Photoelectric lightcurves of asteroids 42 Isis, 45 Eugenia, 56 Melete, 103 Hera, 532 Herculina,and 558 Carmen

Photoelectric observations of six asteroids are presented. The following synodic periods of rotation and amplitudes of variation are reported: 42 Isis, P = 13^h.59, Δm = 0.32; 45 Eugenia, P = 5^h.70, Δm = 0.30; 56 Melete, P = 13^h.7 or 19^h.0, Δm = 0.06; 532 Herculina, P = 9^h.408, Δm = 0.15; 558 Carmen, P ≈ 10^h, Δm ≈ 0.25. The asteroid 103 Hera exhibited no periodic variation in excess of about 0.03 magnitude. The period found for 532 Herculina is one half that previously reported by other observers.     

Asteroid rotation: I. Tabulation and analysis of rates,pole positions and shapes

Data are presented for the 182 asteroids whose rotational properties are available in the literature. Plots are provided for the asteroid rotational frequency f and lightcurve amplitude Δm versus asteroid size; the latter is determined using standard methods if data are available but otherwise is estimated from asteroid albedos, selected depending on taxonomic type or orbital position. A linear least-squares fit to all the data shows that f increases with decreasing size, confirming McAdoo and Burns' (1973) result; this is demonstrated to be primarily caused by relatively more small non-C than C asteroids in our sample, coupled with a slower mean rotation rate for C asteroids (P ≈ 11 hr) than non-C asteroids (P ≈ 9 hr). In terms of the collisional theory of Harris (1979a), this means that the C's are less dense than the other minor planets. Any slight tendency for smaller asteroids to spin faster, even within a taxonomic type, could be due to selection effects; our data are not extensive enough to determine whether the very smallest (? 10-km diameter) spin especially fast. The minor planets of our survey become more irregular at smaller sizes, disputing the conclusions of Bowell (1977b), Degewij (1977), and Degewij et al. (1978), based on other, perhaps more complete, data; selection effects may account for this disagreement. Shapes do not appear to depend on taxonomic type. The dispersion of asteroid rotation rates from the mean is found to be in excellent agreement with a three-dimensional Maxwellian distribution, such as would be developed in a collisionally evolved system. The rotation axes, therefore, appear to be randomly oriented in space. Rotation pole positions are also tabulated and calculated to likely be constant in space over the extent of past observation. Observers are encouraged to measure the rotational properties of faint objects and asteroids of unusual taxonomic types, and to carry out long-time studies of asteroids which over short periods do not seem to vary.     

Rotational properties of asteroids: Correlations and selection effects

Rotational data on 321 asteroids observed as of late 1978 are analyzed. Selection effects within the sample are discussed and used to define a data set consisting of 134 main-belt, nonfamily asteroids having reliably determined periods and amplitudes based on photoelectric observations. In contrast to A. W. Harris and J. A. Burns (1979, Icarus40, 115–144) we found no significant correlation between rotational properties and compositional type. Smaller asteroids have a greater range of rotational amplitudes than the largest asteroids but are not, on the average, appreciably more elongated. While no definite relationship between asteroid size and rotation rate was found the distribution is not random. The largest asteroids have rotation periods near 7 hr compared with 10 hr for the smaller. A group of large, rapidly rotating, high-amplitude asteroids is recognized. A pronounced change in rotational properties occurs near this size range (diam = 200 ± 50 km) which also corresponds to the size at which a change of slope occurs in the size frequency distribution. We believe this size range represents a transition region between very large, rapidly rotating, low-amplitude (primordial?) objects and smaller ones having a considerably greater range of periods and amplitudes. Asteroids in this transition size range display an increase in rotational amplitude with increasing spin rate; other than this, however, there is no correlation between period and amplitude. The region of low spatial density in the asteroid belt centered near 2.9 AU and isolated from the inner and outer belt by the 2:5 and 3:7 commensurabilities is shown to be a region in which non-C or -S asteroids are overrepresented and which have marginally higher rotational amplitudes than those located in more dense regions. We attribute disagreements between our results and other studies of this type to the inclusion of non-main-belt asteroids and photographic data in the earlier analyses.     

