Predictions for eclipses of Nereid by Neptune

Neptune will eclipse its satellite Nereid (Neptune II) on 2007 April 27 from 00 to 06 h UT and on 2008 April 21 from 12 to 17 h UT, with uncertainties of about 3 h; and a third eclipse may occur on 2009 April 17. These events offer unique opportunities for astrometric and geophysical measurement.     

BVR photometry of Hyperion near the time of the 2005 Cassini encounter

Six nights of BVR photometry and three nights of R photometry were collected over a month-long period shortly after the Cassini encounter with Hyperion on September 24 2005. Our observations were designed to help constrain the rotational state of the chaotically rotating satellite. Fourier analysis of our lightcurve data yields three possible periods: 10.2±0.2, 13.9±0.2, and 19.7±0.4 days. Our B-V and V-R colors agree well with previous ground-based and Voyager 2 measurements.     

The phase curve survey of the irregular saturnian satellites: A possible method of physical classification

During its 2005 January opposition, the saturnian system could be viewed at an unusually low phase angle. We surveyed a subset of Saturn's irregular satellites to obtain their true opposition magnitudes, or nearly so, down to phase angle values of 0.01°. Combining our data taken at the Palomar 200-inch and Cerro Tololo Inter-American Observatory's 4-m Blanco telescope with those in the literature, we present the first phase curves for nearly half the irregular satellites originally reported by Gladman et al. [2001. Nature 412, 163-166], including Paaliaq (SXX), Siarnaq (SXXIX), Tarvos (SXXI), Ijiraq (SXXII), Albiorix (SXVI), and additionally Phoebe's narrowest angle brightness measured to date. We find centaur-like steepness in the phase curves or opposition surges in most cases with the notable exception of three, Albiorix and Tarvos, which are suspected to be of similar origin based on dynamical arguments, and Siarnaq.     

Orbital resonances in the inner neptunian system: I. The 2:1 Proteus-Larissa mean-motion resonance

We investigate the orbital resonant history of Proteus and Larissa, the two largest inner neptunian satellites discovered by Voyager 2. Due to tidal migration, these two satellites probably passed through their 2:1 mean-motion resonance a few hundred million years ago. We explore this resonance passage as a method to excite orbital eccentricities and inclinations, and find interesting constraints on the satellites' mean density () and their tidal dissipation parameters (Qs>10). Through numerical study of this mean-motion resonance passage, we identify a new type of three-body resonance between the satellite pair and Triton. These new resonances occur near the traditional two-body resonances between the small satellites and, surprisingly, are much stronger than their two-body counterparts due to Triton's large mass and orbital inclination. We determine the relevant resonant arguments and derive a mathematical framework for analyzing resonances in this special system.     

Orbital resonances in the inner neptunian system: II. Resonant history of Proteus, Larissa, Galatea, and Despina

We investigate the orbital history of the small neptunian satellites discovered by Voyager 2. Over the age of the Solar System, tidal forces have caused the satellites to migrate radially, bringing them through mean-motion resonances with one another. In this paper, we extend our study of the largest satellites Proteus and Larissa [Zhang, K., Hamilton, D.P., 2007. Icarus 188, 386-399] by adding in mid-sized Galatea and Despina. We test the hypothesis that these moons all formed with zero inclinations, and that orbital resonances excited their tilts during tidal migration. We find that the current orbital inclinations of Proteus, Galatea, and Despina are consistent with resonant excitation if they have a common density . Larissa's inclination, however, is too large to have been caused by resonant kicks between these four satellites; we suggest that a prior resonant capture event involving either Naiad or Thalassa is responsible. Our solution requires at least three past resonances with Proteus, which helps constrain the tidal migration timescale and thus Neptune's tidal quality factor: 9000<QN<36,000. We also improve our determination of Qs for Proteus and Larissa, finding 36<QP<700 and 18<QL<200. Finally, we derive a more general resonant capture condition, and work out a resonant overlap criterion relevant to satellite orbital evolution around an oblate primary.     

