A New Determination of the Mass of (1) Ceres

We present result for the mass of (1) Ceres, determined from its close encounter with asteroid (5303) Parijskij. Gravitational effects of (1) Ceres on the motion of (5303) Parijskij is the largest found so far. Also, we analyzed available data of close encounter with (7298) 1992 WM5.     

On three types of fragmentation processes observed in the asteroid belt

From comparison of the mass ratio and velocity dispersion between the asteroid family members, we find that the fragmentation processes in the asteroid belt could be generally classified into three types: (a) surface cratering; (b) spallation; and (c) complete breakup as observed in the laboratory hypervelocity impact experiments. Whether there is ongoing accretion for large bodies like Ceres, as an additional type of collision process, is still an open question to be answered by further study.     

On the composition of ices incorporated in Ceres

We use the clathrate hydrate trapping theory and gas drag formalism to calculate the composition of ices incorporated in the interior of Ceres. Utilizing a time-dependent solar nebula model, we show that icy solids can drift from beyond 5 au to the present location of the asteroid and be preserved from vaporization. We argue that volatiles were trapped in the outer solar nebula in the form of clathrate hydrates, hydrates and pure condensates prior to having been incorporated in icy solids and subsequently in Ceres. Under the assumption that most of volatiles were not vaporized during the accretion phase and the thermal evolution of Ceres, we determine the per mass abundances with respect to H₂O of CO₂, CO, CH₄, N₂, NH₃, Ar, Xe and Kr in the interior of the asteroid. The Dawn space mission, scheduled to explore Ceres in August 2014, may have the capacity to test some predictions. We also show that an in situ measurement of the D/H ratio in H₂O in Ceres could constrain the distance range in the solar nebula where its icy planetesimals were produced.     

Radar observations of asteroid 1 Ceres

Radar observations of asteroid 1 Ceres were made at a 12.6-cm wavelength from the Arecibo Observatory in March/April 1977. The measurements, made with a received circular polarization orthogonal to that transmitted, yield a radar cross section of (0.04 ± 0.01)πR², for R = 510 km. The corresponding radar reflectivity is less than that measured for any other celestial body. Within the accuracy of measurement, no significant variation of cross section with rotational phase is apparent. The shape of the power spectrum suggests that Ceres is rougher at the scale of the observing wavelength than the Moon and inner planets, but smoother than the outer three Galilean satellites.     

The 1.7- to 4.2-μm spectrum of asteroid 1 Ceres: Evidence for structural water in clay minerals

A high-resolution Fourier spectrum (1.7–3.5 μm) and medium-resolution spectrophotometry (2.7–4.2 μm) were obtained for Asteroid 1 Ceres. The presence of the 3-μm absorption feature due to water of hydration was confirmed. The 3-μm feature is compared with the 3-μm bands due to water of hydration in clays and salts. It is concluded that the spectrum of Ceres shows a strong absorption at 2.7–2.8 μm due to structural OH groups in clay minerals. The dominant minerals on the surface of Ceres are therefore hydrated clay minerals structurally similar to terrestrial montmorillonites. There is also a narrow absorption feature at 3.1 μm which is attributable to a very small amount of water ice on Ceres. This is the first evidence for ice on the surface of an asteroid.     

Determining asteroid masses from perturbations on Mars

The orbit of Mars is perturbed more than 5 m, a value compatible with the accuracy of the Viking lander ranging data, by about three dozen asteroids. In addition to larger asteroids throughout the belt, significant perturbations of long period are generated by smaller objects near commensurabilities with Mars. The largest periodic terms induced by 1 Ceres and 2 Pallas have amplitudes of 0.8 and 0.2 km, respectively, both with 10-year periods. Due to a near commensurability, 4 Vesta causes a 5-km, 52-year term. While the Viking ranges will yield significant mass determinations for the largest three asteroids, and some of the smaller bodies should be detectable, it will be difficult to seperate the smaller bodies with useful accuracies. Accurate discrimination must await range data from future missions to Mars or other bodies in the neighborhood of the asteroid belt. The Viking ranges can also yield improved masses for the outer planets (except Pluto), an application which is being exploited by groups analyzing these data. Uncertainties in the asteroid masses limit the ultimate accuracy of the Viking determinations of both the long time scale motion of the system the inner four planets with respect to an inertial frame and the rate of change of the gravitational constant.     

