Numerical Evaluation of the General Yarkovsky Effect: Effects on Eccentricity and Longitude of Periapse

J. N. Spitale and R. Greenberg (2001, Icarus149, 222-234) developed a nonlinearized, finite-difference solution to the heat equation that yields orbital rates of change due to the Yarkovsky effect for small, spherical, bare-rock asteroids and used it to investigate changes in semimajor axis caused by the Yarkovsky effect. Here, we present results for changes in eccentricity and longitude of periapse. These results may be useful as benchmarks for simplified analytical solutions. Moreover, we explore a range of parameters, some of which are inaccessible to most other approaches. Instantaneous rates can be quite fast: For a 1-m scale body rotating with a 5-h period, de/dt can be as fast as 0.1 per million years (da/dt rates for similar test bodies were reported in J. N. Spitale and R. Greenberg (2001, Icarus149, 222-234)). For more typical rotation periods, these rates would be considerably slower. Output from our calculation method could be used in simulations of asteroid population evolution such as that by W. F. Bottke, D. P. Rubincam, and J. A. Burns (2000, Icarus145, 301-331). On long time scales, impacts would randomize the spin axis before significant orbital evolution could occur. Nevertheless, occasional favorable rotation states might persist long enough for substantial eccentricity changes to accumulate (1) if the body is decoupled from the main belt (e.g., many near-Earth asteroids), (2) if the population of very small (mm-scale) main-belt impactors is less than expected, or (3) if our numerical results are scaled up to km-size bodies.     

Constraints to Uranus' Great Collision III: The Origin of the Outer Satellites

The theory of satellite loss resulting from a giant impact on Uranus (Parisi and Brunini 1997, Planet. Space Sci.45, 181-187) is revisited, in the light of the discovery of its five outer moons (Gladman et al. 1998, Nature392, 897-899; Gladman et al. 2000, Icarus147, 320-324; erratum 148, 320). Physical conditions and dynamical constraints in the great collision scenario and restrictions in the possible mechanisms for the origin of the outer uranian satellites are obtained from the knowledge of their actual orbital properties. We conclude that the existence of these moons implies that their origin must be connected to a breakup process. Other scenarios for their origin cast serious doubts on the occurrence of a giant collision at the end of Uranus' formation process to account for its large spin axis obliquity.     

Nature of the small main belt Asteroid 3169 Ostro

We present a set of rotational lightcurve measurements of the small main belt Asteroid 3169 Ostro. Our observations reveal an unambiguous, double-peaked rotational lightcurve with a peak-to-peak variation up to 1.2±0.05 mag and a synodic period of 6.509±0.001 h. From the large flux variation and the overall shape of the lightcurves, we suggest that 3169 Ostro could be a tightly bound binary or a contact binary, similar to the Trojan Asteroid 624 Hektor. A shape model of this system is proposed on the assumption that 3169 Ostro is a Roche binary described by a pair of homogeneous elongated bodies, with a size ratio of 0.87, in hydrostatic equilibrium and in circular synchronous motion around each other. The direction of the spin axis is determined modulo 180° by its J2000 ecliptic coordinates λ₀=50±10°, β₀=±54±5°. The binary interpretation and the pole solution adequately fit the earlier photometric observations made in 1986 and 1988. However, additional supporting lightcurves are highly desirable especially in the next mutual events occurrence of 2008 and 2009 in order to remove the pole ambiguity and to confirm unambiguously the binary nature of 3169 Ostro.     

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.     

Iron(VI) Seems an Unlikely Explanation for Viking Labeled Release Results

Tsapin et al. (2000, Icarus147, 68-78) propose the strong oxidant ferrate(VI) to explain the Viking Labeled Release Mars life detection results. However, their data do not support that theory. Further, sensitive IR searches for oxidants on Mars found none, and Viking produced physical evidence against an oxidizing surface. Finally, Tsapin et al. (2000, Icarus147, 68-78) report no precautions to prevent microbial contamination from confounding their results.     

