Photoelectric lightcurves of the asteroid 1862 Apollo

Photoelectric lightcurves of the asteroid 1862 Apollo were obtained in November–December 1980 and in April–May 1982. The period of rotation is unambiguously determined to be 3.0655 ± 0.0008 hr. The 1980 observations span a range of solar phase angle from 30° to 90°, and the 1982 observations, 0.°2 to 90°. The Lumme-Bowell-Harris phase relation can be fit to the absolute magnitudes at maximum light with an RMS scatter of 0.06 magnitude over the entire range of phase angle. The constants of the solution are absolute V magnitude at zero phase angle and at maximum light, 16.23 ± 0.02; slope parameter, 0.23 ± 0.01. These constant corresponds to values in the linear phase coefficient system of V(1, 0) = 16.50 ± 0.02 and a phase coefficient of β_v = 0.0305 ± 0.0012 mag/degree in the phase range 10°–20°. The slope of the phase curve is typical for a moderate albedo asteroid. The absolute magnitudes observed in 1980 and 1982 fall along a common phase curve. That is, Apollo was not intrinsically brighter at one apparition than the other. This is not surprising, since the two apparitions were almost exactly opposite one another in the sky. A pole position was calculated from the observed deviation of the lightcurve from constant periodicity (synodic-sidereal difference) during both apparitions. The computed 1950 ecliptic coordinates of the pole are: longitude = 56°, latitude = −26°. This is the “north” pole with respect to right-handed (counter-clockwise) rotation. The formal uncertainty of the solution for the pole position is less than 10°, but realistically may be several times that, or even completely wrong. The sidereal period of rotation asscociated with this pole solution is 3.065436 ± 0.000012 hr.     

Speckle interferometry of asteroids: III. 511 Davida and its photometry

511 Davida was observed with the technique of speckle interferometry at Steward Observatory's 2.3-m telescope on May 3, 1982. Assuming Davida to be a featureless triaxial ellipsoid, based on five 7-min observations its triaxial ellipsoid dimensions and standard deviations were found to be (465 ± 90) × (358 ± 58) × (258 ± 356) km. This shape is close to an equilibrium figure (a gravitationally shaped “rubble pile?”) suggesting a density of 1.4 ± 0.4 g/cm³. Simultaneously with the triaxial solution for the size and shape of Davida, we found its north rotational pole to lie within 29° of RA = 19^h08^m, Dec = +15° (λ = 291°, β = +37°). If Davida is assumed to be a prolate biaxial ellipsoid, then its dimensions were found to be (512 ± 100) × (334 ± 39) km, with a north pole within 16° of RA = 10^h52^m, Dec = +16° (λ = 322°, β = +32°). We derive and apply to Davida a new simultaneous amplitude-magnitude (SAM)-aspect method, finding, from photometric data only, axial ratios of a/b = 1.25 ± .02, b/c = 1.14 ± .03, and a rotational pole within 4° of λ = 307°, β = +32°. We also derive a (weighted) linearized form of the amplitude-aspect relation to obtain axial ratios and a pole. However, amplitudes must be known to better than .01 if the b/c or a/c ratios are desired to better than 10%. Combining the speckle and SAM results, we find for the Gehrels and Tedesco phase function a geometric albedo of .033 ± .009 and for the Lumme and Bowell function .041 ± .011, for a unified model of 437 × 350 × 307 km. Differences between the photometric and speckle axial ratios and poles are probably due to the effects of albedo structure over the asteroid; details on individual lightcurves support this conclusion.     

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.     

Pole coordinates of the asteroid 511 Davida as determined via the Amplitude-Magnitude method

The Amplitude-Magnitude (AM) method is used for the pole determination of the asteroid 511 Davida, using observations from six oppositions. The possible North poles are found to be λ₁ = 92° ± 7°; β₁ = 33° ± 6°, and λ₂ = 303° ± 4°; β₂ = 34° ± 5°, when scattering effect is not taken into account. When scattering is accounted for, solutions not significantly different from (λ₁, β₁) and (λ₂, β₂) are obtained. The moderately eccentric and inclined orbit of 511 Davida does not allow us to distinguish between the two pole solutions. A comparison with other methods is necessary in order to make a definitive choice.     

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.     

Pole orientation of asteroid 44 Nysa via photometric astrometry,including a discussion of the method's application and its limitations

The results of photometric astrometry, a method of determining the orientation of a rotation axis, as applied to asteroid 44 Nysa are presented. The pole orientation of Nysa was found to be λ₀ = 100°, β₀ = +60° with an uncertainty of 10°. The sidereal period is 0^d.26755902 ± 0.00000006, and the rotation prograde. Refinements to, and limitations of, the application of the method of photometric astrometry are discussed. In light of the results presented herein, we believe that all photometric astrometry pole determinations of the past should be redone.     

