J.D. Drummond

Photometric geodesy of main-belt asteroids. II - Analysis of lightcurves for poles, periods, and shapes

Abstract Twenty-five of the twenty-six asteroids included in the “photometric geodesy” program (S.J. Weidenschilling, C.R. Chapman, D.R. Davis, R. Greenberg, D.H. Levy, and S. Vail, Icarus 70, 191–245, 1987) have been studied on the assumption that asteroids can be modeled as smooth, featureless, triaxial ellipsoids rotating about their shortest axes. Using all lightcurves available, rotational poles have been obtained by three independent methods. With these poles each asteroids sidereal period and triaxial ellipsoid axial ratios have been determined, along with the associated photometric parameters. The studied asteroids seem to have rotational poles that do not lie near their orbital planes. Two distinct types of asteroids may be indicated by a stronger solar phase angle-amplitude dependence (perhaps due to a rougher surface?) and a weaker phase-amplitude (smoother?) relation. Although no strict hydrostatic equilibrium shape is found, several asteroids are close enough to equilibrium figures to allow an estimate of their densities to be made under certain assumptions.

Speckle interferometry of asteroids: I. 433 eros

Abstract Analytic expressions for the semimajor and semiminor axes and an orientation angle of the ellipse projected by a triaxial ellipsoid (an asteroid) and of the ellipse segment cast by a terminator across the ellipsoid as functions of the dimensions and pole of the body and the asterocenteric position of the Earth and Sun are derived. Applying these formulae to observations of the Earth-approaching asteroid 433 Eros obtained with the speckle interferometry system of Steward Observatory on December 17–18, 1981, and January 17–18, 1982, the following dimensions are derived: (40.5 ± 3.1 km) × (14.5 ± 2.3 km) × (14.1 ± 2.4 km) Eros north pole is found to lie within 14° of RA = 0 h 16 m Dec. = +43° (ecliptic longitude 23°, latitude +37°). Other than knowing the rotation period of Eros, these results are completely independent of any other data, and in the main confirm the results obtained in the 1974–1975 apparition by other methods. These dimensions, together with a lightcurve from December 18, 1981, lead to a geometric albedo of 0.156 ± 0.010. A series of two-dimensional power spectra and autocorrelation functions of the resolved asteroid clearly show it spinning in space.

Speckle interferometry of asteroids IV. Reconstructed images of 4 Vesta

Abstract The first glimpses of an asteroids surface have been obtained from images of 4 Vesta reconstructed from speckle interferometric observations made on November 16 and 17, 1983, using Steward Observatorys 2.3-m telescope coupled with Harvards PAPA camera. From power spectrum analysis of the 10 images Vesta is found to have a “normal” triaxial ellipsoid shape of 584(±16) × 531(±11) × 467(±12) km. Its rotational pole lies within 4° of RA = 21 h 00 m , Dec = +41° (Ecliptic long = 336°, lat = +55°) Our observations definitely support a 5-hr 20.5-min rotational period and do not fit one twice as long. Reconstructed images reveal dark and bright patterns, reminiscent of the Moon, which can be followed across the disk as the asteroid rotates. By placing circular “spots” with diameters of 135 km (= 0.11 arcsec, the effective resolution) over three dark and three bright features, and assigning albedos (relative to the surrounding material) of 0 to the dark spots and 2 to the bright spots (except one with an albedo of 1.2), we are nearly able to match its visible lightcurve. It only requires an additional bright spot deep in Vestas southern hemisphere, an area not visible during our observations, to provide a near perfect match to all low solar phase angle lightcurves ever obtained of this asteroid. At phase angles greater than about 10° the observed amplitude becomes greater by up to 0.02 mag. The dark areas so dominate one face of Vesta that a minimum in the lightcurve occurs when the maximum cross-sectional area is visible. Its lightcurve is determined primarily by albedo structure rather than shape, leading to one maximum and one minimum per rotation instead of the expected two of each associated with its triaxial ellipsoid shape.

The absence of satellites of asteroids

Abstract A CCD-imaging survey was made for satellites of minor planets at distances of about 0.1 to 7 arcmin from 1 Ceres, 2 Pallas, 4 Vesta, 6 Hebe, 7 Iris, 8 Flora, 15 Eunomia, 29 Amphitrite, 41 Daphne, and 44 Nysa, with cursory inspection of 192 Nausikaa. Satellites larger than 3 km were not found in this work, nor in previous photographic surveys. Not finding them appears to be consistent with theoretical studies of collisions in the asteroid belt by several authors. The satellites would have to be larger than at least 30 km to be collisionally stable. Tidal effects would lead to synchronous rotation and therefore long periods of rotation (several days), which are not generally observed. Taking tidal stability into account, we conclude that the only possible satellites for main-belt asteroids, with stability over eons, are near-contact binaries. The only other rare possibility for a satellite might be a piece of debris from a recent collision, and it would now be chaotic and collisionally unstable.

Speckle interferometry of asteroids II. 532 Herculina

Abstract 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 b 47 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 Herculinas lightcurve history. This bright complex, centered at asterocentric latitude −35°, longitude 145–165°, extends over a diameter of 55° (115 km) of the asteroids 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.

