Density of asteroids

Density of asteroids

B. Carry benoit.carry@esa.int European Space Astronomy Centre, ESA, P.O. Box 78, 28691 Villanueva de la Cañada, Madrid, Spain
Abstract

The small bodies of our solar system are the remnants of the early stages of planetary formation. A considerable amount of information regarding the processes that occurred during the accretion of the early planetesimals is still present among this population. A review of our current knowledge of the density of small bodies is presented here. Density is indeed a fundamental property for the understanding of their composition and internal structure. Intrinsic physical properties of small bodies are sought by searching for relationships between the dynamical and taxonomic classes, size, and density. Mass and volume estimates for 287 small bodies (asteroids, comets, and transneptunian objects) are collected from the literature. The accuracy and biases affecting the methods used to estimate these quantities are discussed and best-estimates are strictly selected. Bulk densities are subsequently computed and compared with meteorite density, allowing to estimate the macroporosity (i.e., amount of voids) within these bodies. Dwarf-planets apparently have no macroporosity, while smaller bodies (400 km) can have large voids. This trend is apparently correlated with size: C and S-complex asteroids tends to have larger density with increasing diameter. The average density of each Bus-DeMeo taxonomic classes is computed (DeMeo et al., 2009, Icarus 202). S-complex asteroids are more dense on average than those in the C-complex that in turn have a larger macroporosity, although both complexes partly overlap. Within the C-complex asteroids, B-types stand out in albedo, reflectance spectra, and density, indicating a unique composition and structure. Asteroids in the X-complex span a wide range of densities, suggesting that many compositions are included in the complex. Comets and TNOs have high macroporosity and low density, supporting the current models of internal structures made of icy aggregates. Although the number of density estimates sky-rocketed during last decade from a handful to 287, only a third of the estimates are more precise than 20%. Several lines of investigation to refine this statistic are contemplated, including observations of multiple systems, 3-D shape modeling, and orbital analysis from Gaia astrometry.

keywords:
Minor planets, Mass, Volume, Density, Porosity
journal: PSS

1 Small bodies as remnants of planetesimals

The small bodies of our solar System are the left-overs of the building blocks that accreted to form the planets, some 4.6 Gyr ago. They represent the most direct witnesses of the conditions that reigned in the proto-planetary nebula (2002-AsteroidsIII-1-Bottke). Indeed, terrestrial planets have thermally evolved and in some cases suffered erosion (e.g., plate tectonic, volcanism) erasing evidence of their primitive composition. For most small bodies, however, their small diameter limited the amount of radiogenic nuclides in their interior, and thus the amount of energy for internal heating. The evolution of small bodies is therefore mainly exogenous, through eons of collisions, external heating, and bombardment by high energy particles.
A detailed study of the composition of small bodies can be achieved in the laboratory, by analyzing their terrestrial counterparts: meteorites. The distribution of elements, isotopes in meteorites, together with the level of heating and aqueous alteration they experienced tell us about the temperature, elemental abundance, and timescales during the accretion stages (e.g., 2006-MESS2-Halliday). The connection of this information with specific locations in the Solar System constrains the formation scenarios of our Solar System. This requires the identification of links between the meteorites and the different populations of small bodies.
Indeed, if meteorites are samples from the Solar System, several questions are raised. Is this sampling complete? Is this sampling homogeneous? Some of the identified asteroid types (see Sect. 2) lack of a terrestrial analog. The most flagrant example are the O-type asteroids (3628) Božněmcová and (7472) Kumakiri that appear unlike any measured meteorite assemblage (2011-LPI-Burbine). Coupled mineralogical and dynamical studies have shown that meteorites come from specific locations. Other regions of the Solar System may therefore be unrepresented in our meteorite collection (see the discussions in 2002-AsteroidsIII-5.2-Burbine; 2002-AsteroidsIII-4.1-Bottke; 2008-Nature-454-Vernazza, for instance).
Additionally, the current orbits of small bodies may be different from the place they originally formed. For instance, it has been suggested that the giant planets migrated to their current orbits (the Nice model, see 2005-Nature-435-Tsiganis), injecting material from the Kuiper Belt into the inner Solar System (2009-Nature-460-Levison). Similarly, gravitational interaction among planetary embryos may have caused outward migration of planetesimals from Earth’s vicinity into the main belt (2006-Nature-439-Bottke). Current distribution of small bodies may therefore not reflect the original distribution of material in the Solar System. It however tells us about the dynamical processes that occurred over history. Analysis of the composition of meteorites in the laboratory, of small bodies from remote-sensing, and of their distribution in the Solar System are therefore pre-requisites to understanding the formation and evolution of our Solar System.