Voyager photometry of Rhea,Dione, Tethys,Enceladus and Mimas

Voyager imaging observations provide new photometric data on Saturn's satellites at large phase angles (up to 133° in the case of Mimas) not observable from Earth. Significant new results include the determination of phase integrals ranging from 0.7 in the case of Rhea to 0.9 for Enceladus. For Enceladus we find an average geometric albedo p_v = 1.04 ± 0.15 and Bond albedo of 0.9 ± 0.1. The data indicate an orbital lightcurve with an amplitude of 0.2 mag, the trailing side being the brighter. For Mimas, the lightcurve amplitude is probably less than 0.1 mag. The value of the geometric albedo of Mimas reported here, p_v = 0.77 ± 0.15 (corresponding to a mean opposition magnitude V₀ = +12.5) is definitely higher than the currently accepted value of about 0.5. For Dione, the Voyager data show a well-defined orbital lightcurve of amplitude about 0.6 mag, with the leading hemisphere brighter than the trailing one.     

A photometric study of the minor planet 63 Ausonia

Photoelectric observations of the minor planet 63 Ausonia were obtained on 12 nights during the 1976 opposition at the Astronomical Observatory of Torino. A complete lightcurve with two maxima and two minima was observed with a maximum amplitude of 0.47 mag. The synodic period of rotation, never before determined photoelectrically, was found to be 9^h17^m48^s ± 5^s. The absolute magnitude of the primary maximum, V₀(1, 0) = 7.49 mag, and the phase coefficient, β_v = 0.035 mag/deg, were deduced by the magnitude-phase relation. Comparison with other observations is briefly discussed and a mean radius is determined from a previous value of the geometric albedo.     

Photometric lightcurves and pole determination of 433 Eros

Fourteen photometric lightcurves of 433 Eros were made at the Astronomical Observatory of Torino during the 1974–75 close passage. The absolute magnitude of the primary maximum (10^m78), the phase coefficient (0.023 mag/degree), the synodic and sidereal period of rotation (0^d.21956 and 0^d.21959, respectively) and the ecliptic coordinates of the pole (λ = 17°, β = 10°) were deduced.     

Far-infrared photometry of Titan and Iapetus

Titan was observed in four broad passbands between 35 and 150 μm. The brightness temperature in this interval is roughly constant at 76 ± 3°K. Integrating Titan's spectrum from 5 to 150 μm yields an effective temperature of 86 ± 3°K. Both the bright and dark hemispheres of Iapetus were observed in one broadband filter with λ_e ～ 66 μm. The brightness temperatures for these two sides of Iapetus are 96 ± 9°K and 114 ± 10°K, respectively. The bright-side Bond albedo is calculated to be 0.61_?0.22^+0.16.     

The lightcurve and phase relation of the asteroid 133 Cyrene

The asteroid 133 Cyrene was observed photometrically on 17 nights during oppositions in 1979 and 1980. The synodic period of rotation was found to be 12.^h708 ± 0.^h001 with an amplitude of ～0.^m30 during both oppositions. At large phase angles, the phase relation is quite ordinary (β_v ≈ 0.025 mag/degree); however, the low phase angle observations reveal a dramatic opposition brightening, ～0.2 mag/degree near zero phase angle. The absolute magnitude, V(1,0), extrapolated with the above linear phase coefficient, is 8.40. The following color indicates were also measured: B- V = 0.90, U-B = 0.51.     

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.     

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.     

The diameter and thermal inertia of 433 Eros

Radiometry of Eros at 10 and 20 μm demonstrates that the thermal conductivity of the upper centimeter of the surface is approximately as low as that of the Moon, suggesting that the asteroid has a regolith of highly porous rocky material. When combined with photoelectric photometry, these infrared measurements yield an effective diameter of Eros at maximum light of D₀ = 22 ± 2 km and a geometric albedo of p_v = 0.18 ± 0.03.     

The infrared photometric function of Mars and its bolometric albedo

The photometric properties of local areas on Mars are studied using Minnaert's rule of surface scattering to analyze Mariner 6 and 7 Infrared Spectrometer data. Several bright deserts, Hellas, and the south polar cap are found to obey Minnaert's function well. The coefficients B₀(α, λ) and k(α, λ) are obtained at α = 39, 48, 56, 84° and λ = 1.85, 2.23, 3.50 μm. Observed bright regions all have similar values of k, except for Hellas and the south polar cap. The lower k of Hellas is apparently caused by microscopic effects rather than by large-scale roughness due to cratering. The higher k of the cap is similar to terrestrial snows in the visual at the same phase angle. Using existing Earth-based observations, at smaller α and λ, a bolometric Bond albedo of $\text{A}{}^1\text{= 0.24 ± 0.05}$ is calculated.     