Photometric geodesy of main-belt asteroids. IV, an updated analysis of lightcurves for poles, periods, and shapes

Abstract This is an updated analysis of main-belt asteroids extending that of Drummond et al. (1988, Icarus 76, 19–77) dor derivation of poles, periods, phase functions, and triaxial ellipsoid shapes from analysis of lightcurve maxima and minima with three independent methods. The primary dataset is from the “Photometric Geodesy” program, augmented by data in the literature. Results are presented for the first time for 250 Bettina, and significantly revised results for 10 others (15, 43, 55, 65, 88, 107, 125, 201, 354, and 694). The ensemble of 26 asteroids is also reconsidered in terms of the distributions of obliquities and triaxial shapes. Three remains a weak tendency for poles to avoid asteroid orbital planes. Two kinds of solar phase angle-amplitude relations persist and may reflect a rough/smooth surface dichotomy for our asteroids. Most asteroids studied (a sample selected to emphasize large amplitudes and rapid spins) show shapes significantly deviating from hydrostatic equilibrium figures. Seven objects (39, 45, 55, 65, 107, 130, and 216) could be Jacobi ellipsoids (or 65 a Maclaurin spheroid) if a systematic effect in our analysis slightly exaggerates axial ratios. Perhaps the hypothesized tendency for rubble pile asteroids to form quasi-equilibriu, figures is distorted by the largest cratering events (such as Stickney on Phobos) due to the mass-dominant size distribution of the asteroids.

Speckle interferometric observations of Pluto and Charon

Abstract We report speckle interferometric observations of Pluto and its moon (1978 P1) Charon obtained on 5 June 1980 with a single 1.8-m mirror of the Multiple Mirror Telescope. Our observations yield a separation of 0″.31 (±0″.05) between Pluto and Charon at position angle 285° (±7°) for JD 2444395.75. This result and other direct observations indicate an adjustment of +4.0 hr to the orbital epoch of R. S. Harrington and J. W. Christy [ Astron.J. 86 , 442–443 (1981)]. Our observation, which represents the first resolution of the system near minimum separation, also suggests that the inclination of the orbit to the plane of the sky should be increased by 3°; this will delay the onset of the predicted eclipsee season by one apparition to 1984 or 1985. Our data are consistent with Pluto diameter 0″.14 (±0″.02) = 3000 (±400) km and Charon diameter 0″..05 (±0″.03) = 1100 (±600) km.

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

Abstract 511 Davida was observed with the technique of speckle interferometry at Steward Observatorys 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/cm 3 . 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 h 08 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 h 52 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.

The rotational poles and shapes of 1580 Betulia and 3908 (1980PA) from one apparition

Abstract The rotational poles, triaxial ellipsoid shapes, absolute magnitudes, and phase functions of two Amor asteroids have been calculated from lightcurves obtained in a single apparition. The lightcurves of 1580 Betulia were obtained in 1976, and the present analysis gives a preferred pole within 9° of Ecliptic coordinates (212; −5), with triaxial ellipsoid ratios of a b = 1.62±.20 and b c = 1.39±.09 . Its orbital inclination of 52°, the fourth highest among asteroids to date, makes it a strong defunct comet candidate. Asteroid 3908 (1980PA) is the second most accessible asteroid to the Earth in terms of relative velocity, making it a good candidate for a return sample mission. Its preferred rotational pole, lying within 10° of (312; +61), and its triaxial ellipsoid ratios of a b = 1.36±.03 and b c = 1.27 ± .03 were determined from eight lightcurves obtained in its 1988 apparition, and make this the fastest such calculation ever. Its spectrum, albedo, and phase functions are similar to Vesta, Dembowska, and another Amor 3551 (1983RD), all being reddish and bright. The orbits of 3908 and 3551 are similar to each other and to at least two photographic meteors and one fireball from the Prairie Network. All five objects may be pieces of the eucrite parent body, and the radiants indicate that eucrite falls may peak between late August and late November.

Triaxial ellipsoid dimensions and rotational pole of 2 Pallas from two stellar occultations

Abstract From three stellar occultations we show that it is possible to derive unique triaxial ellipsoid dimensions and a rotational pole for an asteroid. With the two occultations for Pallas, we examine the locus of solutions that fall along a curve in a seven-dimensional parameter space. It appears from this range of solutions that the first occultation (slightly) overestimated the ture size of the outline of the asteroid at that time. Within the errors of this first occultation, however, more plausible solutions are allowed. The best estimate of the lengths of the triaxial ellipsoid axes derived from the two occultations is (in km) (583 ± 18, 527 ± 3, 409 ± 52) and a rotational pole within 10° of RA = 72°, Dec = +3° (or 252°; −3°), corresponding to eliptic coordinates long = 71°, lat = −19°. Combining the occultation model with speckle interferometry results gives a model of (570 ± 22, 525 ± 4, 482 ± 15) km, and for occultation, speckle, and lightcurve methods, a pole at RA = 75°, Dec = +6° (ecliptic coordinates (74°; −17°)), with an error circle of 24° radius. Pallas is more flattened, with a greater b c ratio (and a smaller c) than previously estimated.