2 Linking small bodies with meteorites

Most of our knowledge on the mineralogy of asteroids has been derived by analysis of their reflectance spectra in the visible and near-infrared (VNIR). The shape of these spectra has been used to classify the asteroids into broad groups, following several classification schemes called taxonomies. In what follows, I refer to the taxonomy by 2009-Icarus-202-DeMeo, based on the largest wavelength range (0.4–2.4 m). It encloses 15 classes grouped into three complexes (C, S, and X), with 9 additional classes called end-members (see 2009-Icarus-202-DeMeo, for a detailed description of the classes). Mineralogical interpretations and links with meteorites have been proposed for several classes.
Asteroids belonging to the S complex (S, Sa, Sq, Sr, and Sv) and to the Q class have been successfully linked to the most common meteorites, the ordinary chondrites (OCs). This link had been suggested for years based on the presence of two deep absorption bands in their spectra, around 1 and 2 microns, similar to that of OCs and characteristic of a mixture of olivines and pyroxenes (see for instance 1996-MPS-31-Chapman; 2006-Icarus-184-Brunetto, among many others). The analysis of the sample from the S-type asteroid Itokawa returned by the Hayabusa spacecraft confirmed this link (2011-Science-333-Yurimoto). The two end-member classes A and V have a mineralogy related to the S-complex. A-types are asteroids made of almost pure olivine, which possible analogs are the achondrite meteorites of the Brachinite and Pallasite groups (see, e.g., 1989-AsteroidsII-4-Bell; 2004-AA-422-deLeon). In opposition, V-types are made of pure pyroxenes and are related to the HED achondrite meteorites (e.g., 1970-Science-168-McCord). A- and V-types are believed to correspond to the mantle and the crust of differentiated parent bodies (1996-MPS-31-Burbine).
The link between the hydrated carbonaceous chondrites (CCs) CI and CM and the asteroids in the C-complex seems well established (2011-Icarus-212-Cloutis; 2011-Icarus-216-Cloutis). The anhydrous CV/CO carbonaceous chondrites have also been linked with B-types (2010-JGR-115-Clark). The scarcity and low contrast of absorption features in the VNIR prevents a detailed description of the mineralogy and association with meteorites of these asteroid types (B, C, Cb, Cg, Cgh, Ch). Spectroscopy in the 2.5–4 m wavelength range, however, revealed the presence of hydration features (1978-MNRAS-182-Lebofsky; 1990-Icarus-88-Jones; 2002-AsteroidsIII-2.2-Rivkin). These features were interpreted as evidences for aqueous alteration, similar to that experienced by CI/CM parent bodies (2011-Icarus-212-Cloutis; 2011-Icarus-216-Cloutis). Due to their similar composition to that of the solar photosphere, CI meteorites are often considered the most primitive material in the Solar System (see 2006-MESS2-Weisberg, for an overview of meteorite classes). This has made the compositional study of these so-called primitive asteroids a primary goal in planetary science.
The VNIR spectra of asteroids in the X-complex are devoid of strong absorption bands. However, several weak features (e.g., around 0.9 m) have been identified and used to discriminate sub-classes (2004-AJ-128-Clark; 2010-Icarus-210-Ockert-Bell; 2011-Icarus-214-Fornasier). Proposed meteorite analogs for X, Xc, Xe, and Xk asteroids virtually cover the entire meteorite collection: the anhydrous CV/CO carbonaceous chondrites (2005-AA-430-Barucci; 2012-PSS-Barucci), enstatite chondrites and aubrites (2009-Icarus-202-Vernazza; 2011-Icarus-216-Vernazza; 2010-Icarus-210-Ockert-Bell), mesosiderites (2009-Icarus-202-Vernazza), stony-iron (2010-Icarus-210-Ockert-Bell), and iron meteorites (2011-Icarus-214-Fornasier). The mineralogy represented in the X-complex is therefore probably more diverse than in the S- and C-complexes, due to the limits of the taxonomy based on spectral features only. In is worth noting that in former taxonomies (e.g., 1989-AsteroidsII-Tholen), the X-complex was divided into three main groups, E, M, and P, distinguished by albedo.
L-types have been suggested to be the most ancient asteroids that currently exist. From the comparison of their VNIR spectra with laboratory material, a fraction of 30  10% of Calcium- and aluminum-rich inclusions was proposed (2008-Science-320-Sunshine). This value is significantly higher than that of meteorites. This suggests a very early accretion together with a low degree of alteration while crossing the entire history of the Solar System. With a similar spectral shape, K-types have often be described as intermediates between S- and C-like material (2009-Icarus-202-DeMeo). Most of the K-type are associated with the Eos dynamical family in the outer Main Belt. They have been tentatively linked with the anhydrous CO, CV, and CK, and hydrated but metal-rich CR carbonaceous chondrites meteorites (1989-AsteroidsII-4-Bell; 1998-Icarus-131-Doressoundiram; 2009-Icarus-202-Clark).
The mineralogy of the remaining end-members classes is more uncertain, owing to the apparent absence of strong spectral features (D and T) or to the mismatch of features with any known material (O and R). It has been suggested that T-types contain a high fraction of metallic contents, and may be related to the iron cores of differentiated asteroids, hence iron meteorites (1992-Metic-Britt). D-types are among the reddest objects in the Solar System, not unlike that of comet nuclei and some transneptunian objects (2008-SSBN-3-Barucci). Their emission spectra in the mid-infrared indeed show striking similarities with that of comet nuclei (2006-Icarus-182-Emery; 2011-AJ-141-Emery). Both O and R classes were defined to describe the spectral shape of a single object, (3628) Božněmcová and (349) Dembowska respectively. Both types display broad absorption bands around 1 and 2 microns. These bands are however unlike those of S-types or any type of pyroxenes and olivines in our sample collection (2011-LPI-Burbine).
Comets and transneptunian objects (TNOs) are volatile-rich bodies. These two populations are dynamically linked, the later being one of the reservoir of periodic comets (2004-CometsII-7-Jewitt). Several compositional groups have been identified among TNOs: water ice dominated spectra, methane-rich spectra, and featureless spectra similar to that of comet nuclei (2008-SSBN-3-Barucci). There is no evidence for a meteorite sample from these dynamic classes, although the delivery from Kuiper Belt material to Earth should be possible (2008-SSBN-9-Gounelle).
As seen from this short summary, asteroid-meteorites connections and detailed mineralogy remain open questions in many cases: only about half of the 24 classes defining the taxonomy by 2009-Icarus-202-DeMeo have a mineralogical interpretation. Expanding the taxonomy toward longer wavelengths (2–5 and 5–40 m range) will help in that respect (e.g., 1995-Icarus-117-Rivkin; 2002-AsteroidsIII-2.2-Rivkin; 2006-Icarus-182-Emery). Additional constraints must however be used to refine current mineralogy interpretations, especially for objects with featureless spectra. Visible and radar albedos, thermal inertia, and density provide valuable constraints on the composition of these objects (e.g., 2011-Icarus-214-Fornasier). Among these, the most fundamental property to understand the composition and internal structure is perhaps the density (2002-AsteroidsIII-4.2-Britt; 2008-ChEG-68-Consolmagno).

3 The density: a fundamental property

As described above, from the analysis of the surface properties such as reflectance spectra or albedo, it is possible to make inferences on composition. These observables however tell us about surface composition only, which may or may not be reflective of the bulk composition of the body (2011-EPSL-305-Elkins-Tanton). For instance, the surface of Earth, the Blue Planet, is covered by water while its overall composition is totally different. Earth’s density is indeed indicative of a rocky composition with a core of denser material. Densities of small bodies are much more subtle, but still contain critical information.
From the compilation of the density of about 20 asteroids, 2002-AsteroidsIII-4.2-Britt already showed that differences are visible among that population. In a more recent review including 40 small bodies, 2008-ChEG-68-Consolmagno highlighted four trends in macroporosity (hereafter ). The macroporosity reflects the amount of voids larger than the typical micrometer-sized cracks of meteorites. The largest asteroids (mass above 10 kg) are apparently compact bodies without any macroporosity. This contrasts strongly with all the other less massive small bodies that have 20% or more macroporosity. The fraction of voids increases dramatically for icy bodies (comets and TNOs). Finally, primitive C-type asteroids tends to have larger macroporosity than the basaltic S-type.
Macroporosity, if present to a large extend, may have strong consequences on certain physical properties such as gravity field, thermal diffusivity, seismic velocity, and of course on collisional lifetimes (see the review by 2002-AsteroidsIII-4.2-Britt). Macroporosity can also help in understanding the collisional history: intact bodies are expected to have low-to-no macroporosity, while heavily impacted objects may have large cracks, fractures (i.e., moderate ), or be gravitational re-accumulation of material (i.e., rubble-piles, characterized by high values of ).

4 Determination of density

Direct measurement of the bulk density () involves the independent measures of the mass () and volume (): . Indirect determination of the density are also possible by modeling the mutual eclipses of a binary system (e.g., 2006-AA-446-Behrend) or the non-gravitational forces on a comet nucleus (e.g., 2007-Icarus-187-Davidsson). This study aims at deriving constraints on the intrinsic physical properties of small bodies by searching for relationships between, the dynamical and taxonomic classes, size, and density. An extensive compilation of the mass, volume, and resulting density estimates available in the literature is therefore presented here.
There are 994 published mass estimates for 267 small bodies (Sect. 4.1). For each object, the volume determinations are also compiled here, resulting in 1454 independent estimates (Sect. 4.2). Finally, the density of 24 small bodies has also been indirectly determined (Sect. 4.3). In total, 287 density estimates are available, for small bodies pertaining to all the dynamical classes: 17 near-Earth asteroids (NEAs), 230 Main-Belt (MBAs) and Trojan asteroids, 12 comets, and 28 transneptunian objects (TNOs). There is however a large spread among the independent estimates of the mass and volume estimates of these objects. Additionally, several estimates lead to obvious non-physical densities such as 0.05 or 20, the respective densities of Aerogel and Platinum. A rigorous selection of the different estimates is therefore needed. Some specifics of mass and diameter estimates are discussed below, together with selection criteria.

4.1 Mass estimates

Figure 1: Distribution of the relative accuracy of mass estimates obtained with four different methods (see text): (a) orbit deflection during close encounters, (b) planetary ephemeris, (c) orbit of natural satellites or spacecrafts (gray bar), and (d) indirect determination of density (Sect. 4.3) converted into mass.

The determination of the mass of a minor planet relies on the analysis of its gravitational effects on other objects (see the review by 2002-AsteroidsIII-2.2-Hilton, for instance). The 994 mass estimates for 267 small bodies listed in A can be divided in 4 categories, owing to the gravitational effects that were analyzed:

  1. Orbit deflection during close encounters: The mass of small bodies is several order of magnitude lower than that of planets. Asteroids can nevertheless slightly influence the orbit of other smaller asteroids (e.g., 2000-AA-360-Michalak; 2001-AA-374-Michalak) and of Mars (e.g., 2001-AA-371-Pitjeva; 2009-AA-508-Mouret) during close encounters. This method has been widely used, resulting in 547 mass estimates. An accuracy of few percent can be reached for the most massive asteroids such as (1) Ceres, (2) Pallas, or (4) Vesta (e.g., 2006-Icarus-182-Konopliv; 2011-AJ-142-Zielenbach). The accuracy however drops for smaller asteroids, and about a third have uncertainties cruder than 100% (see, for instance 2010-PSS-58-Somenzi; 2011-AJ-142-Zielenbach, and Fig. 1.a).