The proximity of Mercury's spin to Cassini state 1 from adiabatic invariance

In determining Mercury's core structure from its rotational properties, the value of the normalized moment of inertia, C/MR², from the location of Cassini 1 is crucial. If Mercury's spin axis occupies Cassini state 1, its position defines the location of the state, where the axis is fixed in the frame precessing with the orbit. Although tidal and core-mantle dissipation drive the spin to the Cassini state with a time scale O(¹⁰⁵) years, the spin might still be displaced from the Cassini state if the variations in the orbital elements induced by planetary perturbations, which change the position of the Cassini state, cause the spin to lag behind as it attempts to follow the state. After being brought to the state by dissipative processes, the spin axis is expected to follow the Cassini state for orbit variations with time scales long compared to the 1000 year precession period of the spin about the Cassini state because the solid angle swept out by the spin axis as it precesses is an adiabatic invariant. Short period variations in the orbital elements of small amplitude should cause displacements that are commensurate with the amplitudes of the short period terms. The exception would be if there are forcing terms in the perturbations that are nearly resonant with the 1000 year precession period. The precision of the radar and eventual spacecraft measurements of the position of Mercury's spin axis warrants a check on the likely proximity of the spin axis to the Cassini state. How confident should we be that the spin axis position defines the Cassini state sufficiently well for a precise determination of C/MR²? By following simultaneously the spin position and the Cassini state position during long time scale orbital variations over past 3 million years [Quinn, T.R., Tremaine, S., Duncan, M., 1991. Astron. J. 101, 2287-2305] and short time scale variations for 20,000 years [JPL Ephemeris DE 408; Standish, E.M., private communication, 2005], we show that the spin axis will remain within one arcsec of the Cassini state after it is brought there by dissipative torques. In this process the spin is located in the orbit frame of reference, which in turn is referenced to the inertial ecliptic plane of J2000. There are no perturbations with periods resonant with the precession period that could cause large separations. We thus expect Mercury's spin to occupy Cassini state 1 well within the uncertainties for both radar and spacecraft measurements, with correspondingly tight constraints on C/MR² and the extent of Mercury's molten core. Two unlikely caveats for this conclusion are: (1) an excitation of a free spin precession by an unknown mechanism or (2) a displacement by a dissipative core mantle interaction that exceeds the measurement uncertainties.     

An Evolutionary Turbulent Model of Saturn's Subnebula: Implications for the Origin of the Atmosphere of Titan

We have elaborated an evolutionary turbulent model of the subnebula of Saturn derived from that of Dubrulle (1993, Icarus106, 59-76) for the solar nebula, which is valid for a geometrically thin disk. We demonstrate that if carbon and nitrogen were in the form of CO and N₂, respectively, in the early subnebula, these molecules were not subsequently converted into CH₄ and NH₃ during the evolution of the disk, contrary to the current scenario initially proposed by Prinn and Fegley (1981, Astrophys. J., 249, 308-317). However, if the early subnebula contained some CH₄ and NH₃, these gases were not subsequently converted into CO and N₂. We argue that Titan must have been formed from planetesimals migrating from the outer part of the subnebula to the present orbit of the satellite. These planetesimals were relics of those embedded in the feeding zone of Saturn prior to the completion of the planet and contained hydrates of NH₃ and clathrate hydrates of CH₄. It is shown that, for plausible abundances of CH₄ and NH₃ in the solar nebula at 10 AU, the masses of methane and nitrogen trapped in Titan were higher than the estimate of masses of these components in the primitive atmosphere of the satellite. If our scenario is valid and if our turbulent model properly describes the structure and the evolution of the actual subnebula of Saturn, the Xe/C ratio should be six times higher in Titan's atmosphere today than in the Sun, while the current scenario would probably result in a quasi solar Xe/C ratio. The mass spectrometer and gas chromatograph instrument aboard the Huygens Titan probe of the Cassini mission has the capability of measuring this ratio in 2004, thus permitting us to discriminate between the current scenario and the one proposed in this report.     

