UBV photometry of Vesta

A lightcurve of Vesta, obtained on four nights between June 23 and 30 June 1978 during the coordinated campaign for the determination of the rotation period, is presented. The observations were performed at the 91-cm telescope of the Catania Observatory employing UBV filters and a photon counting photometer. The V lightcurve apparently shows a single maximum, suggesting that the 5^h20^m29^s.2 period is the correct one. Features are evident near the maximum and the minimum closely resembling those of Johnson's lightcurve of 22 December 1950 and Taylor's of January 21, 1973. The amplitude in V light is 0^m.105 and small variations are also found in the color indices. The largest color variation is for the U-V with Δm = 0.^m.05, which is slightly larger than the value 0^m.02 found by T. Gehrels [Astron. J.72, 929 (1967)]. The maximum and minimum values occur at the same phase with respect to the maximum V light as found by Gehrels, i.e., Vesta appears bluer near 0^p.25 and redder near 0^p.7. Corrections with the solar phase angle were made using the coefficients given by Gehrels for the B-V and U-V while a new value of 0.036 mag/deg was assumed for the V observations. The available amplitudes of Vesta's lightcurve were analyzed with respect to the longitude position and the solar phase angle.     

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°.     

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.     

Convex profiles from asteroid lightcurves

Integral geometry is used to solve a two-dimensional simplification of the three-dimensional lightcurve inversion problem, and a method is introduced for obtaining a convex profile, $\text{P}$, from asteroid lightcurve data. Whenever four ideal conditions are satisfied, $\text{P}$ is an estimator for the asteroid's “mean cross section,” $\text{C}$, a convex set defined as the average of all cross sections $\text{C}$ cut by planes a distance z above the asteroid's equatorial plane. $\text{C}$ is therefore a two-dimensional average of the asteroid's three-dimensional shape. The ideal conditions are that (A) each curve $\text{C}\text{(z)}$ is convex. (B) the asteroid's scattering law is uniform and geometric, (C) the astrocentric declinations of the Sun and Earth are zero, and (D) the solar phase angle θ ≠ 0. If Condition C is known to hold, the extend to which the lightcurve can be accounted for by a geometrically scattering convex object can be quantified in terms of an appropriate “goodness-of-fit” static. If the solar phase angle is zero, as for radar “lightcurve,” then (i) method yields a profile $\text{P}{}_{\mathrm{<mtext>s</mtext>}}$ the symmetrization $\text{C}{}_{\mathrm{<mtext>s</mtext>}}$ of $\text{C}$; (ii) Condition A need not hold and if it does not, then the inversion yields the symmetrization of the asteroid's mean convex hull; and (iii) Fourier analysis of the lightcurve can reveal violation of Condition B. Doppler-frequency resolution of radar echoes at several rotational phases adds information by constraining the convex hull $\text{H}{}_{\mathrm{<mtext>p</mtext>}}$ of the asteroid's (not necessarily convex) polar silhouette. Estimation of a convex profile from a photoelectric or radar lightcurve is a problem in weighted-least-squares optimization subject to inequality constraints. The solution uses a recursive quadratic programming algorithm to derive a Fourier parameterization for $\text{P}$ from the coefficients in the lightcurve's Fourier expansion. The method has been tested by inverting analytically generated lightcurves for geometrically scattering ellipsoids with semiaxes a ? b ? c, and the inversion yields $\text{P}\text{=}\text{P}{}_{\mathrm{<mtext>s</mtext>}}\text{?}\text{C}\text{=}\text{C}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{H}{}_{\mathrm{<mtext>p</mtext>}}$ when the viewing geometry (Condition C) is close to ideal. For situations when the asteroid's pole direction is unknown, a test is offered of the hyphothesis that a given lightcurve can be due to a geometrically scattering ellipsoid with $\text{a}\text{c}\text{? ?}$, where ? is an priori upper bound on the maximum axis ratio. Convex profiles are presented for 15 Eunomia, 118 Peitho, 246 Asporina, 281 Lucretia. 790 Pretoria, 1685 Toro, and 1978 CA.     

The period of rotation and the photoelectric lightcurve of the minor planet 79 eurynome

The minor planet 79 Eurynome was observed during the 1974 opposition for four nights in November, using a photoelectric photometer attached to the 60 cm telescope at the Observatoire de Haute Provence, France. A synodic period of P_syn = 5^h 58^m46^s ± 6^s m.e. was derived. The total amplitude of the lightcurve is only 0.05 mag. The lightcurve shows a double maximum and double minimum. Both minima appear to be at the same level. Observations were carried out in an instrumental filter system (UBV)' Results are shown only for V′, but U′ and B′ measurements supplement the conclusions concerning the rotation. The phase angle α, covered by the observations, ranges from 3 to 5°. The present results for 79 Eurynome rule out the longer period of 0^d.49830 derived by F. Scaltriti and V. Zappalà in favor of their possible period of 0^d.24915.     