  2. Planetary ephemeris: Numerical models have been developed to describe and predict the position of planets and minor planets around the Sun. In addition to the Sun and the planets, the gravitational influence of several asteroids must be taken into account to properly describe the observed position of planets, satellites, and spacecrafts (see 2008-CeMDA-100-Baer; 2011-AJ-141-Baer; 2008-AA-477-Fienga; 2009-AA-507-Fienga; 2010-SciNote-Fienga; 2009-SciNote-Folkner, for details). In that respect, this method is similar to the analysis of close encounters. There is however a strong philosophical difference between these two methods: analysis of close encounters consists of considering N times a 1-to-1 gravitational interaction, while planetary ephemeris are conceptually closer to a N-to-1 interaction. Similarly to the results obtained from close encounters, the best accuracy is achieved for largest asteroids and becomes cruder for smaller objects. The mean accuracy is of 45%, but values are distributed up to 100% (Fig. 1.b).

  3. Spacecraft tracking: The Doppler shifts of the radio signals sent by spacecraft around an asteroid can be used to determine its orbit or the deflection of its trajectory during a flyby. These frequency shifts are imposed by the gravitational perturbation and are related to the mass of the asteroid (1997-Science-278-Yeomans; 2000-Science-289-Yeomans; 2006-Science-312-Fujiwara; 2011-Science-334-Paetzold). It is by far the most precise technique with a typical accuracy of a couple of percent (Fig. 1.c). It will however remain limited to a handful of small bodies (only four to date).

  4. Orbit of a satellite: From optical or radar images of the components of the system, their mutual orbit can be determined and the mass derived with Kepler’s third law (see, for instance, 1997-Icarus-130-Petit; 1999-Nature-401-Merline; 2002-AsteroidsIII-2.2-Merline; 2002-Science-296-Margot; 2005-Icarus-178-Marchis; 2008-Icarus-196-Marchis; 2008-Icarus-195-Marchis; 2005-ApJ-632-Brown; 2010-AJ-139-Brown; 2011-AA-534-Carry; 2011-AJ-141-Fang). The 28 mass estimates available for TNOs were derived from optical imaging with the Hubble space telescope or large ground-based telescopes equipped with adaptive-optics cameras (e.g., 2009-Icarus-200-Grundy; 2011-AA-528-Dumas). Similarly, the 17 mass estimates for NEAs were all derived from radar (e.g., 2006-Science-314-Ostro; 2006-Icarus-184-Shepard), with the exception of Itokawa which was the target of the Hayabusa sample-return mission (2006-Science-312-Fujiwara). Additionally, the mass of 26 MBAs was determined by optical imaging. In total, 68 mass estimates have been derived by analyzing the orbit of a satellite. It is the second most-precise technique with a typical accuracy of about 10–15% (Fig. 1.c). It is the most productive method of accurate mass determinations. With currently more than 200 known binaries, many mass estimates are still to come.

Based on these considerations and a close inspection of the different mass estimates available (e.g., Fig. 2), the following criteria for selecting mass estimates were applied: Mass estimates derived from either the third or the fourth method (spacecraft or satellite) prevail upon the first two methods (deflection and ephemeris). Mass estimates leading to non-physical densities are discarded. Mass estimates that do not agree within uncertainties with the range drawn by the weighted average and standard deviation are discarded. The weighted average and standard deviation are subsequently recomputed. The 994 mass estimates are provided in A together with bibliographic references and notes on selection.

Figure 2: The 18 mass estimates for (52) Europa (see D for the references). Top: The different mass estimates M, in 10 kg. Symbols indicate the method used to determine the mass: deflections (gray disk) or planetary ephemeris (open circle). Crossed estimates were discarded from the analysis (see text). Horizontal solid and dashed lines are respectively the weighted average () and standard deviation () of the mass estimates before selection. Bottom: Same as above, but plotted as a function of the distance to the average value, in units of deviation: (M - )/ . Similar plots for each of the 140 small bodies with multiple mass estimates are provided in A.

A summary of the precision achieved on mass estimates is presented in Fig. 3. The contribution provided here is illustrated by the difference between the cumulative distribution of relative precision before (dashed line) and after (solid line) the selection (about 20% of the estimates were discarded). For estimates with a relative uncertainty below 50% , the selection of estimates slightly improves the final accuracy, increasing the number of accurate estimates by 5 to 10%. The apparent degradation introduced by the selection for low-precision estimates is due to rejection of about 10% of these estimates. In other words, these estimates lead to unrealistic densities and should not be considered. Furthermore, the distribution presented in Fig. 3 is based on the uncertainties reported by the different authors. The discrepancy between estimates however often reaches disconcerting levels. For instance, the estimates M (2001-IAA-Krasinsky), M (2008-DPS-40-Baer), M (2009-AA-507-Fienga), and M (2009-SciNote-Folkner) of the mass of (52) Europa fall within the range drawn by the weighted mean and deviation (Fig. 2). They nevertheless strongly disagree: the different values are between 4 and 11  one from each other.
Such differences are indicative of underestimated uncertainties. Accuracy is often reported as the formal standard deviation (), which in some cases may be small compared to systematics. The uncertainties on the mass determinations should therefore be considered as lower limits, to which some systematics could be added. As a result, the cumulative distribution of the relative precision presented in Fig. 3 is optimistic and gives an upper limit to the amount of accurate estimates. Therefore, even with mass estimates available for more than 250 small bodies, our knowledge is still very limited: Only about half of the estimates are more accurate than 20%, and no more than 70% of the estimates are more accurate than 50% (higher uncertainties preventing any firm conclusion).

Figure 3: Cumulative distribution of the accuracy on the diameter (black), mass (blue), and density (red) estimates. Dashed and solid lines represent the distributions before and after selection of best estimates (see text for details). Three reference levels for the relative accuracy are drawn: 20%, 50% and 100%, with the fraction of targets with a better accuracy reported for each estimate (after selection only).

4.2 Volume estimates

Figure 4: Distribution of the relative accuracy of diameter estimates obtained with four classes of different methods (see text): (a) crude estimates from absolute magnitude, (b) thermal radiometry, (c) direct measurement limited to a single geometry, and (d) shape modeling based on several geometries (gray bars represent the diameters derived from spacecraft encounters). Although estimates in sub-plot (d) are expected to be the most precise, it is not reflected in their relative uncertainty distribution. The possible underestimation of biases in other techniques may be the cause (see text).

As already noted by several authors, the most problematic part of determining the density of a small body is to measure any mass at all (e.g., 2002-AsteroidsIII-2.2-Merline; 2008-ChEG-68-Consolmagno). The number of density estimates presented here is limited by the number of mass estimates, and not by the number of volume estimates (generally reported as volume-equivalent diameter, hereafter ). Many different observing techniques and methods of analysis have been used to evaluate the diameter of small bodies (see the review by 2012-PSS--Carry). The 1454 diameter estimates listed in B were derived with 15 different methods, that can be grouped into 4 categories:

Figure 5: The 10 diameter estimates for (52) Europa (see D for the references). Top: The different diameter estimates , in km. Symbols indicate the method used to determine the diameter: mid-infrared radiometry modeled using the Standard Thermal Model (STM: , , , and ) and the near-Earth asteroid thermal model (NEATM: and ), disk-resolved imaging on a single epoch (), combination of lightcurves and stellar occultations (), or shape modeling (). See B for a complete description of the symbols. Crossed estimates were discarded from the analysis (see text). Horizontal solid and dashed lines are respectively the weighted average () and standard deviation () of the diameter estimates before selection. Bottom: Same as above, but plotted as a function of the distance to the average value, in units of deviation: ( - )/ . Similar plots for each of the 246 small bodies with multiple diameter estimates are provided in B.
  1. Absolute magnitude: It could almost be considered an absence of size estimate. It is the crudest method to evaluate the diameter of a small body (Fig. 4.a). From the absolute magnitude and an assumed geometric albedo , the diameter is given by (2007-Icarus-190-Pravec, and references therein). The diameter of 29 small bodies presented here were derived using their absolute magnitude, in absence of any other estimates. This particularly applies to TNOs.