Neptune’s cloud and haze variations 1994-2008 from 500 HST-WFPC2 images

The analysis of all suitable images taken of Neptune with the Wide Field Planetary Camera 2 on the Hubble Space Telescope between 1994 and 2008 revealed the following results. The activity of discrete cloud features located near Neptune’s tropopause remained roughly constant within each year but changed significantly on the time scale of ∼5 years. Discrete clouds covered 1% of the disk on average, but more than 2% in 2002. The other ∼99% of the disk probed Neptune’s hazes at lower altitudes. At red and near-infrared wavelengths, two dark bands around −70° and 10° latitude were perfectly steady and originated in the upper two scale heights of the troposphere, either by decreased haze opacity or by an increased methane relative humidity. At blue wavelengths, a dark band between −60° and −30° latitude was most obvious during the early years, caused by dark aerosols below the 3-bar level with single scattering albedos reduced by ∼0.04, and this contrast was constant between 410 and 630 nm wavelength. The dark band decayed exponentially with a time constant of 5 ± 1 years, which can be explained by settling of the dark aerosols at a rate of 1 bar pressure difference per year. The other latitudes brightened with the same time constant but lower amplitudes. The only exception was a darkening event in the 15-30° latitude region between 1994 and 1996, which coincides with two dark spots observed in the same region during the same time period, the only dark spots seen since Voyager. The dark aerosols had a similar latitudinal distribution as the discrete clouds near the tropopause, although both were separated by four scale heights. Photometric analysis revealed a phase coefficient of 0.0028 ± 0.0010 mag/deg for the 0-2° phase-angle range observable from Earth. Neptune’s sub-Earth latitude varied by less than 3° throughout the observation period providing a data set with almost constant viewing geometry. The trends observed up to 2008 continued into 2010 based on images taken with the Wide Field Camera 3.     

The nature of Neptune’s increasing brightness: evidence for a seasonal response

Hubble Space Telescope (HST) observations in August 2002 show that Neptune’s disk-averaged reflectivity increased significantly since 1996, by 3.2 ± 0.3% at 467 nm, 5.6 ± 0.6% at 673 nm, and 40 ± 4% in the 850-1000 nm band, which mainly results from dramatic brightness increases in restricted latitude bands. When 467-nm HST observations from 1994 to 2002 are added to the 472-nm ground-based results of Lockwood and Thompson (2002, Icarus 56, 37-51), the combined disk-averaged variation from 1972 to 2002 is consistent with a simple seasonal model having a hemispheric response delay relative to solar forcing of ∼30 years (∼73% of a full season).     

Near-infrared spectral monitoring of Triton with IRTF/SpeX II: Spatial distribution and evolution of ices

This report arises from an ongoing program to monitor Neptune’s largest moon Triton spectroscopically in the 0.8 to 2.4 μm range using IRTF/SpeX. Our objective is to search for changes on Triton’s surface as witnessed by changes in the infrared absorption bands of its surface ices N₂,CH₄,H₂O, CO, and CO₂. We have recorded infrared spectra of Triton on 53 nights over the ten apparitions from 2000 to 2009. The data generally confirm our previously reported diurnal spectral variations of the ice absorption bands (Grundy and Young, 2004). Nitrogen ice shows a large amplitude variation, with much stronger absorption on Triton’s Neptune-facing hemisphere. We present evidence for seasonal evolution of Triton’s N₂ ice: the 2.15 μm absorption band appears to be diminishing, especially on the Neptune-facing hemisphere. Although it is mostly dissolved in N₂ ice, Triton’s CH₄ ice shows a very different longitudinal variation from the N₂ ice, challenging assumptions of how the two ices behave. Unlike Triton’s CH₄ ice, the CO ice does exhibit longitudinal variation very similar to the N₂ ice, implying that CO and N₂ condense and sublimate together, maintaining a consistent mixing ratio. Absorptions by H₂O and CO₂ ices show negligible variation as Triton rotates, implying very uniform and/or high latitude spatial distributions for those two non-volatile ices.     