Moonlet Collisions and the Effects of Tidally Modified Accretion in Saturn's F Ring

We both test and offer an alternative to a meteoroid bombardment model (M. R. Showalter 1998, Science282, 1099-1102) and suggest that anomalous localized brightenings in the F ring observed by Voyager result from disruptive collisions involving poorly consolidated moonlets, or “rubble piles.” This model can also explain the transient events observed during ring plane crossing. We have developed an evolutionary model that considers both the competing effects of accretion and disruption at the location of the F ring. Our numerical model is a Markov process where probabilities of mass transfer between the states of the system form a “transition matrix.” Successive multiplications of this matrix by the state vector generate expectation values of the distribution after each time step as the system approaches quasi-equilibrium. Competing effects of accretion and disruption in the F ring are found to lead to a bimodal distribution of ring particle sizes. In fact, our simulation predicts the presence of a belt of kilometer-sized moonlets in the F ring. These moonlets may continually disrupt one another and re-accrete on short time scales. We also agree with J. N. Cuzzi and J. A. Burns (1988, Icarus74, 284-324), who suggest that the classical F ring itself may be the consequence of a relatively recent collision between two of the largest of these yet unseen objects. Cassini observations can confirm the existence of the moonlet belt by directly observing these objects or the waves they create in the rings.     

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.     

Carbon Monoxide on Jupiter: Evidence for Both Internal and External Sources

Thirteen lines of the CO band near 4.7 μm have been observed on a jovian hot spot at a resolution of 0.045 cm⁻¹. The measured line profiles indicate that the CO mole fraction is 1.0±0.2 ppb around the 6-bar level and is larger in the upper troposphere and/or stratosphere. An external source of CO providing an abundance of 4⁺³₋₂×10¹⁶ molecules cm⁻² is implied by the observations in addition to the amount deposited at high altitude by the Shoemaker-Levy 9 collision. From a simple diffusion model, we estimate that the CO production rate is (1.5-10)×10⁶ molecules cm⁻² s⁻¹ assuming an eddy diffusion coefficient around the tropopause between 300 and 1500 cm² s⁻¹. Precipitation of oxygen atoms from the jovian magnetosphere or photochemistry of water vapor from meteoroidal material can only provide a negligible contribution to this amount. A significant fraction of the CO in Jupiter's upper atmosphere may be formed by shock chemistry due to the infall of kilometer- to subkilometer-size Jupiter family comets. Using the impact rate from Levison et al. (2000, Icarus143, 415-420) rescaled by Bottke et al. (2002, Icarus156, 399-433), this source can provide the observed stratospheric CO only if the eddy diffusion coefficient around the tropopause is 100-300 cm² s⁻¹. Higher values, ∼700 cm² s⁻¹, would require an impact rate larger by a factor of 5-10, which cannot be excluded considering uncertainties in the distribution of Jupiter family comets. Such a large rate is indeed consistent with the observed cratering record of the Galilean satellites (Zahnle et al. 1998, Icarus136, 202-222). On the other hand, the ∼1 ppb concentration in the lower troposphere requires an internal source. Revisiting the disequilibrium chemistry of CO in Jupiter, we conclude that rapid vertical mixing can provide the required amount of CO at ∼6 bar for a global oxygen abundance of 0.2-9 times the solar value considering the uncertainties in the convective mixing rate and in the chemical constants.     