A Semianalytical Method for Constructing Nearly Equatorial Orbits of Hypothetical Satellites of Asteroids with an Almost Spheroidal Shape

Solar System Research - The problem of the motion of a particle with a negligible mass (satellite) near the equatorial plane of a spheroidal body, in particular, an asteroid, is considered. To a...     

Asteroids 1 ceres and 4 vesta: Objects of the Dawn space mission

The Dawn spacecraft of the NASA space mission to asteroids 1 Ceres and 4 Vesta was launched in September 2007. The choice of these two asteroids is deeply grounded: they are the largest and most massive objects of the main belt that are completely different in material composition, evolution history, and internal structure. Recently, the results of observations and numerical modeling have shown their amazing uniqueness: they both have experienced the complex process of thermal evolution and differentiation of their internal mineral resources, but have a completely different internal structure. Being the largest bodies, have they managed to resist the process of collisional evolution in the asteroid belt and have survived in their “primitive form.” Because of this, their study is very important from the point of view of cosmogonic problems regarding the asteroid belt and the Solar System as a whole. The present paper shortly reviews the recent progress in the study of Ceres and Vesta achieved due to observations performed on the Earth (including the polarimetric observations made by the authors) and from the Hubble Space Telescope (HST) before the long-term orbital investigations performed by the Dawn spacecraft.     

Radar observations of asteroid 1999 JM8

Abstract— We report results of delay‐Doppler observations of 1999 JM8 with the Goldstone 8560 MHz (3.5 cm) and Arecibo 2380 MHz (13 cm) radars over 18 days in July‐August 1999. The images place thousands of pixels on the asteroid and achieve range resolutions as fine as 15 m/pixel. The images reveal an asymmetric, irregularly shaped object with a typical overall dimension within 20% of 7 km. If we assume that 1999 JM8's effective diameter is 7 km, then the absolute magnitude, 15.15, and the average Goldstone radar cross section, 2.49 km², correspond to optical and radar albedos of 0.02 and 0.06, establishing that 1999 JM8 is a dark object at optical and radar wavelengths. The asteroid is in a non‐principal axis spin state that, although not yet well determined, has a dominant periodicity of ?7 days. However, images obtained between July 31 and August 9 show apparent regular rotation of features from day to day, suggesting that the rotation state is not far from principal axis rotation. 1999 JM8 has regions of pronounced topographic relief, prominent facets several kilometers in extent, numerous crater‐like features between ?100 m and 1.5 km in diameter, and features whose structural nature is peculiar. Arecibo images provide the strongest evidence to date for a circular polarization ratio feature on any asteroid. Combined optical and radar observations from April 1990 to December 2000 permit computation of planetary close approach times to within ± 10 days over the interval from 293 to at least 2907, one of the longest spans for any potentially hazardous asteroid. Integration of the orbit into the past and future shows close approaches to Earth, Mars, Ceres, and Vesta, but the probability of the object impacting Earth is zero for at least the next nine centuries.     

The celestial bodies motion theories: on the required accuracy of the motion theories of the perturbing bodies

The equation for calculation of the required accuracy of the perturbing bodies motion theories is obtained. The equation relates the accuracy required to take into account perturbing acceleration, acting on the perturbed body, with the accuracy of the motion theory of the perturbing body. The solutions for estimation of the required accuracy both for the inner and the external cases in the spherical coordinates are coincided. The solution for the calculation of the required accuracy for the general case (combining the inner and the external cases) in Cartesian coordinates is obtained. The special cases for the solution in Cartesian coordinates are studied. As an example, the estimations of the required accuracy of the motion theories of the solar system planets for some perturbed bodies (the near-Earth asteroid 4179 Toutatis, the main belt asteroid 208 Larcimosa, the trojan asteroid 588 Achilles, the centaur asteroid 5145 Pholus, the Kuiper belt asteroid 1995 QZ9, the comet Halley) are obtained. The conditions of the use of the obtained results are discussed.     