  2. Thermal modeling of mid-infrared radiometry: It is by far the main provider of diameter estimates: 1233 diameter estimates out of the 1454 listed in B (i.e., 85%). Asteroids are indeed among the brightest sources in the sky at mid-infrared wavelengths (5–20 m), so infrared satellites (IRAS, ISO, AKARI, Spitzer, and WISE) have been able to acquire observations of a vast number of these objects (see 2002-AJ-123-Tedesco-a; 2010-AJ-140-Ryan; 2011-PASJ-63-Usui; 2011-ApJ-741-Masiero; 2011-AJ-141-Mueller). The diameter and albedo of the colder TNOs have also been studied at longer wavelengths with Spitzer and Herschel (e.g., 2008-SSBN-3-Stansberry; 2009-EMP-105-Muller). As visible in Fig. 4.b, the typical uncertainty is of only few percent. In many case, however, the different estimates from thermal modeling disagree above their respective quoted uncertainty (see Table 3 in 2009-PSS-57-Delbo, illustrating the issue). For instance, in the case of Europa (Fig. 5), both diameter estimates (2010-AJ-140-Ryan) where based on the same data, but used two different thermal modeling, and disagree at more than 6 . Such differences are again indicative of underestimated uncertainties. Accuracy is often reported as the formal standard deviation (), which in some cases may be small compared to systematics. In the present case, the simplified standard thermal model (1986-Icarus-68-Lebofsky) and near-Earth asteroid thermal model (1998-Icarus-131-Harris) widely used do not take into account the spin and shape of the small body into account, and can therefore be strongly biased. A more realistic level of accuracy is about 10% (2010-AA-518-Lim), at which these estimates are still highly valuable given the huge number of small bodies that have been studied that way.

  3. Direct measurements of a single geometry: Stellar occultations or disk-resolved images can provide an extremely precise measure of the apparent size and shape of a small body (e.g., 2004-AJ-127-Brown; 2006-ApJ-643-Brown; 2006-Icarus-185-Marchis; 2008-Icarus-196-Marchis; PDSSBN-OCC). When these direct measurements are limited to a single geometry, however, the evaluation of the diameter may be biased. The volume is 3-D while a single geometry only provides 2-D constraints. The typical accuracy of 5% (Fig. 4.c) may therefore be optimistic. Nevertheless, these estimates are highly valuable, being based on direct measurements.

  4. Shape modeling based on several geometries: The least numerous but most precise diameter estimates are derived when the spin and 3-D shape of the objects are modeled, thus limiting the 2-D to 3-D related biases (Fig. 4.d). Small bodies can be modeled as smooth tri-axial ellipsoids (e.g., 2005-Nature-437-Thomas; 2009-Science-326-Schmidt; 2009-Icarus-202-Drummond; 2010-AA-523-Drummond), convex shapes (2007-Icarus-187-Descamps; 2011-Icarus-214-Durech), or realistic 3-D shapes (2000-Science-289-Veverka; 2006-Science-314-Ostro; 2010-Icarus-207-Ostro; 2010-Icarus-205-Carry-a; 2010-AA-523-Carry; 2011-Science-334-Sierks). In particular, spacecraft encounters with (25 143) Itokawa and (21) Lutetia have shown that multi-data approaches provide reliable and precise diameter estimates: e.g., lightcurve-derived shape model with thermal radiometry (2006-AA-447-Mueller) or combined inversion of disk-resolved imaging and lightcurves (2011-IPI-5-Kaasalainen; 2010-AA-523-Carry; 2012-PSS--Carry).

As visible in Figs. 3 and 4, the diameter estimates are generally intrinsically much more precise than the mass determination: all the estimates are known to better than 50% relative precision, and a large majority to better than 10%. Diameter estimates from different techniques moreover generally agree, suggesting that systematics are commensurable with formal uncertainties. The same selection criteria than for mass estimates were applied here, and about 15% of the estimates were discarded. Paradoxically, once the mass is determined, the uncertainty on the volume () often becomes the major source of uncertainty on the density (). Indeed,

(1)

The contribution of the uncertainty on the diameter () therefore easily overwhelms that of the mass () . In the compilation presented here, however, the mass is the limiting factor for 61% of the objects, contributing to 72% of the density uncertainty. This is mainly due to the high number of non-precise mass estimates (Fig. 3). If only the density estimates with a relative precision better than 20% are considered, then the situation is reversed: the diameter is the limiting factor for 75% of the objects, contributing to 68% of the density uncertainty. For these reasons, the mass should therefore be considered the limiting factor in most of the cases. As already discussed elsewhere, however, when a reliable mass estimate is available (i.e., usually from the presence of a satellite), the precision on the volume generally limits the accuracy on the density (2002-AsteroidsIII-2.2-Merline; 2002-AsteroidsIII-4.2-Britt; 2008-ChEG-68-Consolmagno).

4.3 Indirect density estimates

For small bodies with diameters of a few to tens of kilometers the methods to estimate their mass listed above (Sect. 4.1) cannot be used. The gravitational influence of these very small bodies is too tiny to be measured. Even in the case of binary systems, their angular extent is generally too small to be imaged with current technology. The only exception are the small binary NEAs that can be imaged with radar during close approaches with Earth. Yet, a large fraction of the currently known binaries are small-sized systems discovered by studying their lightcurves (86 out of 207, e.g., 2000-Icarus-146-Mottola; 2002-AsteroidsIII-2.2-Pravec; 2006-Icarus-181-Pravec). Indeed, photometric observations of the mutual eclipses of a system provide many constraints, for instance, on the ratio between the diameters of the two components or between the primary diameter and the orbit semi-major axis (see 2009-Icarus-200-Scheirich).
Nevertheless, these parameters are dimensionless from lightcurve observations only. The absolute scale, hence semi-major axis and thus mass, cannot be derived. Usually, both components are assumed to have the same bulk density to bypass this restriction (e.g., 2009-Icarus-200-Scheirich). These estimates are indirect, being derived without measuring the mass nor the size. The accuracy reached greatly depends on each system, and ranges from a few percent to 100% (Fig. 1.d). It is worth noting that if small-sized binaries are formed by rotational breakup (2008-Nature-454-Walsh) as suggested by the fast rotations of the primaries (2002-AsteroidsIII-2.2-Pravec; 2006-Icarus-181-Pravec; 2010-Nature-466-Pravec), the porosity, hence density, of the components may be significantly different. These density estimates may therefore be biased, in absence of an independent measure of the scale of the systems.
Measuring the mass of comets is another challenge. With diameters typically smaller than 10 km, comets have very small masses. In absence of a satellite, studying their gravitational effect on other objects is hopeless. The activity of their nucleus however provides an indirect way to estimate their mass. Indeed, the forces resulting from the gas jets slowly change the orbit of the nucleus around the Sun. Modeling this non-gravitational effect provides the mass of the nucleus (e.g., 2004-Icarus-168-Davidsson; 2005-Icarus-176-Davidsson; 2006-Icarus-180-Davidsson; 2007-Icarus-187-Davidsson; 2009-MNRAS-393-Sosa). The masses of 11 comets have been derived using this approach. 2007-Icarus-190-Richardson have also studied the expansion of ejecta created by the Deep Impact experiment on the comet 9P/Tempel1. This is the most direct measurement of the mass of a comet, independent of the non-gravitational effect.

A summary of the mass, volume-equivalent diameter and bulk density of the 287 small bodies compiled here is provided in Table 1. The values listed are the weighted average and standard deviation of all the selected estimates (see A, B, and C). The density is given normalized to that of liquid water (1 000 kg m), i.e., dimensionless. The estimates have been ranked from A to E, owing to the level of relative accuracy achieved on the density: B better than 20%, C between 20 and 50%, D between 50 and 100%, and E cruder than 100%. A stands for reliable estimates (more precise than 20%), based on more than 5 mass estimates and 5 diameter estimates, or a spacecraft encounter. Irrelevant densities are tagged with a cross (✗). Only about a third of the 287 density estimates have a relative precision better than 20% (Fig. 3), and two third better than 50%, above which level nothing relevant can be derived.