Lightcurves and Synodic Periods for Asteroids 1998 ST49, (13154) and (27529)

The first photometric observations of the near-Earth asteroid 1998 ST₄₉ and the main belt asteroids (13154) and (27529) are reported. The synodic rotation periods and amplitudes of the lightcurves are:

? 2.3017 h, 0.11 mag for 1998 ST₄₉;

? 2.98502 h, 0.18 mag for (13154);

? 4.1290 h, 0.51 mag for (27529).

The periods for the first two asteroids are unambiguous, while the period of 4.1570 h is not ruled out for the third asteroid. Despite fast rotations, none of the presented asteroids exhibited any sign of binarity. Lightcurves were obtained at Modra Observatory.     

Further evidence for collisions among asteroids

The 64 asteroids with reliably known rotational properties [rotation period P, magnitude B(1, 0) and maximum change of magnitude Δm] are studied. A plot of B(1,0) vs P illustrates that smaller asteroids tend to rotate faster than larger asteroids. The mean P for all 64 asteroids is 8.8 hr. The class of irregular asteroids (taken to be those with Δm >0.38, i.e., those whose axes differ by more than 40%) called group C are studied separately; they are shown to rotate much faster (mean P = 7.7 hr) than the remaining more regular asteroids (mean P = 9.2 hr). The smaller bodies are more irregular on the average. These results are interpreted in terms of a model in which collisions break asteroids into irregular fragments. Since angular momentum is transmitted in such collisions, significant increases in the mean can occur in the angular velocity of the largest fragment. The effect of interasteroid collisions on the mean orbital parameters is briefly discussed and is shown to be masked by selection effects.     

The rotation,color, phase coefficient,and diameter of 1915 quetzalcoatl

Photoelectric observations of 1915 Quetzalcoatl on March 2, 1981 show that this asteroid has a rotational period of 4.9 ± 0.3 hr and a lightcurve amplitude of 0.26 magnitudes. B-V and U-B colors are found to be 0.83 ± 0.04 and 0.43 ± 0.03, respectively, consistent with Quetzalcoatl being an S-type asteroid. Additional observations from March 31, 1981 give a linear phase coefficient of 0.033 mag deg^?1 and a mean B(1,0) magnitude of 20.10. The resulting estimated mean diameter for Quetzalcoatl is only 0.37 km, making it one of the smallest asteroids for which physical observations have yet been made.     

Asteroid rotation rates

The dependence of rotational frequency on diameter, taxonomic type, and family membership is analyzed for 217 main-belt asteroids with statistically useful periods extracted from the file published by Harris and Young ((1983). Icarus54, 59–109). It is shown that for asteroids with diameters ? 120 km, mean rotational frequency increases with increasing diameter. This trend is equally present in all subsets of M-, S-, and C-type asteroids, for both family and nonfamily members alike, and cannot be accounted for by observational selection. For asteroids with diameters ? 120 km, mean rotational frequency increases with decreasing diameter; however, within this group there is a subset of asteroids with exceptionally long rotational periods. This marked change in the distribution at diameter ～ 120 km could separate primordial asteroids from their collision products. However, it is probable that the sample is biased in favor of small asteroids with short rotational periods and that the apparent increase of mean rotational frequency with decreasing diameter for small asteroids is at least partly the product of observational selection. An observational program that could test this hypothesis is described. If asteroids of any one diameter are considered, then, on average, M asteroids rotate faster than S asteroids which in turn rotate faster than C asteroids. This shows that asteroids which have been classified by their surface properties alone have different bulk properties. There is also some evidence that for all asteroidal types, of all diameters, family members rotate faster than nonfamily members.     

1580 Betulia: An unusual asteroid with an extraordinary lightcurve

Results of UBV photometry and polarimetry of 1580 Betulia during its 1976 apparition are presented. The synodic period of rotation is found to be 6.130 hr. The linear phase coefficient and absolute magnitude of the primary maximum in V are 0.032 mag/deg and 14.88, respectively. No color variations with rotation or solar phase angle detected, the mean colors being B?V = 0.66 and U?B = 0.24. Betulia's lightcurve is unique among asteroids studied to date in that it displays three maxima and three minima within one rotational cycle, indicative of a region of greater roughness and/or a dark spot on one of its broad faces. Polarization results indicate a low albedo and a mean diameter of about 7 km, establishing Betulia as the first C type asteroid to be found among the Mars crossers. A model accounting for most features of Betulia's lightcurve is given by a prolate spheroid rotating about one of its shorter axes having an axis ratio of 1:1.21 with a major topographic feature on one of its broad faces.     