Influence of the largest asteroids on the orbital motions of terrestrial planets: application to the Earth and Mars

The level of precision of modern numerical ephemeris of the Solar System necessitates taking into account the gravitational influence of the largest asteroids on the terrestrial planets. This can be done in a straightforward manner when assuming that the mass of the asteroid is well known. Nevertheless, this is rarely the case, even for the largest asteroids. In this paper, we use recent determinations of the masses of Ceres, Pallas, and Vesta to both qualitatively and quantitatively determine the action of these asteroids on the orbital parameters of the Earth and Mars. This is done by the numerical integration by comparing the orbital motions of the perturbed planet when adding or not the perturbing asteroid to the classical 9 bodies problem (the Sun + the eight planets). Some preliminary results are discussed. Published in Russian in Astronomicheskii Vestnik, 2009, Vol. 43, No. 1, pp. 83–86. The text was submitted by the autors in English.     

Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite

Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body–full body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth Factor of Nearby Orbits). We present stability maps in the plane (\fracbd, \fraccd){\left(\frac{b}{d}, \frac{c}{d}\right)} where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1 : 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed.     

The magmatic activity on asteroids

The tidal effects on a fractured asteroid are considered. The asteroid is assumed to consist of two parts. In gravitational field of another body the motion of one part of the asteroid in relation to second part may be initiated. The necessary conditions for this motion are determined and amount of heat that can be generated is calculated for some cases. It is suggested that metamorphic episodes found in some meteorites are the results of such heating.     

Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison

The discovery of the asteroid Ceres by Piazzi in 1801 motivated the development of a mathematical technique proposed by Gauss, (Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, 1963) which allows to recover the orbit of a celestial body starting from a minimum of three observations. Here we compare the method proposed by Gauss (Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, New York, 1963) with the techniques (based on three observations) developed by Laplace (Collected Works 10, 93–146, 1780) and by Mossotti (Memoria Postuma, 1866). We also consider another method developed by Mossotti (Nuova analisi del problema di determinare le orbite dei corpi celesti, 1816–1818), based on four observations. We provide a theoretical and numerical comparison among the different procedures. As an application, we consider the computation of the orbit of the asteroid Juno.     

Asteroid sizes and albedos

The radiometric method of determining diameters of asteroids is reviewed, and a synthesis of radiometric and polarimetric measurements of the diameters and geometric albedos of a total of 187 asteroids is presented. All asteroids with diameters greater than 250 km are identified, and statistical studies can be carried out of the size distributions of different albedo classes down to 80-km diameter for the entire main asteroid belt (2.0–3.5 AU). The distribution of albedos is strongly bimodal, with mean albedos for the C and S groups of 0.035 and 0.15, respectively. The C asteroids outnumber the S at all sizes and all values of semi-major axis, increasing from a little over half the population inside 2.5 AU to more than 95% beyond 3.0 AU; for all objects with D > 70 km, the ratio C/(C+S) is 0.88 ± 0.04. More than half of all asteroids in this size range have a > 3.0 AU. The M asteroids constitute about 5% of the population for a < 3.0 AU, but no members of of this class have been identified in the outer belt. There are no significant differences between the distributions of C, S, and M asteroids for the largest asteroids (D > 200 km) and for those of intermediate size (200–270 km). The total mass in the belt, down to 70-km size, but excluding Ceres, is about 2 × 10²⁴ g. Evidence is presented that several large asteroids rotate in a prograde sense, and that a real difference existsbetween the bulk densities of Ceres and Vesta.     

Radii and albedos of asteroids 1, 2, 3, 4, 6, 15, 51, 433, and 511

We derive the following radii (in kilometers) and visual geometric albedos for nine asteroids from 10- and 20-μm radiometry: 1 Ceres (540, .16); 2 Pallas (275, .08); 3 Juno (125, .14); 4 Vesta (270, .21); 6 Hebe (110, .16); 15 Eunomia (135, .15); 51 Nemausa (80, .05); 433 Eros (12, .07); and 511 Davida (180, .04). Vesta has the highest albedo measured for an asteroid, while Davida, the lowest-albedo object in the sample, is one of the darkest known objects in the solar system. The median of all asteroid albedos measured to date is 0.1.     