Photometric study of Centaur (60558) 2000 EC98 and trans-neptunian object (55637) 2002 UX25 at different phase angles

We present photometric observations of Centaur (60558) 2000 EC₉₈ and trans-neptunian object (55637) 2002 UX₂₅ at different phase angles and with different filters (mainly R but also V and B for some data). Results for 2000 EC₉₈ are: (i) a rotation period of 26.802±0.042 h if a double-peaked lightcurve is assumed, (ii) a lightcurve amplitude of 0.24±0.06 for the R band, (iii) a phase curve with H=9.03±0.01 and G=−0.39±0.08 (R filter) and H=9.55±0.04 and G=−0.50±0.35 (V filter) or a slope of (R filter) and 0.22±0.06 (V filter), (iv) the color indices B-V=0.76±0.15 and V-R=0.51±0.09 (for α=0.1-0.5°) and 0.55±0.08 (for α=1.4-1.5°). The rotation period is amongst the longest ever measured for Centaurs and TNOs. We also show that our photometry was not contaminated by any cometary activity down to magnitude ?27/arcsec². For 2002 UX₂₅ the results are: (i) a rotation period of 14.382±0.001 h or 16.782±0.003 h (if a double-peaked lightcurve is assumed) (ii) a lightcurve amplitude of 0.21±0.06 for the R band (and the 16.782 h period), (iii) a phase curve with H=3.32±0.01 and G=+0.16±0.18 or a slope of (R filter), (iv) the color indices B-V=1.12±0.26 and V-R=0.61±0.12. The phase curve reveals also a possible very narrow and bright opposition surge. Because such a narrow surge appears only for one point it needs to be confirmed.     

Coordinated observations of asteroids 1219 Britta and 1972 Yi Xing

Identified as possible flyby targets for the Galileo spacecraft, Asteroids 1219 Britta and 1972 Yi Xing became the focus of a coordinated observing program. Although a subsequent change in the launch date removed these asteroids from consideration for the Galileo mission, the ground-based observing program yielded a substantial amount of information on these previously unobserved asteroids. Britta's sideral rotation period is found to be 5.57497 ± 0.00013 hr and its rotation is retrograde. The lightcurve amplitude ranged from 0.60 to 0.70 mag, depending on phase angle. Britta can be classified as an S-type asteroids based on its measured spectra and albedo. The absolute magnitude and slope parameter derived from the lightcurve maxima are H₀ = 11.67 ± 0.03 and G₀ = 0.03 ± 0.04. A 0.002 mag deg⁻¹ phase reddening in B·V was also measured. 1972 Yi Xing was less well observed but a unique synodic period of 14.183 ± 0.003 hr was determined. The observed lightcurve amplitude was 0.18 mag. Five-color measurements are consistent with an S-type classification. For an assumed slope parameter G = 0.25, Yi Xing's (lightcurve maximum) absolute magnitude H₀ = 13.32 ± 0.01.     

Radar observations of asteroid 1580 Betulia

Radar observations of the asteroid 1580 Betulia, made at a wavelength of 12.6 cm, show a mean radar cross section of 2.2 ± 0.8 km² and a total spectral bandwidth of 26.5 ± 1.5 Hz. Combining our bandwidth measurements with the optically determined rotation period sets a lower limit to the asteroid's radius of 2.9 ± 0.2 km.     

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.     

Radar and photoelectric observations of asteroid 2100 Ra-Shalom

Results of 13-cm-wavelength radar observations and V-filter photoelectric observations of Ra- Shalom during its 1981 Aug–Sep apparition are reported. The radar data yid detections of echoes in the same sense of circular polarization as transmitted (i.e., the SC sense) as well as in the opposite (OC) sense. The estimate of the ratio of SC to OC echo power, μ_c = 0.14 ± 0.02, indicates that most, but certainly not all, of the backscattering is due to single reflections from surface elements that are fairly smooth at decimeter scales. The value obtained for the OC radar cross section on Aug 26 (1.2 ± 0.3 km²) is about three times larger than those obtained on Aug 23, 24, and 25. The echo bandwidth appears to be within about 1.5 Hz of 5.0 Hz on each date. The photoelectric data suggest a value, P_syn = 19.79 hr, for the synodic rotation period, and yield a composite lightcurve with two pairs of extrema. Combining this value for P_syn with a firm lower bound (4 Hz) on the maximum echo bandwidth yields a lower bound of 1.4 km on the maximum distance between Ra-Shalom's spin axis and any point on its surface.     