Asteroid rotation: IV. 1979 observations

Results of photoelectric lightcurve observations made during 1979 are reported. Of a total of 53 asteroids observed, reliable rotation periods are reported for 22 asteroids for which no previous values are known, 7 periods are reported which are revisions of previously reported values, and for 12 other asteroids periods are suggested which are admittedly of low reliability and those objects should be reobserved. In addition, phase relations are presented for many of the asteroids, fitted to the theoretical phase function of Lumme and Bowell (Astron. J., 86, 1705, 1981). Adopting their formalism, mean absolute magnitudes at zero phase angle, $\text{V}\text{(0°)}$, for 52 asteroids, and values of the multiple scattering parameter, Q, for 22 asteroids are reported. For comparison purposes, the absolute magnitude, V(1,0) and the linear phase coefficient, βv, in the traditional system are computed. In the appendixes (1) the methods of observation and data reduction are discussed, which are recommended to other lightcurve observers in the hope of standardizing reporting practices as much as possible; and (2) a cumulative index of all asteroid rotation data of which the authors are aware is presented.     

Polarimetry of main belt asteroids: Wavelength dependence

New UBVRI polarimetric observations of ten asteroids, including space mission targets 1 Ceres and 21 Lutetia, are presented. These observations were obtained with the 1.25-m telescope of the Crimean Astrophysical Observatory and have been used to study the wavelength dependence of polarization for a sample of asteroids belonging to the M and low albedo classes. A more general analysis including also a larger data set of UBVRI polarimetric observations available in the literature for more than 50 main belt asteroids belonging to different taxonomic classes shows that the variation of the polarization degree Pr as a function of wavelength is generally well described by a linear trend. It typically does not exceed 0.2% in the studied spectral range 0.37-0.83 microns and tends to increase for increasing phase angle. Asteroids belonging to the S and M classes are found to exhibit a deeper negative branch and smaller positive polarization for increasing wavelength (negative sign of the slope of ΔPr/Δλ). Since the objects belonging to these classes are known to exhibit reddish reflectance spectra, the observed wavelength behavior of negative polarization contradicts the well-known inverse correlation of Pmin and albedo. Low albedo asteroids show larger dispersion of spectral slopes, but the overall trend is characterized by a shallower negative branch and a larger positive polarization for increasing wavelength (positive sign of the slope of ΔPr/Δλ). A few exceptions from this general trend are discussed. The observed variety in the wavelength dependence of asteroid polarization seems to be mainly attributed to surface composition.     

Orientation of the hipparcos frame with respect to the reference frames of the DE403/LE403 and DE405/LE405 ephemerides based on asteroid observations

Highly accurate observations of 116 asteroids are used to determine the orientation of the Hipparcos frame with respect to the reference frames of the DE403/LE403 and DE405/LE405 majorplanet ephemerides. These observations include the photographic observations of 15 asteroids obtained as part of the programs for observing selected asteroids and reduced to the Hipparcos frame using dependences, the space observations of 48 asteroids obtained by the Hipparcos satellite, and the presentday observations of 116 asteroid performed in the frame of the ACT catlog. The total number of observations used is more than 50 000 in the interval 1949–2007. Processing this series has yielded the following estimates of the orientation parameters: ω _x = 0.12 ± 0.08 mas yr^?1, ω _y = 0.66 ± 0.09 mas yr^?1, and ω _z = ?0.56 ± 0.16 mas yr^?1. This rotation may be attributable to a peculiarity of the transition from the reference frame of the DE200/LE200 ephemerides to that of DE403/LE403 ephemerides (since October 1, 1988, to J2000) that consists in the the assumption that the former reference frame has no rotation relative to the ICRF.     