The fraction of volume occupied by voids, the macroporosity , is also reported, computed as:

(2)

with the asteroid bulk density and the bulk density of the associated meteorite (Table 2). The macroporosity is the least constrained of all the quantities discussed here. Indeed, it is affected by the uncertainties and possible biases on the diameter and mass estimates and also from the possible ambiguous links with meteorites (Sect. 2 and Table 3). Depending on the meteorite association, the macroporosity may change by 30–40%. For instance, while (16) Psyche was the most porous asteroid listed by 2002-AsteroidsIII-4.2-Britt and 2008-ChEG-68-Consolmagno with a macroporosity of about 70%, it stands in the low macroporosity range (about 18%). A low macroporosity is actually more consistent with the link between Psyche and iron meteorites than the very high value of 75% found previously.

Designation Classification Masses (kg) Diameter (km) Density Porosity Rank
# Name Dyn. Tax. Met. Fig. Fig.
1 Ceres MBA C CM 9.44   0.06   1 944. 79   22. 99 1 2. 13   0. 15 4  7 A
2 Pallas MBA B CK 2.04   0.04   2 514. 41   19. 12 2 2. 86   0. 32 0  11 A
3 Juno MBA Sq OC 2.73   0.29   3 241. 79   10. 58 3 3. 68   0. 62 0  16 A
4 Vesta MBA V HED 2.63   0.05   4 519. 33   6. 84 4 3. 58   0. 15 0  4 A
5 Astraea MBA S OC 2.64   0.44   5 113. 41   3. 53 5 3. 45   0. 66 0  19 B
6 Hebe MBA S OC 1.39   0.10   6 190. 92   7. 15 6 3. 81   0. 50 0  13 A
7 Iris MBA S OC 1.29   0.21   7 225. 89   25. 94 7 2. 14   0. 81 35  38 C
8 Flora MBA S OC 9.17   1.75   8 139. 12   2. 26 8 6. 50   1. 28 0  19
9 Metis MBA S OC 8.39   1.67   9 164. 46   7. 67 9 3. 60   0. 87 0  24 C
10 Hygiea MBA C CM 8.63   0.52   10 421. 60   25. 69 10 2. 19   0. 42 2  19 A
11 Parthenope MBA Sq OC 5.91   0.45   11 151. 07   5. 11 11 3. 27   0. 41 1  12 A
12 Victoria MBA L CO 2.45   0.46   12 124. 09   8. 31 12 2. 45   0. 67 19  27 C
13 Egeria MBA Ch CM 8.82   4.25   13 214. 73   11. 53 13 1. 70   0. 86 24  50 D
14 Irene MBA S OC 2.91   1.88   14 147. 75   5. 03 14 1. 72   1. 12 48  65 D
15 Eunomia MBA K CV 3.14   0.18   15 256. 63   1. 04 15 3. 54   0. 20 0  5 B
16 Psyche MBA Xk Ata 2.72   0.75   16 248. 45   17. 13 16 3. 38   1. 16 15  34 C
17 Thetis MBA S OC 1.33   0.12   17 82. 76   8. 79 17 4. 48   1. 48 0  33 C
18 Melpomene MBA S OC 3.22   1.28   18 141. 72   4. 86 18 2. 15   0. 88 35  41 C
19 Fortuna MBA Ch CM 8.60   1.46   19 206. 90   6. 49 19 1. 85   0. 35 17  19 A
20 Massalia MBA S OC 5.00   1.04   20 136. 99   8. 82 20 3. 71   1. 05 0  28 C
21 Lutetia MBA Xk EH 1.70   0.01   21 98. 00   5. 00 21 3. 44   0. 52 0  15 A
22 Kalliope MBA X Ata 7.96   0.31   22 170. 23   10. 46 22 3. 08   0. 58 23  18 B
23 Thalia MBA S OC 1.96   0.09   23 106. 81   3. 23 23 3. 07   0. 31 7  10 B
24 Themis MBA C CM 5.89   1.91   24 183. 84   11. 40 24 1. 81   0. 67 19  37 C
25 Phocaea MBA S OC 5.99   0.60   25 80. 19   4. 66 25 2. 21   0. 44 33  20 C
26 Proserpina MBA S OC 7.48   8.95   89. 63   3. 55 26 1. 98   2. 38 40  E
27 Euterpe MBA S OC 1.67   1.01   26 105. 80   7. 23 27 2. 69   1. 71 19  63 D
28 Bellona MBA S OC 2.62   0.15   27 108. 10   11. 49 28 3. 95   1. 28 0  32 C
29 Amphitrite MBA S OC 1.29   0.20   28 217. 59   10. 71 29 2. 38   0. 51 28  21 C
30 Urania MBA S OC 1.74   0.49   29 94. 48   5. 37 30 3. 92   1. 29 0  32 C
31 Euphrosyne MBA C CM 1.27   0.65   30 272. 92   8. 85 31 1. 18   0. 61 47  52 D
33 Polyhymnia MBA S OC 6.20   0.74   53. 98   0. 91 75. 28   9. 71 0  12
34 Circe MBA Ch CM 3.66   0.03   31 113. 02   4. 90 32 4. 83   0. 63 0  13
36 Atalante MBA C CM 4.32   3.80   110. 14   4. 38 33 6. 17   5. 48 0  88 E
38 Leda MBA Cgh CM 5.71   5.47   115. 41   1. 33 34 7. 09   6. 79 0  95 E
39 Laetitia MBA S OC 4.72   1.14   32 153. 80   4. 14 35 2. 47   0. 63 25  25 C
41 Daphne MBA Ch CM 6.31   0.11   33 181. 05   9. 60 36 2. 03   0. 32 9  16 B
42 Isis MBA S OC 1.58   0.52   34 102. 73   2. 73 37 2. 78   0. 93 16  33 C
43 Ariadne MBA Sq OC 1.21   0.22   35 63. 61   4. 66 38 8. 99   2. 57 0  28
45 Eugenia MBA C CM 5.79   0.14   36 201. 81   14. 77 39 1. 34   0. 29 40  22 C
46 Hestia MBA Xc Mes 5.99   0.49   37 125. 29   5. 21 40 5. 81   0. 87 0  14 E
47 Aglaja MBA B CV 3.25   1.68   38 141. 90   8. 72 41 2. 17   1. 19 22  55 D
48 Doris MBA Ch CM 6.12   2.96   39 211. 67   10. 85 42 1. 23   0. 62 45  50 D
49 Pales MBA Ch CM 4.22   2.15   40 150. 82   3. 81 43 2. 35   1. 21 0  51 D
50 Virginia MBA Ch CM 2.31   0.70   41 99. 42   0. 46 44 4. 49   1. 35 0  30 E
51 Nemausa MBA Ch CM 2.48   0.86   42 148. 85   3. 56 45 1. 43   0. 50 36  35 C
52 Europa MBA C CM 2.38   0.58   43 310. 21   10. 34 46 1. 52   0. 39 32  26 C
53 Kalypso MBA C CM 5.63   5.00   109. 06   7. 27 47 8. 28   7. 54 0  91
54 Alexandra MBA Cgh CM 6.16   3.50   44 149. 68   9. 85 48 3. 50   2. 11 0  60 D
56 Melete MBA Xk Mes 4.61   0.00   45 113. 63   8. 27 49 6. 00   1. 31 0  21 C
57 Mnemosyne MBA S OC 1.26   0.24   46 113. 01   4. 46 50 16. 62   3. 73 0  22