The photometric functions of Phobos and Deimos I. Disc-integrated photometry

We have used the integrated brightnesses from Mariner 9 high-resolution images to determine the large phase angle (20° to 80°) phase curves of Phobos and Deimos. The derived phase coefficients are β = 0.032 ± 0.001 mag/deg for Phobos and β = 0.030 ± 0.001 mag/deg for Deimos, while the corresponding phase integrals are q_Phobos = 0.52 and q_Deimos = 0.57. The predicted intrinsic phase coefficients of the surface material are β_i = 0.019 mag/deg and β_i = 0.017 mag/deg for Phobos and Deimos, respectively. The phase curves, phase coefficients and phase integrals are typical of objects whose surface layers are dark and intricate in texture, and are consistent with the presence of a regolith on both satellites. The relative reflectance of Deimos to Phobos is 1.15±0.10. The presence of several bright patches on Deimos could account for this slight difference in average reflectance.     

Galactic kinematics from data on open star clusters from the MWSC catalogue

Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V ₀ = 236 ± 6 km s^?1 for the adopted Galactocentric distance of the Sun R ₀ = 8.3 ± 0.2 kpc. The derived angular velocity parameters are Ω ₀ = 28.48 ± 0.36 km s^?1 kpc^?1, Ω’₀ = ?3.50 ± 0.08 km s^?1 kpc_?2, and Ω″₀ = 0.331 ± 0.037 km s^?1 kpc^?3. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f ^θ = 5.6 ± 1.6 km s^?1 and f _R = 7.7 ± 1.4 km s^?1, respectively; the perturbation wavelengths are λ _θ = 2.6 ± 0.5 kpc (i _θ = ^?11? ± 2?) and λ _R = 2.1 ± 0.5 kpc (i _R = ?9? ± 2?) for the adopted four-armed model (m = 4). The Sun’s phase in the spiral density wave is (χ_⊙)_θ = ?62? ± 9? and (χ_⊙)_R = ?85? ± 10? from the residual tangential and radial velocities, respectively.     

The photometric functions of Phobos and Deimos. II. Surface photometry of Deimos

To a good approximation the face of Deimos observed by Mariner 9 is covered uniformly by a dark, texturally complex material obeying a Hapke-Irvine scattering law. The intrinsic 20° to 80° phase coefficient of this material is β_i = 0.017 ± 0.001 mag/deg, corresponding to a disc-integrated value of β = 0.030 mag/deg. There is also evidence of a slightly brighter (by ～30%) unit near some craters which may have been produced by the cratering events. Its texture appears to be identical to that of the average material. No evidence of quasi-specular reflection has been found, suggesting that large-scale exposures of unpulverized rock are absent.     

Photometry of Phoebe

Observatios of Phoebe (S9) in the V filter at small solar phase angles (0.2° to 1.2°) with the MIT SNAPSHOT CCD are presented. The value of Phoebe's sideral rotational period is refined to 9.282 ± 0.015hr. Assuming the Voyager-derived 110 km radius, Phoebe's observed mean opposition V magnitude of 16.176 ± 0.033 (extrapolated from small angles) corresponds to a geometric albedo of 0.084 ± 0.003. A strong opposition effect is indicated by the 0.180 ± 0.035 mag/deg solar phase coefficient observed at these small phase angles. The data are shown to be compatible with a phase function for C-type asteroids (K. Lumme and E. Bowell, 1981, Astron. J. 86, 1705–1721; K. Lumme, E. Bowell, and A. W. Harris, 1984, Bull. Amer. Astron. Soc. 16, 684), but give a poorer fit to the average asteroid phase relation of T. Gehrels and E.F. Tedesco (1979, Astron. J. 84, 1079–1087). Phoebe's rotational lightcurve in the V filter is roughly sinusoidal, with a 0.230-mag peak-to-peak amplitude and weaker higher order harmonics indicating primarily bimodal surface feature contrast. In addition to these photometric results, precise positions on 3 nights are given.     

Analysis of 27 satellite orbits to determine odd zonal harmonics in the geopotential

The odd zonal harmonics in the geopotential are the terms independent of longitude and antisymmetric about the Equator: they define the ‘pear-shape’ effect. The coeffecients J₃, J₅, J₇,…of these harmonics have been evaluated by analysing the variations in eccentricity of 27 orbits covering wide range of inclinations. We use again most of the orbits from our previous (1969) evaluations, but we now have the advantage of 3 accurate orbits at inclinations between 60° and 66°, where the variations in eccentricity become very large, and 3 near-equatorial orbits, at inclinations between 3° and 15°, whereas previously there were none at inclinations lower than 28°. The new data lead to much more accurate and reliable values for the coeffecients. Our recommended set, which terminates at J₁₇, is

$\text{10}{}^9\text{J}{}_3\text{= ?2531 ± 7}\text{10}{}^9\text{J}{}_{11}\text{= 159 ± 16}\text{J}{}_5\text{= ?246 ± 9}\text{J}{}_{13}\text{= ?131 ± 22}\text{J}{}_7\text{= ?326 ± 11}\text{J}{}_{15}\text{= ?26 ±24}\text{J}{}_9\text{= ?94 ± 12}\text{J}{}_{17}\text{= ?258 ± 19}$

. With this new set of values the pear-shape tendency of the Earth amounts to 44.7 m at the poles, instead of the previous 40 m, though the new geoid is within 1 m of the old at latitudes away from the poles.