Expression of Cassini's third law for Callisto, and theory of its rotation

The rotation of the main natural satellites of the Solar System is widely assumed to be synchronous, because this corresponds to an equilibrium state. In the case of the Moon, 3 laws have been formulated by Cassini, assuming a spin-orbit resonance and a 1:1 nodal resonance. The recent gravitational data collected by the spacecrafts Galileo (in the jovian system) and Cassini (in the saturnian system) allows us to study the rotation of other natural satellites, and to check the universality of Cassini's laws. This paper deals with the rotation of the Galilean satellites of Jupiter J-4 Callisto. In this study we use both analytical (like Lie transforms) and numerical methods (numerical detection of chaos, numerical integration, frequency analysis) to first check the reliability of Cassini Laws for Callisto, and then to give a first theory of its rotation, Callisto's being considered as a rigid body. We first show that the Third Cassini Law (i.e. the nodal resonance), is not satisfied in every reference frame, in particular in the most natural one (i.e. the J2000 jovian equator). The difference of the nodes presents a chaotic-like behavior, that we prove to be just a geometrical illusion. Moreover, we give a mathematical condition ruling the choice of an inertial reference frame in which the Third Cassini Law is fulfilled. Secondly, we give a theory of Callisto's rotation in the International Celestial Reference Frame (ICRF). We highlight a small motion (i.e. <200 m) of its rotation axis about its body figure, a 11.86-yr periodicity in Callisto's length-of-day, and the proximity of a resonance that forces 182-yr librations in Callisto's obliquity.     

Generalized YORP evolution: Onset of tumbling and new asymptotic states

Asteroids have a wide range of rotation states. While the majority spin a few times to several times each day in principal axis rotation, a small number spin so slowly that they have somehow managed to enter into a tumbling rotation state. Here we investigate whether the Yarkovsky-Radzievskii-O'Keefe-Paddack (YORP) thermal radiation effect could have produced these unusual spin states. To do this, we developed a Lie-Poisson integrator of the orbital and rotational motion of a model asteroid. Solar torques, YORP, and internal energy dissipation were included in our model. Using this code, we found that YORP can no longer drive the spin rates of bodies toward values infinitely close to zero. Instead, bodies losing too much rotation angular momentum fall into chaotic tumbling rotation states where the spin axis wanders randomly for some interval of time. Eventually, our model asteroids reach rotation states that approach regular motion of the spin axis in the body frame. An analytical model designed to describe this behavior does a good job of predicting how and when the onset of tumbling motion should take place. The question of whether a given asteroid will fall into a tumbling rotation state depends on the efficiency of its internal energy dissipation and on the precise way YORP modifies the spin rates of small bodies.     

The interior structure of Mercury and its core sulfur content

Depth-dependent interior structure models of Mercury are calculated for several plausible chemical compositions of the core and of the mantle. For those models, we compute the associated libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential. In particular we study the relation between the interior structure parameters for five different mantle mineralogies and two different temperature profiles together with two extreme crust density values. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner and outer core size. We show that a sulfur concentration above 10 wt% is unlikely if the temperature at the core-mantle boundary is above 1850 K and the silicate shell at least 240 km thick. The interior models can only have an inner core if the sulfur weight fraction is below 5 wt% for core-mantle boundary temperature in the 1850-2200 K range. Within our modeling hypotheses, we show that with the expected precision on the moment of inertia the core size can be estimated to a precision of about 50 km and the core sulfur concentration with an error of about 2 wt%. This uncertainty can only be reduced when more information on the mantle mineralogy of Mercury becomes available. However, we show that the uncertainty on the core size estimation can be greatly reduced, to about 25 km, if tidal surface displacements and tidal variations in the external potential are considered.     

Jupiter's polar clouds and waves from Cassini and HST images: 1993-2006

For a variety of reasons, Jupiter's polar areas are probably the less observed regions of the planet. To study the dynamics and cloud vertical structure in the polar regions of the planet (latitudes 50° to 80° in both hemispheres) we have used images of Jupiter obtained from the ultraviolet to near infrared (258 to 939 nm) by the Cassini Imagining Science Subsystem (ISS) in December 2000. The temporal coverage was complemented with archived images from the Hubble Space Telescope (1993-2006) in a similar spectral range. The zonal wind velocities have been measured at three Cassini ISS wavelengths (CB2, MT3 and UV1, corresponding to 750, 890 and 258 nm) sounding different altitude levels. The three eastward jets detected in CB2 images (lower cloud) go to zero velocity when measured in the UV1 filter (upper haze). A radiative transfer analysis has been performed to characterize the vertical structure of cloud and hazes distribution at the poles. We also present a characterization (phase speed, amplitude and zonal wavenumber) of the previously detected circumpolar waves at 67° N and S at 890 nm and at about 50° N and −57° S at 258 nm that are a permanent phenomenon in Jupiter with some variability in its structure during the analyzed period. From the ensemble of data analyzed we propose the waves are Rossby waves whose dynamic behavior constrains plausible values for their meridional and vertical wavenumbers. This work demonstrates the long-term nature of Jupiter's polar waves, providing a dynamical and vertical characterization which supports a detailed analysis of these phenomena in terms of a Rossby wave model.     

Astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn

We describe the astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn discovered in images obtained using the Imaging Science Subsystem (ISS) of the Cassini spacecraft. Included are details of 63 observations, of which 28 were obtained with Cassini's narrow-angle camera (NAC) and 35 using its wide-angle camera (WAC), covering an observation time-span of approximately 3 years. We estimate the diameter of Anthe to be ∼1.8 km. Orbit modeling based on a numerical integration of the full equations of motion fitted to the observations show that Anthe is in a first-order 11:10 mean motion resonance with Mimas. Two resonant arguments are librating: ?₁=11λ^′−10λ−? and ?₂=11λ^′−10λ−?^′−Ω^′+Ω, where λ, ? and Ω refer to the mean longitude, longitude of pericenter and longitude of ascending node of Mimas and Anthe, with the primed quantities corresponding to Anthe. These resonances cause periodic variations in the orbital elements. The semi-major axis varies by ±26 km over a 913-day period. Anthe is also close to a second-order eccentricity-type mean motion resonant relationship of the form 77:75 with Methone. Since Methone is also in a first-order resonance with Mimas [Spitale, J.N., Jacobson, R.A., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 692-710], an additional indirect perturbation exists between Methone and Anthe via Mimas. Neither effect is detectable in the orbit fitting and the short-term dynamical evolution of Anthe is dominated by the Mimas-Anthe resonances alone. The expected modulation effect from the Mimas-Tethys 4:2 inclination resonance is also insignificant over this time period. By including Cassini ISS observations of Mimas in the numerical integration fit, we estimate the GM of Mimas to be , consistent with Jacobson et al. [Jacobson, R.A., Spitale, J., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 711-713].     

Deep Impact's target Comet 9P/Tempel 1 at multiple apparitions: Seasonal and secular variations in gas and dust production

We present results from multi-apparition narrowband photometry of Deep Impact target Comet 9P/Tempel 1. In support of the mission, we obtained data during monthly observing runs between March and September 2005, and these are combined with and compared to observations obtained during the 1983 and 1994 apparitions. A strong seasonal effect is seen, with peak production rates occurring 4-8 weeks before perihelion, with some variation evident among the different species. There is also evidence of a slight systematic shift towards a later time of peak production in 2005 as compared to 1983. Early in the apparition, the radial profile of the dust was much steeper than the canonical 1/ρ, but the slope became progressively smaller until very little departure from 1/ρ remained by late June, a change possibly associated with the general seasonal effects. Unexpectedly, an unprecedented large overall decrease in production rates has taken place since 1983, with water at only about 42% of the 1983 values, CN at about 53%, and dust, based on the proxy A(θ)fρ, at about 77%. Other gas species exhibited declines intermediate between that of CN and of the dust. The large differences in the amount of secular decline among all of the species implies compositional inhomogeneities among source regions on the surface of the nucleus, with one region progressively becoming less active over only a few orbits. While the simplest explanation would invoke either devolatilization or covering up of the ice, no other comet has shown such a rapid change in outgassing unless accompanied by a significant change in its orbit. We, therefore, hypothesize that a change in available solar radiation due to precession of the pole might instead be causing the progressive drop in cometary activity. Given the small obliquity of the rotation axis derived from the Deep Impact observations, and a presumed small rate of precession, the source region would need to be located near the pole to explain both the large secular and seasonal trends.     