Table 1: Compilation of the average mass () and volume-equivalent diameter () estimates (see A, B, and C), and resulting bulk density () and macroporosity () for 287 objects, with their associated uncertainties. For each object, the dynamical class is listed (Dyn.), together with the taxonomic class (Tax., for asteroids only) and associated meteorite (Met.). The density estimates are ranked A to E, owing to the level of confidence at which they are determined (see text). Unrealistic density estimates are marked with a cross (✗) and uncertainties on the macroporosity larger than 100% are listed as . References: (1) 2010-JGR-115-Clark, (2) 2010-Icarus-210-Ockert-Bell, and (3) 2011-Icarus-214-Fornasier.
Designation Class Masses (kg) Diameter (km) Density Porosity Rank
# Name Dyn. Tax. Met. Fig. Fig.
59 Elpis MBA B CV 3.00   0.50   47 163. 61   6. 50 51 1. 30   0. 26 53  20 C
60 Echo MBA S OC 3.15   0.32   48 60. 00   1. 33 52 2. 78   0. 33 16  12 B
61 Danae MBA S OC 2.89   2.78   82. 52   2. 73 53 9. 81   9. 49 0  96 D
63 Ausonia MBA S OC 1.53   0.15   49 94. 45   7. 15 54 3. 46   0. 86 0  24 C
65 Cybele MBA Xk Mes 1.36   0.31   50 248. 29   17. 59 55 1. 70   0. 52 59  30 C
67 Asia MBA S OC 1.03   0.10   60. 99   2. 41 56 8. 66   1. 32 0  15
68 Leto MBA S OC 3.28   1.90   51 124. 96   6. 42 57 3. 21   1. 92 3  60 D
69 Hesperia MBA Xk Mes 5.86   1.18   52 136. 69   4. 71 58 4. 38   0. 99 0  22 C
70 Panopaea MBA Cgh CM 4.33   1.09   133. 43   7. 58 59 3. 48   1. 05 0  30 C
72 Feronia MBA D CM 3.32   8.49   83. 95   4. 02 60 10. 71   27. 44 0 
74 Galatea MBA C CM 6.13   5.36   120. 67   7. 15 61 6. 66   5. 94 0  89 D
76 Freia MBA C CM 1.97   4.20   53 167. 87   8. 73 62 0. 79   1. 69 64  E
77 Frigga MBA Xe EH 1.74   0.68   66. 97   1. 28 63 11. 05   4. 34 0  39
78 Diana MBA Ch CM 1.27   0.13   54 123. 63   4. 57 64 1. 28   0. 19 42  14 B
81 Terpsichore MBA Cb CM 6.19   5.31   121. 77   2. 34 65 6. 54   5. 62 0  85 D
84 Klio MBA Ch CM 5.47   4.06   79. 40   1. 95 66 2. 08   1. 55 7  74 D
85 Io MBA Cb CM 2.57   1.48   55 155. 00   6. 00 67 1. 31   0. 77 41  58 D
87 Sylvia MBA X CV 1.48   0.00   56 278. 14   10. 75 68 1. 31   0. 15 52  11 B
88 Thisbe MBA B CV 1.53   0.31   57 204. 04   9. 12 69 3. 44   0. 84 0  24 C
89 Julia MBA X CV 6.71   1.82   58 147. 57   8. 32 70 3. 98   1. 27 0  31 C
90 Antiope MBA C CM 8.30   0.20   59 122. 15   2. 77 71 0. 86   0. 06 61  7 B
92 Undina MBA Xk Mes 4.43   0.25   60 124. 44   3. 25 72 4. 39   0. 42 0  9 B
93 Minerva MBA C CM 3.50   0.40   149. 79   8. 08 73 1. 98   0. 39 11  19 B
94 Aurora MBA C CM 6.23   3.64   61 186. 35   8. 84 74 1. 83   1. 10 18  60 D
96 Aegle MBA T Ata 6.48   6.26   62 167. 92   5. 49 75 2. 61   2. 53 34  97 D
97 Klotho MBA Xc Ata 1.33   0.13   84. 79   3. 13 76 4. 16   0. 62 0  14 B
98 Ianthe MBA Ch CM 8.93   1.99   63 106. 16   3. 76 77 1. 42   0. 35 36  24 C
105 Artemis MBA Ch CM 1.53   0.54   64 119. 10   6. 78 78 1. 73   0. 67 23  38 C
106 Dione MBA Cgh CM 3.06   1.54   65 147. 17   3. 34 79 1. 83   0. 92 18  50 D
107 Camilla MBA X CV 1.12   0.03   66 210. 68   8. 89 80 2. 28   0. 29 18  12 B
111 Ate MBA Ch CM 1.76   0.44   67 142. 85   5. 94 81 1. 15   0. 32 48  27 C
112 Iphigenia MBA Ch CM 1.97   6.78   71. 07   0. 52 82 10. 48   36. 06 0 
117 Lomia MBA X CV 6.08   0.63   68 146. 78   3. 96 83 3. 67   0. 48 0  13 B
121 Hermione MBA Ch CM 4.97   0.33   69 195. 36   10. 62 84 1. 27   0. 22 43  17 B
126 Velleda MBA S OC 0.47   5.79   44. 79   1. 33 85 10. 00   123. 00 0 
127 Johanna MBA Ch CM 3.08   1.35   70 116. 14   3. 93 86 3. 75   1. 68 0  44 C
128 Nemesis MBA C CM 5.97   2.56   71 184. 19   5. 19 87 1. 82   0. 79 18  43 C
129 Antigone MBA X Ste 2.65   0.89   72 119. 44   3. 91 88 2. 96   1. 04 29  35 C
130 Elektra MBA Ch CM 6.60   0.40   73 189. 62   6. 81 89 1. 84   0. 22 17  12 B
132 Aethra MBA Xe EH 0.41   2.71   35. 83   6. 59 90 17. 09   112. 83 0 
135 Hertha MBA Xk Ata 1.21   0.16   74 76. 12   3. 29 91 5. 23   0. 96 0  18 B
137 Meliboea MBA C CM 7.27   3.07   75 145. 92   3. 58 92 4. 46   1. 91 0  42 E
138 Tolosa MBA S OC 4.93   2.59   51. 86   3. 07 93 6. 74   3. 74 0  55 E
139 Juewa MBA X CV 5.54   2.20   76 161. 43   7. 38 94 2. 51   1. 05 9  41 C
141 Lumen MBA Ch CM 8.25   5.77   131. 35   5. 21 95 6. 95   4. 93 0  70
144 Vibilia MBA Ch CM 5.30   1.20   77 141. 34   2. 76 96 3. 58   0. 84 0  23 C
145 Adeona MBA Ch CM 2.08   0.57   78 149. 50   5. 45 97 1. 18   0. 34 47  29 C
147 Protogeneia MBA C CM 1.23   0.05   118. 44   10. 45 98 14. 13   3. 78 0  26
148 Gallia MBA S OC 4.89   1.67   83. 45   5. 07 99 16. 06   6. 22 0  38
150 Nuwa MBA C CM 1.62   0.20   79 146. 54   9. 15 100 0. 98   0. 22 56  22 C
152 Atala MBA S OC 5.43   1.24   60. 03   3. 01 101 47. 92   13. 10 0  27
154 Bertha MBA Cb CM 9.19   5.20   80 186. 85   1. 83 102 2. 69   1. 52 0  56 D
156 Xanthippe MBA Ch CM 6.49   3.71   116. 34   4. 14 103 7. 86   4. 57 0  58
163 Erigone MBA Ch CM 2.01   0.68   72. 70   1. 95 104 9. 99   3. 45 0  34
Table 1: Continued
Designation Class Masses (kg) Diameter (km) Density Porosity Rank
# Name Dyn. Tax. Met. Fig. Fig.
164 Eva MBA X CV 9.29   7.76   101. 77   3. 61 105 1. 68   1. 41 39  84 D
165 Loreley MBA C CM 1.91   0.19   81 164. 92   8. 14 106 8. 14   1. 46 0  17
168 Sibylla MBA Ch CM 3.92   1.80   82 149. 06   4. 29 107 2. 26   1. 05 0  46 C