The rotation of small asteroids

The addition of the unbiased sample of R. P. Binzel and J. D. Mulholland (Icarus56, 519–533) nearly triples the sample size of photoelectrically determined rotational parameters for main belt asteroids with estimated diameters (D) ≤30 km. Nonparametric stattistical tests which require no assumptions about the distributions or variances of the samples are used to examine rotational parameters for all D ≤ 30 km asteroids. A comparison of photoelectric and photographic results shows that the techniques have a highly significant difference in the range of detected frequencies. This difference does not allow photographic and photoelectric observations to be combined for meaningful statistical tests since a photographic bias toward smaller sample variances can induce statistical results that appear overly significant. Photographic observations also show a highly significant bias toward detecting asteroids with larger lightcurve amplitudes. The fit of a Maxwellian to the observed rotational frequency distribution can be rejected at a highly significant confidence level but the observed distribution can be acceptably fit by two Maxwellian distributions, which is consistent with the hypothesis that there are separate populations of slow and fast rotating asteroids. The frequency distributions of <15 km main belt asteroids and Earth and Mars crossers are not found to differ significantly. However, the larger mean lightcurve amplitude of the Earth and Mars crossing asteroids is found to be statistically significant. This latter result is interesting in view of the lack of any strong inverse amplitude versus diameter relation for small asteroids. No significant diameter dependence on rotational frequency is seen among only D ≤ 30 km asteroids. However, the inverse frequency versus diameter relation for D ≤ 120 km asteroids found by S. F. Dermott, A. W. Harris, and C. D. Murray (Icarus, in press) is found to be statistically significant using a linear least-squares analysis of photoelectric data only. No significant diameter dependence on rotational lightcurve amplitude is seen using linear least-squares analysis of photoelectric data for D≤30 and D≤90 km asteroids. However, a significant inverse amplitude versus diameter relation is found when this analysis is extended to D≤120 km asteroids. This finding may be consistent with the hypothesis of Dermott et al. that near 120 km there is a transition between primordial asteroids and their collisional fragments.     

Comparison between the Shkuratov and Hapke Scattering Theories for Solid Planetary Surfaces: Application to the Surface Composition of Two Centaurs

This project examines the different approaches which deal with the theory of radiative transfer on atmosphereless bodies. We present the relative merits of two scattering theories based on the equivalent slab model: the extensively used Hapke theory (Hapke 1981, J. Geophys. Res.86, 3039-3054) and the Shkuratov theory (Shkuratov et al. 1999, Icarus141, 132-155). We found that their main difference is the role of the phase function of individual particles of regolith, which is predicted (and generally forward directed) in the case of the Shkuratov model instead of being a free parameter as formulated in the Hapke model. We also emphasize that different assumptions as to the manner in which different constituents are physically mixed in either model have a substantial effect on the synthetic spectra inferred. This leads to a significant extension of the validity of Hapke's or similar practical approaches to areas where these approaches are valid.We used two objects (the Centaurs 5145 Pholus and 8405 Asbolus) as examples. Previous modeling of the spectra of these two bodies with the Hapke approach gave suspect results in terms of the derived grain sizes, which were smaller than the wavelength, violating key assumptions of the model (Cruikshank et al. 1998, Icarus135, 389-407 for Pholus; Barucci et al. 2000, Astron. Astrophys.357, L53-56 for Asbolus). We considered several different types of powdered surfaces to interpret the surface composition of these two Centaurs. The effect of fine-scale contamination of water ice grains by small amounts of carbon and/or tholins is also explored. We can explain the strong red color and the rich near-infrared spectral signatures of Pholus using a five-component surface (contaminated water ice, amorphous carbon, Titan tholin, olivine, and methanol ice) where the grain sizes are consistent with the model assumptions. These components are similar to those inferred by Cruikshank et al. (1998), but we obtain very different grain sizes and relative abundances. For example, we obtain a relative abundance of water ice on the surface of Pholus of about 40% instead of 6% found with the Hapke model. Organic and carbonaceous components change by similar amounts. In the case of Asbolus, a tholin and amorphous carbon areal mixture can reproduce the spectrum, with water remaining at 9% or less. Using the albedo published by Fernandez et al. (2002, Astron. J.123, 1050-1055) which is higher than most workers assume for Centaurs and Kuiper belt objects, a surface composition similar to that of Pholus is found. It appears that model-based uncertainties in relative compositions must be regarded with more attention.     

