, we have determined the pattern pitch angle $i = - 6_.^ \circ 5$ and the phase of the Sun in the spiral wave χ ₀ = 150°.