173 Ino MBA X CV 4.79   3.11   83 160. 07   6. 04 108 2. 23   1. 47 20  65 D
179 Klytaemnestra MBA S OC 2.49   1.19   75. 02   3. 21 109 1. 12   0. 55 66  49 C
185 Eunike MBA C CM 3.56   2.61   84 160. 61   5. 00 110 1. 64   1. 21 27  74 D
187 Lamberta MBA Ch CM 1.80   0.85   85 131. 31   1. 08 111 1. 51   0. 71 32  47 C
189 Phthia MBA Sa OC 3.84   0.81   40. 91   1. 36 112 1. 07   0. 25 67  23 C
192 Nausikaa MBA S OC 1.79   0.42   86 90. 18   2. 80 113 4. 64   1. 17 0  25 C
194 Prokne MBA Ch CM 2.68   0.29   87 170. 33   6. 92 114 1. 03   0. 16 53  16 B
196 Philomela MBA S OC 4.00   1.53   88 145. 29   7. 71 115 2. 48   1. 02 25  41 C
200 Dynamene MBA Ch CM 1.07   0.16   130. 71   3. 01 116 9. 14   1. 51 0  16
204 Kallisto MBA S OC 0.60   1.81   50. 36   1. 69 117 8. 98   27. 07 0 
209 Dido MBA Xc Mes 4.59   7.42   140. 35   10. 12 118 3. 17   5. 17 25  E
210 Isabella MBA Cb CM 3.41   1.09   73. 70   8. 47 119 16. 26   7. 65 0  47
211 Isolda MBA Ch CM 4.49   2.43   89 149. 81   6. 10 120 2. 54   1. 41 0  55 D
212 Medea MBA D CM 1.32   0.10   144. 13   7. 23 121 8. 41   1. 43 0  17
216 Kleopatra MBA Xe Ata 4.64   0.20   90 127. 47   8. 44 122 4. 27   0. 86 0  20 C
217 Eudora MBA X CV 1.52   0.06   68. 62   1. 41 123 8. 98   0. 65 0  7
221 Eos MBA K CV 5.87   0.34   103. 52   5. 60 124 10. 10   1. 74 0  17
230 Athamantis MBA S OC 1.89   0.19   110. 17   4. 57 125 2. 69   0. 43 19  15 B
234 Barbara MBA L CO 0.44   1.45   45. 62   1. 93 126 8. 84   29. 17 0 
238 Hypatia MBA Ch CM 4.90   1.70   91 146. 13   2. 66 127 2. 99   1. 05 0  35 C
240 Vanadis MBA C CM 1.10   0.92   92 94. 03   5. 37 128 2. 53   2. 15 0  84 D
241 Germania MBA Cb CM 0.86   5.00   178. 60   7. 84 129 0. 28   1. 67 87 
243 Ida MBA S OC 3.78   0.20   31. 29   1. 20 130 2. 35   0. 29 29  12 A
253 Mathilde MBA Cb CM 1.03   0.04   93 53. 00   2. 59 131 1. 32   0. 20 41  15 A
259 Aletheia MBA X CV 7.79   0.43   94 190. 05   6. 82 132 2. 16   0. 26 22  12 B
266 Aline MBA Ch CM 4.15   0.42   107. 95   6. 62 133 6. 29   1. 32 0  20 E
268 Adorea MBA X CV 3.25   2.26   95 140. 31   3. 34 134 2. 24   1. 56 19  69 D
283 Emma MBA C CM 1.38   0.03   96 132. 74   10. 13 135 1. 12   0. 25 49  23 C
304 Olga MBA Xc Mes 1.15   1.12   70. 30   2. 32 136 6. 31   6. 18 0  97 D
306 Unitas MBA S OC 5.33   5.77   52. 88   3. 48 137 6. 88   7. 57 0  E
322 Phaeo MBA D CM 1.86   0.04   71. 88   4. 32 138 9. 56   1. 73 0  18
324 Bamberga MBA Cb CM 1.03   0.10   97 234. 67   7. 80 139 1. 52   0. 20 32  13 A
328 Gudrun MBA S OC 3.16   0.46   98 122. 59   3. 72 140 3. 27   0. 55 1  17 B
334 Chicago MBA C CM 5.06   5.63   99 167. 26   7. 27 141 2. 06   2. 31 8  E
337 Devosa MBA Xk Hex 1.08   0.16   100 63. 87   3. 14 142 7. 91   1. 65 0  20
344 Desiderata MBA C CM 1.39   0.48   101 129. 20   3. 37 143 1. 22   0. 43 45  35 C
345 Tercidina MBA Ch CM 2.68   1.18   102 98. 78   2. 63 144 5. 30   2. 37 0  44 C
346 Hermentaria MBA S OC 6.33   0.18   93. 27   3. 05 145 14. 89   1. 52 0  10
349 Dembowska MBA R OC 3.58   1.03   103 145. 23   17. 21 146 2. 23   1. 01 33  45 C
354 Eleonora MBA A Pal 7.18   2.57   104 154. 34   5. 65 147 3. 73   1. 39 21  37 C
356 Liguria MBA Ch CM 7.83   1.50   134. 76   5. 17 148 6. 10   1. 36 0  22
365 Corduba MBA Ch CM 5.84   0.95   104. 51   2. 42 149 9. 76   1. 73 0  17
372 Palma MBA X CV 5.15   0.64   105 191. 12   2. 68 150 1. 40   0. 18 49  13 B
375 Ursula MBA Xc Mes 8.45   5.26   106 191. 65   4. 01 151 2. 29   1. 43 46  62 D
379 Huenna MBA C CM 3.83   0.20   87. 28   5. 70 152 1. 10   0. 22 51  20 C
381 Myrrha MBA X CV 9.18   0.80   123. 41   6. 30 153 9. 32   1. 64 0  17
386 Siegena MBA Ch CM 8.14   1.58   107 170. 35   8. 40 154 3. 14   0. 76 0  24 C
387 Aquitania MBA L CO 1.90   0.64   108 103. 51   2. 23 155 3. 27   1. 11 0  34 C
404 Arsinoe MBA B CV 3.42   3.03   96. 97   3. 01 156 7. 16   6. 38 0  89 D
405 Thia MBA Ch CM 1.38   0.14   122. 14   7. 69 157 1. 44   0. 30 35  21 C
409 Aspasia MBA Xc Mes 1.18   0.23   109 176. 33   4. 50 158 4. 10   0. 84 3  20 C
Table 1: Continued
Designation Class Masses (kg) Diameter (km) Density Porosity Rank
# Name Dyn. Tax. Met. Fig. Fig.
410 Chloris MBA Ch CM 6.24   0.30   110 115. 55   8. 22 159 7. 72   1. 69 0  21
416 Vaticana MBA S OC 3.27   3.10   87. 10   2. 57 160 9. 44   8. 99 0  95 D
419 Aurelia MBA Cb CM 1.72   0.34   111 124. 47   3. 08 161 1. 70   0. 35 24  21 C
420 Bertholda MBA X CV 1.48   0.09   141. 54   2. 08 162 9. 96   0. 75 0  7
423 Diotima MBA C CM 6.91   1.93   112 211. 64   16. 02 163 1. 39   0. 50 38  35 C
433 Eros NEA S OC 6.69   0.00   16. 20   0. 16 164 3. 00   0. 08 9  2 B
442 Eichsfeldia MBA Ch CM 1.95   0.20   65. 58   1. 70 165 1. 32   0. 16 41  12 B
444 Gyptis MBA C CM 1.06   0.28   113 164. 63   2. 60 166 4. 55   1. 23 0  27 C
445 Edna MBA Ch CM 3.47   0.78   88. 60   4. 10 167 9. 52   2. 50 0  26
449 Hamburga MBA C CM 1.57   1.40   66. 76   4. 82 168 10. 07   9. 24 0  91 E
451 Patientia MBA Cb CM 1.09   0.53   114 234. 42   10. 17 169 1. 60   0. 80 28  50 D
455 Bruchsalia MBA Xk Mes 1.19   0.12   88. 13   6. 89 170 3. 32   0. 84 21  25 C
469 Argentina MBA Xk Mes 4.53   1.76   115 126. 00   4. 91 171 4. 32   1. 75 0  40 C