The lightcurve and rotation period of asteroid 139 Juewa

Results of broad-band photoelectric photometry of 139 Juewa during 5 consecutive nights in March 1974 are presented. The synodic period found is 20.9 hr. A linear phase coefficient, β = 0.080 ± 0.004, is determined between phase angles of 0.9° to 1.5°. This value is similar to that for the lunar highlands and for three other asteroids (4 Vesta, 20 Massalia, 110 Lydia) at similar phase angles, indicating that these surfaces have comparable porosities. The composite lightcurve presented covers 80% of the rotational period; short timescale features in the lightcurve are seen which correspond to topography a few kilometers in size.     

Hidden Mass in the Asteroid Belt

The total mass of the asteroid belt is estimated from an analysis of the motions of the major planets by processing high precision measurements of ranging to the landers Viking-1, Viking-2, and Pathfinder (1976-1997). Modeling of the perturbing accelerations of the major planets accounts for individual contributions of 300 minor planets; the total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Mass M_ring of the ring and its radius R are considered as solve-for parameters. Masses of the 300 perturbing asteroids have been derived from their published radii based mainly on measured fluxes of radiation, making use of the corresponding densities. This set of asteroids is grouped into three classes in accordance with physical properties and then corrections to the mean density for each class are estimated in the process of treating the observations. In this way an improved system of masses of the perturbing asteroids has been derived.The estimate M_ring≈(5±1)×10⁻¹⁰M_⊙ is obtained (M_⊙ is the solar mass) whose value is about one mass of Ceres. For the mean radius of the ring we have R≈2.80 AU with 3% uncertainty. Then the total mass M_belt of the main asteroid belt (including the 300 asteroids mentioned above) may be derived: M_belt≈(18±2)×10⁻¹⁰M_⊙. The value M_belt includes masses of the asteroids which are already discovered, and the total mass of a large number of small asteroids—most of which cannot be observed from the Earth. The second component M_ring is the hidden mass in the asteroid belt as evaluated from its dynamical impact onto the motion of the major planets.Two parameters of a theoretical distribution of the number of asteroids over their masses are evaluated by fitting to the improved set of masses of the 300 asteroids (assuming that there is no observational selection effect in this set). This distribution is extrapolated to the whole interval of asteroid masses and as a result the independent estimate M_belt≈18×10⁻¹⁰M_⊙ is obtained which is in excellent agreement with the dynamical finding given above.These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H. Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H<14 have been discovered (according to the derived distribution, about 130,000 such asteroids are expected to exist).     

A possible rotation period for the minor planet 164 Eva

The minor planet 164 Eva passed through opposition on December 1, 1975 with a magnitude B_opp = 11.3 mag. Photoelectric observations at the Observatory of Torino, Italy, were carried out in two nights on Oct. 27/28 and Nov. 11, each with a run of about 3 hr. Two further successful photoelectric observations were carried out at the OHP, France, each with a run of about 6 hr. From all observed parts of the lightcurve a resulting synodic period of rotation of about 27.3 hr can be deduced, with a range of the total amplitude of at least Δm = 0.07 mag. With this period of 27.3 hr the minor planet 164 Eva is one more long period object, falling now between 654 Zelinda (H. J. Schober, 1975, Astron. Astrophys.44, 85–89) and 139 Juewa (J. Goguen et al., 1976, Icarus29, 137–142), at the high end in the histogram of the distribution of minor planet rotation periods.     

Rotational properties of ten main belt asteroids: Analysis of the results obtained by photoelectric photometry

V photoelectric lightcurves of ten main belt asteroids (11 Partenope, 20 Massalia, 31 Euphrosyne, 41 Daphne, 55 Pandora, 71 Niobe, 79 Eurynome, 129 Antigone, 344 Desiderata, and 387 Aquitania), obtained during the 1981–1983 oppositions, are reported. The rotation period of 11 Partenope is P = 7.83 hr and that of 344 Desiderata P = 10.53 hr. The shape and the pole coordinates of 20 Massalia, 31 Euphrosyne, and 129 Antigone were also derived and those of 41 Daphne confirmed. The lightcurves of the remaining objects are presented: a preliminary discussion of their possible rotational properties and their morphological features is given.     