Orbital dynamics and equilibrium points around an asteroid with gravitational orbit–attitude coupling perturbation

The strongly perturbed dynamical environment near asteroids has been a great challenge for the mission design. Besides the non-spherical gravity, solar radiation pressure, and solar tide, the orbital motion actually suffers from another perturbation caused by the gravitational orbit–attitude coupling of the spacecraft. This gravitational orbit–attitude coupling perturbation (GOACP) has its origin in the fact that the gravity acting on a non-spherical extended body, the real case of the spacecraft, is actually different from that acting on a point mass, the approximation of the spacecraft in the orbital dynamics. We intend to take into account GOACP besides the non-spherical gravity to improve the previous close-proximity orbital dynamics. GOACP depends on the spacecraft attitude, which is assumed to be controlled ideally with respect to the asteroid in this study. Then, we focus on the orbital motion perturbed by the non-spherical gravity and GOACP with the given attitude. This new orbital model can be called the attitude-restricted orbital dynamics, where restricted means that the orbital motion is studied as a restricted problem at a given attitude. In the present paper, equilibrium points of the attitude-restricted orbital dynamics in the second degree and order gravity field of a uniformly rotating asteroid are investigated. Two kinds of equilibria are obtained: on and off the asteroid equatorial principal axis. These equilibria are different from and more diverse than those in the classical orbital dynamics without GOACP. In the case of a large spacecraft, the off-axis equilibrium points can exist at an arbitrary longitude in the equatorial plane. These results are useful for close-proximity operations, such as the asteroid body-fixed hovering.     

Computer simulation of the formation of asteroid belt structure

The system of two gravitational centers with variable separation between components one of which (the primary) loses its mass onto another (the secondary) is investigated under condition of total mass and angular momentum conservation. When the primary/secondary mass ratio becomes about that of Jupiter/Sun the small bodies ejected with the gaseous matter through the inner Lagrange point from the Roche lobe of the primary form a ring similar to the asteroid belt of the solar system. The formation of ring structure is calculated by numerical integration of Newtonian equations of N-body problem in orbital plane of the gravitational centers. The results are compared with the planar subsystem of the asteroid belt. The presence of the main gaps in the distribution of their mean motions at 2/1, 3/1, 5/2 and some other commensurabilities with the primary mean motion is found. More fine details of the belt structure are obtained, e.g. the gap asymmetry and a qualitative agreement with the eccentricity distribution. Within the scope of the same model the external part of the ring is investigated all the pairwise interactions being included. The clustering of bodies near 3/2 commensurability isolated from the main belt by the wide gap centered at 5/3 commensurability is obtained. It is supposed that the ring structure and the interplanetary spacing law for the terrestrial planets are due to the same mechanism.     

On the stability of circular ‘asteroid’ orbits in anN-planetary system

The restricted problem of the motion of a point of negligible mass (asteroid) in anN-planetary system is considered. It is assumed that all the planets move about the central body (Sun) along circular orbits in the same plane and the mean motions of the asteroid and the planets are incommensurable. The asteroid orbit evolution is described as a first approximation by secular equations with the perturbing function averaged by the mean longitudes of the asteroid and the planets. For small values of the asteroid orbit eccentricity an expression for the secular part of the perturbing function has been obtained. This expression holds for the arbitrary values of the asteroid orbit semiaxis which are different from those of the planet orbit radii. The stability of the asteroid circular orbits in a linear approximation with respect to the eccentricity is studied. The critical inclinations for a Solar system model are calculated.     

The composition of asteroid 2 Pallas and its relation to primitive meteorites

High resolution spectroscopic observations of asteroid 2 Pallas from 1.7-3.5 μm are reported. These data are combined with previous measurements from 0.4-1.7 μm to interpret Pallas' surface mineralogy. Evidence is found for low-Fe²⁺ hydrated silicates, opaque components, and low-Fe²⁺ anhydrous silicates. This assemblage is very similar to carbonaceous chondrite matrix material such as is found in type CI and CM meteorites, but it has been subjected to substantial aqueous alteration and there is a major extraneous anhydrous silicate component. This composition is compared to that of asteroid 1 Ceres. Although there are substantial differences in their broad band spectral reflectances, it appears that both asteroids are genetically related to known carbonaceous chondrites.