471 Papagena MBA S OC 3.05   1.73   116 124. 55   8. 77 172 3. 01   1. 82 9  60 D
481 Emita MBA Ch CM 5.78   1.45   107. 23   4. 71 173 8. 95   2. 53 0  28 C
485 Genua MBA S OC 1.36   0.44   56. 31   4. 15 174 14. 53   5. 68 0  39
488 Kreusa MBA Ch CM 2.48   1.14   117 162. 32   9. 54 175 1. 10   0. 54 50  49 C
490 Veritas MBA Ch CM 5.99   2.23   118 110. 96   3. 80 176 8. 37   3. 23 0  38 C
491 Carina MBA X CV 4.82   1.95   97. 36   3. 18 177 9. 97   4. 15 0  41 C
503 Evelyn MBA Ch CM 2.85   0.34   87. 58   3. 58 178 8. 10   1. 38 0  17
505 Cava MBA Xk LL 3.99   3.84   101. 51   1. 83 179 7. 28   7. 02 0  96 D
508 Princetonia MBA X CV 2.99   0.65   119 139. 69   3. 40 180 2. 09   0. 47 25  22 C
511 Davida MBA C CM 3.38   1.02   120 298. 28   11. 92 181 2. 43   0. 79 0  32 C
516 Amherstia MBA X CV 1.43   1.33   69. 84   4. 38 182 8. 01   7. 60 0  94 D
532 Herculina MBA S OC 1.15   0.28   121 217. 49   5. 10 183 2. 12   0. 53 36  25 C
536 Merapi MBA X CV 2.61   0.47   122 155. 17   3. 53 184 13. 36   2. 59 0  19
554 Peraga MBA Ch CI 6.59   0.66   123 96. 46   1. 68 185 1. 40   0. 15 12  11 B
582 Olympia MBA S OC 0.43   1.17   43. 39   1. 49 186 10. 00   27. 35 0 
584 Semiramis MBA S OC 8.23   5.77   51. 78   2. 15 187 11. 31   8. 06 0  71
602 Marianna MBA Ch CM 1.02   0.05   127. 95   2. 86 188 9. 29   0. 76 0  8
604 Tekmessa MBA Xc Mes 1.45   0.28   64. 42   3. 01 189 10. 35   2. 46 0  23
617 Patroclus MBA X CV 1.36   0.11   143. 14   8. 37 190 0. 88   0. 17 68  19 B
624 Hektor MBA X CV 9.95   0.12   226. 68   15. 15 191 1. 63   0. 32 41  20 C
626 Notburga MBA Cb CM 3.24   1.30   124 96. 84   4. 67 192 6. 81   2. 90 0  42 E
654 Zelinda MBA Ch CM 1.35   0.14   127. 83   5. 23 193 1. 23   0. 19 45  15 B
665 Sabine MBA X CV 6.98   3.98   52. 71   0. 72 194 9. 10   5. 20 0  57 E
675 Ludmilla MBA S OC 1.20   0.24   67. 66   0. 94 73. 99   15. 05 0  20
679 Pax MBA L CO 7.14   1.99   64. 88   3. 64 195 4. 99   1. 62 0  32 C
680 Genoveva MBA X CV 2.69   0.04   84. 69   1. 71 196 8. 45   0. 52 0  6
690 Wratislavia MBA B CV 1.28   0.03   146. 21   11. 02 197 7. 81   1. 77 0  22
702 Alauda MBA B CV 6.06   3.60   125 191. 65   8. 22 198 1. 64   0. 99 41  60 D
704 Interamnia MBA B CI 3.28   0.45   126 317. 19   4. 65 199 1. 96   0. 28 0  14 A
720 Bohlinia MBA Sq OC 5.97   0.80   127 34. 64   1. 81 200 2. 74   0. 56 17  20 C
735 Marghanna MBA Ch CM 2.15   0.68   72. 27   2. 22 201 10. 87   3. 56 0  32
739 Mandeville MBA Xc Mes 1.16   1.07   105. 53   1. 68 202 1. 88   1. 74 55  92 D
747 Winchester MBA B CV 3.81   2.22   128 170. 07   6. 70 203 1. 47   0. 87 47  59 D
751 Faina MBA Ch CM 3.27   0.58   129 107. 31   1. 48 204 5. 05   0. 92 0  18 B
758 Mancunia MBA X CV 9.31   0.80   87. 08   1. 31 205 2. 69   0. 26 3  9 B
760 Massinga MBA S OC 1.33   1.32   70. 82   0. 92 206 7. 15   7. 10 0  99 D
762 Pulcova MBA Cb CM 1.40   0.10   130 138. 40   5. 96 207 1. 00   0. 14 55  14 B
769 Tatjana MBA CM 6.31   0.64   106. 27   4. 02 208 10. 03   1. 52 0  15
776 Berbericia MBA Cgh CM 2.20   2.71   131 152. 29   4. 25 209 1. 18   1. 46 47  E
784 Pickeringia MBA C CM 3.74   0.32   82. 52   7. 18 210 12. 70   3. 49 0  27
786 Bredichina MBA C CM 2.82   2.79   98. 34   6. 00 211 5. 66   5. 69 0  E
Table 1: Continued
Designation Class Masses (kg) Diameter (km) Density Porosity Rank
# Name Dyn. Tax. Met. Fig. Fig.
790 Pretoria MBA X CV 4.58   0.28   132 160. 98   11. 16 212 2. 09   0. 45 24  21 C
804 Hispania MBA C CM 5.00   1.78   133 148. 25   4. 08 213 2. 93   1. 06 0  36 C
809 Lundia MBA V HED 9.27   3.09   10. 26   0. 07 1. 64   0. 10 49  6 B
854 Frostia MBA V HED 1.06   0.95   8. 39   1. 27 214 0. 88   0. 13 72  14 B
895 Helio MBA B CV 9.87   6.05   134 148. 43   5. 02 215 5. 76   3. 58 0  62 D
914 Palisana MBA Ch CM 2.35   0.24   81. 27   5. 34 216 8. 36   1. 85 0  22
949 Hel MBA Xk Mes 1.73   0.62   63. 56   4. 01 217 12. 86   5. 19 0  40
1013 Tombecka MBA Xk Mes 0.17   1.43   35. 18   2. 24 218 7. 50   62. 74 0  E
1015 Christa MBA Xc Mes 4.77   0.68   99. 77   2. 46 219 9. 17   1. 46 0  15
1021 Flammario MBA Cb CM 5.14   0.12   99. 27   3. 27 220 10. 03   1. 02 0  10
1036 Ganymed NEA S OC 1.67   3.18   34. 28   1. 38 221 7. 91   15. 10 0 
1089 Tama MBA S OC 8.90   3.20   13. 44   0. 61 222 2. 52   0. 29 24  11 B
1171 Rusthawelia MBA X CV 1.81   0.20   70. 98   2. 42 223 9. 66   1. 45 0  15
1313 Berna MBA S OC 2.25   2.00   13. 93   0. 64 224 1. 21   0. 14 63  11 B
1669 Dagmar MBA Cg CM 3.98   0.80   135 42. 99   2. 86 225 0. 95   0. 27 57  28 C
1686 De Sitter MBA CM 6.76   3.18   30. 60   1. 41 226 450. 51   220. 97 0  49
3169 Ostro MBA Xe EH 1.86   0.62   5. 15   0. 08 2. 59   0. 20 25  7 B
3671 Dionysus NEA Cb CM 8.38   2.79   0. 92   0. 05 227 1. 60   0. 60 28  37 C
3749 Balam MBA S OC 5.09   0.20   6. 99   3. 00 228 2. 83   3. 64 14  E
4492 Debussy MBA CM 3.33   3.00   15. 78   1. 91 229 0. 90   0. 10 60  11 B
5381 Sekhmet NEA S OC 1.04   0.35   1. 00   0. 10 1. 98   0. 65 40  32 C
25143 Itokawa NEA S OC 3.50   0.10   0. 32   0. 01 230 1. 91   0. 21 42  11 A
26308 1998 SM165 TNO Ice 6.78   2.40   284. 37   5. 07 231 0. 56   0. 20 43