Speckle interferometry of asteroids II. 532 Herculina

Speckle interferometry of 532 Herculina performed on January 17 and 18, 1982, yields triaxial ellipsoid dimensions of (263 ± 14) × (218 ± 12) × (215 ± 12) km, and a north pole for the asteroid within 7° of RA = 7^b47^m and DEC = ?39° (ecliptic coordinates γ = 132° β = ?59°). In addition, a “spot” some 75% brighter than the rest of the asteroid is inferred from both speckle observations and Herculina's lightcurve history. This bright complex, centered at asterocentric latitude ?35°, longitude 145–165°, extends over a diameter of 55° (115 km) of the asteroid's surface. No evidence for a satellite is found from the speckle observations, which leads to an upper limit of 50 km for the diameter of any satellite with an albedo the same as or higher than Herculina.     

Motion in the interiors and atmospheres of Jupiter and Saturn: scale analysis,anelastic equations,barotropic stability criterion

If Jupiter's and Saturn's fluid interiors were inviscid and adiabatic, any steady zonal motion would take the form of differentially rotating cylinders concentric about the planetary axis of rotation. B. A. Smith et al. [Science215, 504–537 (1982)] showed that Saturn's observed zonal wind profile extends a significant distance below cloud base. Further extension into the interior occurs if the values of the eddy viscosity and superadiabaticity are small. We estimate these values using a scaling analysis of deep convection in the presence of differential rotation. The differential rotation inhibits the convection and reduces the effective eddy viscosity. Viscous dissipation of zonal mean kinetic energy is then within the bounds set by the internal heat source. The differential rotation increases the superadiabaticity, but not so much as to eliminate the cylindrical structure of the flow. Very large departures from adiabaticity, necessary for decoupling the atmosphere and interior, do not occur. Using our scaling analysis we develop the anelastic equations that describe motions in Jupiter's and Saturn's interiors. A simple problem is solved, that of an adiabatic fluid with a steady zonal wind varying as a function of cylindrical radius. Low zonal wavenumber perturbations are two dimensional (independent of the axial coordinate) and obey a modified barotropic stability equation. The parameter analogous to β is negative and is three to four times larger than the β for thin atmospheres. Jupiter's and Saturn's observed zonal wind profiles are close to marginal stability according to this deep sphere criterion, but are several times supercritical according to the thin atmosphere criterion.     

Variability of Neptune

Earth-based observers of Neptune have found that the planet varies in brightness at various wavelengths in ways that suggest that changes occur in the planet's atmosphere on several different time scales. Global inhomogeneities in high-altitude haze distribution that are stable for several days permit measurements of the planet's rotation period (about 18 hr), but this stability sometimes breaks down, obscuring the diurnal lightcurve. In addition, there is an apparent long-term variability of the brightness of Neptune in anticorrelation with the cycle of solar activity. This slow variability of low amplitude may be punctuated by outburst of high-altitude condensation of particles in the atmosphere whose decay time is several months.     

The angular momenta of solar system bodies: Implications for asteroid strengths

The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [Icarus18, 285–293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [Icarus7, 251–256 (1967]) and W. K. Hartmann and S. M. Larson [Icarus7, 257–260 (1967)], H is approximately proportional to $\text{M}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects.The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm^?3. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.     

A test of the plausibility of eclipsing binary asteroids

We present an analytic method for producing the lightcurve of a system of spherical bodies in circular orbit about their common center of mass and then use it to model a lightcurve of 171 Ophelia. We find that a model in which the components have a diameter ratio of 1:2.96, have equal albedos, and circle one another in a synchronous orbit (period = 13.146 hr) inclined by 15° to our line of sight provides a reasonable fit to the observed lightcurve. An expression is given for the density in terms of the model parameters. If this lightcurve of Ophelia is produced by mutual eclipses of spherical components the mean density of the system can not exceed 1.7 g cm^?3. In view of these results we conclude that it is possible for Ophelia to be a binary.     

Lunar occultation of Saturn: III. How big is Iapetus?

By considering both the orbital lightcurve of Iapetus and data obtained during the March 30, 1974, occultation of the satellite by the Moon, we obtain information about the brightness distribution on the bright face of Iapetus and derive an accurate value for the satellite's radius. From the observed orbital lightcurve we find that the trailing face of Iapetus must consist predominantly of a single bright material with an effective limb-darkening parameter of k = 0.62_?0.12^0.10. Given this result the occultation observations imply a radius of 718_?78⁺⁸⁷ km. If the patchy albedo model proposed by Morrison et al. represents the surface of Iapetus accurately (as far as the relative albedo distribution is concerned) then the radius of Iapetus is 724 ± 60 km. Both estimates are consistent with the radiometric radius of 835 (+50, ?75) km derived by Morrison et al. Combining our results with the value of 0.60 ± 0.14 for the normal reflectance (in V) of the material at the center of the bright face derived by Elliot et al. we find that the normal reflectance of the dark side material is 0.11_?0.03^+0.04. These values are higher than the corresponding values of 0.35 and 0.05 quoted by Morrison et al.     