Lightcurves and phase relations of the asteroids 82 alkmene and 444 Gyptis

The asteroids 82 Alkmene and 444 Gyptis were observed photoelectrically at Table Mountain Observatory and at Torino Observatory during their 1979 oppositions. The rotation periods and amplitudes of variation observed were, for 82: P_syn = 12.^h999, Δm = 0.55; and for 444: P_syn = 6.^h214, Δm = 0.15. The phase relation of 82 Alkmene can be well fit to the theory of K. Lumme and E. Bowell (Astron. J. (1981), 86, 1705). It showed a probable decrease in brightness of ～0.04 mag from 1 month before opposition to 2 months after opposition, which can be attributed to the changing viewing aspect coupled with polar flattering of the asteroid. The phase relation of 444 Gyptis is poorly fit by the Lumme and Bowell theory when only Q and V(0η) are treated as variables. A good fit can be obtained by adjusting some of the other parameters of their theory, but the physical interpretation is ambiguous.     

CCD and photon-counting photometric observations of asteroids carried out at Padova and Catania observatories

We present the results of observational campaigns of asteroids performed at Asiago Station of Padova Astronomical Observatory and at M.G. Fracastoro Station of Catania Astrophysical Observatory, as part of the large research programme on Solar System minor bodies undertaken since 1979 at the Physics and Astronomy Department of Catania University. Photometric observations of six Main-Belt asteroids (27 Euterpe, 173 Ino, 182 Elsa, 539 Pamina, 849 Ara, and 984 Gretia), one Hungaria (1727 Mette), and two Near-Earth Objects (3199 Nefertiti and 2004 UE) are reported. The first determination of the synodic rotational period of 2004 UE was obtained. For 182 Elsa and 1727 Mette the derived synodic period of 80.23±0.08 and , respectively, represents a significant improvement on the previously published values. For 182 Elsa the first determination of the H-G magnitude relation is also presented.     

The Near-Earth Objects Follow-Up Program

We present the results of photometric observations of the near-Earth asteroids (1943) Anteros, (2102) Tantalus, (2212) Hephaistos, (3199) Nefertiti, (5751) Zao = 1992 AC, (6322) 1991 CQ, (7474) 1992 TC, and 1989 VA made between 1982 and 1995. Synodic rotation periods in the range from 2.39 to 5.54 hr were derived for five of them, and we were able to place lower limits on periods of (2212) and (5751)—both > 20 hr. Only the period of the low amplitude case of (1943) was not constrained. The most interesting results were obtained for the following objects: (2102), a fast rotator (period 2.39 hr) in an extremely inclined orbit (i≈ 64°); (2212), a low amplitude slow rotator considered as an inactive cometary nucleus candidate; (3199), which showed similar lightcurves at quite different positions of the phase angle bisector, constraining its rotational pole; and 1989 VA, an unusual Aten asteroid with a rotation period of 2.51 hr and a relatively large amplitude. Overall, these results continue the pattern that NEO spins exhibit a bimodal distribution of spin rates.     

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.     

Secular spin dynamics of inner main-belt asteroids

Understanding the evolution of asteroid spin states is challenging work, in part because asteroids have a variety of orbits, shapes, spin states, and collisional histories but also because they are strongly influenced by gravitational and non-gravitational (YORP) torques. Using efficient numerical models designed to investigate asteroid orbit and spin dynamics, we study here how several individual asteroids have had their spin states modified over time in response to these torques (i.e., 951 Gaspra, 60 Echo, 32 Pomona, 230 Athamantis, 105 Artemis). These test cases which sample semimajor axis and inclination space in the inner main belt, were chosen as probes into the large parameter space described above. The ultimate goal is to use these data to statistically characterize how all asteroids in the main belt population have reached their present-day spin states. We found that the spin dynamics of prograde-rotating asteroids in the inner main belt is generally less regular than that of the retrograde-rotating ones because of numerous overlapping secular spin-orbit resonances. These resonances strongly affect the spin histories of all bodies, while those of small asteroids (?40 km) are additionally influenced by YORP torques. In most cases, gravitational and non-gravitational torques cause asteroid spin axis orientations to vary widely over short (?1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and s₆ spin-orbit resonances. This hinders our ability to investigate its past evolution and infer whether thermal torques have acted on Gaspra's spin axis since its origin.