Evolution of Planetesimal Velocities Based on Three-Body Orbital Integrations and Growth of Protoplanets

We obtain the viscous stirring and dynamical friction rates of planetesimals with a Rayleigh distribution of eccentricities and inclinations, using three-body orbital integration and the procedure described by Ohtsuki (1999, Icarus137, 152), who evaluated these rates for ring particles. We find that these rates based on orbital integrations agree quite well with the analytic results of Stewart and Ida (2000, Icarus 143, 28) in high-velocity cases. In low-velocity cases where Kepler shear dominates the relative velocity, however, the three-body calculations show significant deviation from the formulas of Stewart and Ida, who did not investigate the rates for low velocities in detail but just presented a simple interpolation formula between their high-velocity formula and the numerical results for circular orbits. We calculate evolution of root mean square eccentricities and inclinations using the above stirring rates based on orbital integrations, and find excellent agreement with N-body simulations for both one- and two-component systems, even in the low-velocity cases. We derive semi-analytic formulas for the stirring and dynamical friction rates based on our numerical results, and confirm that they reproduce the results of N-body simulations with sufficient accuracy. Using these formulas, we calculate equilibrium velocities of planetesimals with given size distributions. At a stage before the onset of runaway growth of large bodies, the velocity distribution calculated by our new formulas are found to agree quite well with those obtained by using the formulas of Stewart and Ida or Wetherill and Stewart (1993, Icarus106, 190). However, at later stages, we find that the inclinations of small collisional fragments calculated by our new formulas can be much smaller than those calculated by the previously obtained formulas, so that they are more easily accreted by larger bodies in our case. The results essentially support the previous results such as runaway growth of protoplanets, but they could enhance their growth rate by 10-30% after early runaway growth, where those fragments with low random velocities can significantly contribute to rapid growth of runaway bodies.     

2 Pallas: 1982 and 3 lightcurves and a new pole solution

Photoelectric lightcurves of asteroid 2 Pallas obtained in March 1982 and May 1983 display amplitudes of 0.04 and 0.10 magnitude respectively. The latter lightcurve shows that Pallas was at a V(1,0) magnitude of 4.51 ± 0.02 when it occulted 1 Vulpeculae on May 29 1983. A least-squares best fit to an amplitude-aspect relation for all available lightcurve observations of Pallas between 1951 and 1983 yields two solutions for its pole position: λ = 200, β = 40 and λ = 220, β = 15, where the uncertainty regions corresponds to an overall estimate of ± degrees. Use of phase angle bisector coordinates (A. W. Harris, J. W. Young, F. Scaltriti, and V. Zappalà (1984) Icarus57, 251–258) gave lower residuals than geocentric coordinates. The (220,15) pole position is favored since it is in very good agreement with an independent pole solution obtained by photometric astrometry (J. V. Lambert 1983 personal communication). This pole position implies that the latitude of the sub-Earth point at the time of the occultation was 22 degrees.     

The Existence of a Planet beyond 50 AU and the Orbital Distribution of the Classical Edgeworth-Kuiper-Belt Objects

We study the effects of a Mars-like planetoid with a semimajor axis at about ∼60 AU orbiting embedded in the primordial Edgeworth-Kuiper belt (EKB). The origin of such an object can be explained in the framework of our current understanding of the origin of the outer Solar System, and a scenario for the orbital transport mechanism to its present location is given. The existence of such an object would produce a gap in the EKB distribution with an edge at about 50 AU, which seems to be in agreement with the most recent observations. No object at low eccentricity with semimajor axis beyond 50 AU has been detected so far, even though the present observing capabilities would allow an eventual detection (B. Gladman et al. 1998, Astron. J.116, 2042-2054; D. Jewitt et al. 1998, Astron. J.115, 2125-2135; E. I. Chiang and M. E. Brown 1999, Astron. J.118, 1411-1422; R. L. Allen et al. 2000, Astrophys. J.549, 241-244; C. A. Trujillo et al. 2001, Astron. J.122, 457-473; B. Gladman et al. 2001, Astron. J.122, 1051-1066; C. A. Trujillo and M. E. Brown 2001, Astrophys. J.554, 95-98). Finally, ranges for the magnitude and proper motion of the proposed object are given.     