Revised vertical cloud structure of Uranus from UKIRT/UIST observations and changes seen during Uranus’ Northern Spring Equinox from 2006 to 2008: Application of new methane absorption data and comparison with Neptune

Long-slit spectroscopy observations of Uranus by the United Kingdom InfraRed Telescope UIST instrument in 2006, 2007 and 2008 have been used to monitor the change in Uranus’ vertical and latitudinal cloud structure through the planet’s Northern Spring Equinox in December 2007.These spectra were analysed and presented by Irwin et al. (Irwin, P.G.J., Teanby, N.A., Davis, G.R. [2009]. Icarus 203, 287-302), but since publication, a new set of methane absorption data has become available (Karkoschka, E., Tomasko, M. [2010]. Methane absorption coefficients for the jovian planets from laboratory, Huygens, and HST data. Icarus 205, 674-694.), which appears to be more reliable at the cold temperatures and high pressures of Uranus’ deep atmosphere. We have fitted k-coefficients to these new methane absorption data and we find that although the latitudinal variation and inter-annual changes reported by Irwin et al. (2009) stand, the new k-data place the main cloud deck at lower pressures (2-3 bars) than derived previously in the H-band of ∼3-4 bars and ∼3 bars compared with ∼6 bars in the J-band. Indeed, we find that using the new k-data it is possible to reproduce satisfactorily the entire observed centre-of-disc Uranus spectrum from 1 to 1.75 μm with a single cloud at 2-3 bars provided that we make the particles more back-scattering at wavelengths less than 1.2 μm by, for example, increasing the assumed single-scattering albedo from 0.75 (assumed in the J and H-bands) to near 1.0. In addition, we find that using a deep methane mole fraction of 4% in combination with the associated warm ‘F’ temperature profile of Lindal et al. (Lindal, G.F., Lyons, J.R., Sweetnam, D.N., Eshleman, V.R., Hinson, D.P. [1987]. J. Geophys. Res. 92, 14987-15001), the retrieved cloud deck using the new (Karkoschka and Tomasko, 2010) methane absorption data moves to between 1 and 2 bars.The same methane absorption data and retrieval algorithm were applied to observations of Neptune made during the same programme and we find that we can again fit the entire 1-1.75 μm centre-of-disc spectrum with a single cloud model, providing that we make the stratospheric haze particles (of much greater opacity than for Uranus) conservatively scattering (i.e. ω = 1) and we also make the deeper cloud particles, again at around the 2 bar level more reflective for wavelengths less than 1.2 μm. Hence, apart from the increased opacity of stratospheric hazes in Neptune’s atmosphere, the deeper cloud structure and cloud composition of Uranus and Neptune would appear to be very similar.     

Photometry of pluto in the last decade and before: evidence for volatile transport?

Photometric observations of Pluto in the BVR filter system were obtained in 1999 and in 1990-1993, and observations in the 0.89-μm methane absorption band were obtained in 2000. Our 1999 observations yield lightcurve amplitudes of 0.30 ± 0.01, 0.26 ± 0.01, and 0.21 ± 0.02 and geometric albedos of 0.44 ± 0.04, 0.52 ± 0.03, and 0.58 ± 0.02 in the B, V, and R filters, respectively. The low-albedo hemisphere of Pluto is slightly redder than the higher albedo hemisphere. A comparison of our results and those from previous epochs shows that the lightcurve of Pluto changes substantially through time. We developed a model that fully accounts for changes in the lightcurve caused by changes in the viewing geometry between the Earth, Pluto, and the Sun. We find that the observed changes in the amplitude of Pluto’s lightcurve can be explained by viewing geometry rather than by volatile transport. We also discovered a measurable decrease since 1992 of ∼0.03 magnitudes in the amplitude of Pluto’s lightcurve, as the model predicts. Pluto’s geometric albedo does not appear to be currently increasing, as our model predicts, although given the uncertainties in both the model and the measurements of geometric albedo, this result is not firm evidence for volatile transport. The maximum of methane-absorption lightcurve occurs near the minimum of the BVR lightcurves. This result suggests that methane is more abundant in the brightest regions of Pluto. Pluto’s phase coefficient exhibits a color dependence, ranging from 0.037 ± 0.01 in the B filter to 0.032 ± 0.01 in the R filter. Pluto’s phase curve is most like those of the bright, recently resurfaced satellites Triton and Europa. Although Pluto shows no strong evidence for volatile transport now (unlike Triton), it is important to continue to observe Pluto as it moves away from perihelion.     