Asteroid 532 Herculina: Lightcurves,pole orientation and a model

Photoelectric lightcurves of 532 Herculina in 1984 show two maxima and two minima with a synodic rotation period of 0.39185 ± 0.00002 day (1σ). During some other oppositions the Herculina lightcurve has only one maximum and one minimum over that same rotation period. The absolute magnitude in V is 6.13 ± 0.02 mag, the phase coefficient in V is 0.037 ± 0.002, and the mean colors are B−V = +0.86 ± 0.04 and U−B = +0.43 ± 0.02. We applied photometric astrometry and the results indicate a sideral period of 0.3918711 ± 0.0000001 day with retrograde rotation for a north pole at 276° long and +1° lat. The uncertainty of the pole is ±1°. A model of Herculina is presented that generates lightcurves consistent with both the observed amplitudes and the timings of extrema over precisely 28,630 sideral rotations during 30 years. The model is a sphere with two dark regions that are each about 0.13 times the brightness of the surrounding surface. The regions are at 0° asterocentric longitude, +15° lat, with a radius of 30°, and 170° long, −38° lat, with a radius of 26°. With the photometric astrometry pole and the model with two dark regions, predicted lightcurves are shown for the next four oppositions.     

Decametric radio measurement of Jupiter's rotation period

A total of 26 measurements of Jupiter's 12-year average rotation period were made at frequencies of 18, 20, and 22.2 MHz at observatories in Florida and Chile. An improved method was employed in which histograms of occurrence probability vs central meridian longitude obtained at the same frequency and observatory during apparitions about 12 years (one Jovian year) apart were cross correlated. The longitude shift giving maximum cross correlation was used to correct the initially assumed rotation period value. The mean of the measurements is 9 hr 55 min 29.689 sec, with a standard deviation of the mean of 0.005 sec. This is about 0.02 sec, or 4 standard deviations, less than the System III (1965) value. The measurements indicate that the rotation period was not changing (linearly) at a rate in excess of 0.03 sec/yr. If the synoptic monitoring program is continued through the next maximum of the jovicentric declination of the Earth (D_E), we will probably be able to detect a rate of change in rotation period as small as 0.002 sec/yr. This accuracy might be sufficient to reveal a secular drift in Jupiter's magnetic field.     

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.     

First lightcurve observations and rotation of minor planet 127 Johanna

Photoelectric observations of the minor planet 127 Johanna were made in the UBV (RI)_c photometric system during its apparition in 1991 at the Piszkéstetõ mountain-station of Konkoly Observatory from August to December, when it showed a brightness variation with an amplitude of about 0.2 magnitude. The derived H, G values in the two-parameter magnitude system in V are 8.459 ± 0.013 and 0.114 ± 0.020, respectively. The determined V linear phase coefficient is of 0.036 ± 0.001 (mag/deg). The value of G and the observed values of color indices (U-B), (B-V) confirm that this asteroid belongs to the C taxonomic class as it was previously classified. The estimated effective diameter is between 96 and 118 km if the assumed V geometric albedo is of 0.06 and 0.04, respectively. The available data suggest a pure principal axis rotation mode. The mean synodic rotational period of the asteroid 127 Johanna is 6.94 ± 0.29 h. The uncertainty is due to the changing of aspect geometry. This value of the synodic rotation period means that this asteroid has an intermediate rotation period. The sense of rotation is prograde as indicated by the temporal evolution of the time derivative of the ecliptic longitude of the phase angle bisector as well as with the increasing synodic period of rotation during the same interval (October/November and December in 1991). The composite lightcurves created for short arc time data reveal structures with breakings and linear portions in V; this fact and the Fourier coefficients indicate a probably irregularly shaped body. There are slight indications that the B-V is redder close to the brightness minimum and the V-R_c is redder at the brightness maximum, and the periodic behavior cannot be proved in V-I_c. The less full rotational phase coverage of the observational data is insufficient to construct a shape model. The accurate pole orientation obviously cannot be determined using one opposition lightcurve data only. Further observations are required to get a more accurate knowledge of the physical parameters of this asteroid. For this purpose, a good opportunity to perform observations arose in December 1996, when this asteroid was in opposition at the northernmost declination.