Long- and Short-Term Photometric Behavior of Comet Hyakutake (1996 B2)

Narrowband filter photometry observations of Comet Hyakutake (1996 B2) were used to investigate this comet's short-term variability as well as its behavior for the apparition as a whole. Utilizing measurements obtained on a total of 13 nights between February 9, 1996, and April 14, 1996, we find that the heliocentric distance (r_H) dependence of the production rates of OH and NH were much shallower than those for either the carbon-bearing species or the visible dust. Based on the OH measurements, the derived water r_H-dependence was also significantly less steep than expected from a basic water vaporization model and required an effective active surface area of about 29 km² at r_H=1.8 AU, 16 km² at r_H=1 AU, and only 13 km² at r_H=0.6 AU. This decrease in active area may be due to seasonally induced variations of a heterogeneous surface, or due to a decreasing contribution of gas from icy grains in the innermost coma. The relative abundances of the minor gas species place Hyakutake into the “typical” category of comets in the A'Hearn et al. (1995, Icarus118, 223-270) taxonomic classification system. The spectrum is generally redder at shorter wavelengths throughout the apparition; however, the dust color progressively changes from being significantly reddened (37%/1000 Å) at large r_H to near-solar at small r_H. This change of color with distance implies a significant change in grain sizes or a changing proportion between two or more grain populations.A major outburst was initiated near March 19.9, just prior to the comet's close approach to Earth. The characteristic recovery from the outburst differed among the observed species, with OH recovering most rapidly, essentially returning to its baseline values by March 25. The spatial radial fall-off of OH throughout this interval was consistent with the expected nominal spatial distribution, while CN and C₂ displayed fall-offs consistent with a distributed source, and the dust fall-off was significantly less steep than 1/ρ, possibly due to fragmenting grains. Rotational lightcurve amplitudes were largest for the OH, NH, and dust, again consistent with the carbon-bearing species primarily originating from a distributed source. Significant variations were observed in the lightcurve amplitude and phase shifts as functions of aperture size. Finally, a refined value for the rotation period of 0.2614±0.0003 day was determined.     

The free precession and libration of Mercury

An analysis based on the direct torque equations including tidal dissipation and a viscous core-mantle coupling is used to determine the damping time scales of O(¹⁰⁵) years for free precession of the spin about the Cassini state and free libration in longitude for Mercury. The core-mantle coupling dominates the damping over the tides by one to two orders of magnitude for the plausible parameters chosen. The short damping times compared with the age of the Solar System means we must find recent or on-going excitation mechanisms if such free motions are found by the current radar experiments or the future measurement by the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show that the average precession rate is increased by about 30% over that obtained from the traditional precession constant because of a spin-orbit resonance induced contribution by the C₂₂ term in the expansion of the gravitational field. The C₂₂ contribution also causes the path of the spin during the precession to be slightly elliptical with a variation in the precession rate that is a maximum when the obliquity is a minimum. An observable free precession will compromise the determination of obliquity of the Cassini state and hence of C/MMR² for Mercury, but a detected free libration will not compromise the determination of the forced libration amplitude and thus the verification of a liquid core.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

Photometric observations of 107P/Wilson-Harrington

We present lightcurve observations and multiband photometry for 107P/Wilson-Harrington using five small- and medium-sized telescopes. The lightcurve has shown a periodicity of 0.2979 day (7.15 h) and 0.0993 day (2.38 h), which has a commensurability of 3:1. The physical properties of the lightcurve indicate two models: (1) 107P/Wilson-Harrington is a tumbling object with a sidereal rotation period of 0.2979 day and a precession period of 0.0993 day. The shape has a long axis mode (LAM) of L₁:L₂:L₃ = 1.0:1.0:1.6. The direction of the total rotational angular momentum is around λ = 310°, β = −10°, or λ = 132°, β = −17°. The nutation angle is approximately constant at 65°. (2) 107P/Wilson-Harrington is not a tumbler. The sidereal rotation period is 0.2979 day. The shape is nearly spherical but slightly hexagonal with a short axis mode (SAM) of L₁:L₂:L₃ = 1.5:1.5:1.0. The pole orientation is around λ = 330°, β = −27°. In addition, the model includes the possibility of binary hosting. For both models, the sense of rotation is retrograde. Furthermore, multiband photometry indicates that the taxonomy class of 107P/Wilson-Harrington is C-type. No clear rotational color variations are confirmed on the surface.