Titania's radius and an upper limit on its atmosphere from the September 8, 2001 stellar occultation

On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V=7.2, K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: (1-σ error bar). This implies a density of using the value derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362-374]. We do not detect any significant difference between equatorial and polar radii, in the limit , in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: ΔαTcos(δT)=−108±13 mas and ΔδT=−62±7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: and ΔδU=−85±25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of ΔαTcos(δT)=−127±20 mas and ΔδT=−97±13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10-20 nbar. More specifically, we find an upper limit of 13 nbar (1-σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO₂ atmosphere. We also provide an upper limit of 8 nbar for a possible CH₄ atmosphere, and 22 nbar for pure N₂, again at the 1-σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54±0.03 mas (corresponding to projected at Titania). With a distance of 170±25 parsecs, this corresponds to a radius of 9.8±0.2 solar radii for HIP 106829, typical of a K0 III giant.     

Interacting ellipsoids: a minimal model for the dynamics of rubble-pile bodies

A simple mechanical model is formulated to study the dynamics of rubble-pile asteroids, formed by the gravitational re-accumulation of fragments after the collisional breakup of a parent body. In this model, a rubble-pile consists of N interacting fragments represented by rigid ellipsoids, and the equations of motion explicitly incorporate the minimal degrees of freedom necessary to describe the attitude and rotational state of each fragment. In spite of its simplicity, our numerical examples indicate that the overall behavior of our model is in line with several known properties of collisional events, like the energy and angular momentum partition during high velocity impacts. Therefore, it may be considered as a well defined minimal model.     

The equilibrium of rubble-pile satellites: The Darwin and Roche ellipsoids for gravitationally held granular aggregates

Many new small moons of the giant planets have been discovered recently. In parallel, satellites of several asteroids, e.g., Ida, have been found. Strikingly, a majority of these new-found planetary moons are estimated to have very low densities, which, along with their hypothesized accretionary origins, suggests a rubble internal structure. This, coupled to the fact that many asteroids are also thought to be particle aggregates held together principally by self-gravity, motivates the present investigation into the possible ellipsoidal shapes that a rubble-pile satellite may achieve as it orbits an aspherical primary. Conversely, knowledge of the shape will constrain the granular aggregate's orbit—the closer it gets to a primary, both primary's tidal effect and the satellite's spin are greater. We will assume that the primary body is sufficiently massive so as not to be influenced by the satellite. However, we will incorporate the primary's possible ellipsoidal shape, e.g., flattening at its poles in the case of a planet, and the proloidal shape of asteroids. In this, the present investigation is an extension of the first classical Darwin problem to granular aggregates. General equations defining an ellipsoidal rubble pile's equilibrium about an ellipsoidal primary are developed. They are then utilized to scrutinize the possible granular nature of small inner moons of the giant planets. It is found that most satellites satisfy constraints necessary to exist as equilibrated granular aggregates. Objects like Naiad, Metis and Adrastea appear to violate these limits, but in doing so, provide clues to their internal density and/or structure. We also recover the Roche limit for a granular satellite of a spherical primary, and employ it to study the martian satellites, Phobos and Deimos, as well as to make contact with earlier work of Davidsson [Davidsson, B., 2001. Icarus 149, 375–383]. The satellite's interior will be modeled as a rigid-plastic, cohesion-less material with a Drucker–Prager yield criterion. This rheology is a reasonable first model for rubble piles. We will employ an approximate volume-averaging procedure that is based on the classical method of moments, and is an extension of the virial method [Chandrasekhar, S., 1969. Ellipsoidal Figures of Equilibrium. Yale Univ. Press, New Haven] to granular solid bodies.     

Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect

Thermal inertia determines the temperature distribution over the surface of an asteroid and therefore governs the magnitude the Yarkovsky effect. The latter causes gradual drifting of the orbits of km-sized asteroids and plays an important role in the delivery of near-Earth asteroids (NEAs) from the main belt and in the dynamical spreading of asteroid families. At present, very little is known about the thermal inertia of asteroids in the km size range. Here we show that the average thermal inertia of a sample of NEAs in the km-size range is . Furthermore, we identify a trend of increasing thermal inertia with decreasing asteroid diameter, D. This indicates that the dependence of the drift rate of the orbital semimajor axis on the size of asteroids due to the Yarkovsky effect is a more complex function than the generally adopted D⁻¹ dependence, and that the size distribution of objects injected by Yarkovsky-driven orbital mobility into the NEA source regions is less skewed to smaller sizes than generally assumed. We discuss how this fact may help to explain the small difference in the slope of the size distribution of km-sized NEAs and main-belt asteroids.