Models,figures, and gravitational moments of the Galilean satellites of Jupiter and icy satellites of Saturn

A general theory for the figures of satellites, which are synchronously rotating in the gravitational field of a planet, is developed to the first approximation. Love numbers, figure parameters, and gravitational moments for two- and three-layer models of the Galilean satellites, Titan, and Saturn's icy satellites are calculated. With the assumed accuracy for flyby measurements of gravitational moments it should be possible to determine the degree of differentiation of Ganymede. The differences between equatorial a and polar c semiaxes, as derived from the observational data, appear to be exaggerated for Io and Mimas (although better agreement between calculated and observed values of (a?c) could be obtained if this satellite had a larger mass). For Enceladus the observed value of (a?c) is in satisfactory agreement with calculations, based on different types of trial models. However, in order to discriminate between different Enceladus trial models, it is necessary to determine the figure parameters more precisely.     

The absence of satellites of asteroids

A CCD-imaging survey was made for satellites of minor planets at distances of about 0.1 to 7 arcmin from 1 Ceres, 2 Pallas, 4 Vesta, 6 Hebe, 7 Iris, 8 Flora, 15 Eunomia, 29 Amphitrite, 41 Daphne, and 44 Nysa, with cursory inspection of 192 Nausikaa. Satellites larger than 3 km were not found in this work, nor in previous photographic surveys. Not finding them appears to be consistent with theoretical studies of collisions in the asteroid belt by several authors. The satellites would have to be larger than at least 30 km to be collisionally stable. Tidal effects would lead to synchronous rotation and therefore long periods of rotation (several days), which are not generally observed. Taking tidal stability into account, we conclude that the only possible satellites for main-belt asteroids, with stability over eons, are near-contact binaries. The only other rare possibility for a satellite might be a piece of debris from a recent collision, and it would now be chaotic and collisionally unstable.     

Physicomechanical properties and gravitational deformation of metallic asteroids

A review is given of the mineralogical and chemical composition of iron meteorites and the problems associated with their origin. A detailed discussion is presented of the physical and mechanical properties of iron meteorites and their dependence on the structure, chemical composition, and temperature. Iron meteorites are shown to characterize, with no distortions, the physical and mechanical properties of their parent bodies (metallic asteroids). The population of M-type asteroids and the main characteristics of the identified metallic asteroids are examined. Compared with iron meteorites, metallic asteroids have a different shape and are not fragments of larger metallic parent bodies. The estimates for the current deviatoric stress in metallic asteroids show that, since their formation, asteroids have not been heated to over 600°C and certainly have not been subjected to partial or complete melting. An empirical dependence is found of the critical dimensions of small metallic objects (which allow for gravitational deformation) on the yield strength at temperatures below 300 K. It is shown that the physical and mechanical data are also a strong argument against the hypothesis of the origin of iron meteorites and metallic asteroids from the iron core of a differentiated parent body.     

Shapes and rotational properties of thirty asteroids from photometric data

We have analyzed photometric lightcurves of 30 asteroids, and present here the obtained shapes, rotational periods and pole directions. We also present new photometric observations of five asteroids. The shape models indicate the existence of many features of varying degrees of irregularity. Even large main-belt asteroids display such features, so the resulting poles and periods are more consistent than those obtained by simple ellipsoid-like models. In some cases the new rotational parameters are rather different from those obtained previously, and in a few cases there were no proper previous estimates at all.     

Shapes of the saturnian icy satellites and their significance

The sizes and shapes of six icy saturnian satellites have been measured from Cassini Imaging Science Subsystem (ISS) data, employing limb coordinates and stereogrammetric control points. Mimas, Enceladus, Tethys, Dione and Rhea are well described by triaxial ellipsoids; Iapetus is best represented by an oblate spheroid. All satellites appear to have approached relaxed, equilibrium shapes at some point in their evolution, but all support at least 300 m of global-wavelength topography. The shape of Enceladus is most consistent with a homogeneous interior. If Enceladus is differentiated, its shape and apparent relaxation require either lateral inhomogeneities in an icy mantle and/or an irregularly shaped core. Iapetus supports a fossil bulge of over 30 km, and provides a benchmark for impact modification of shapes after global relaxation. Satellites such as Mimas that have smoother limbs than Iapetus, and are expected to have higher impact rates, must have relaxed after the shape of Iapetus was frozen.     

Radii and Albedos of four Trojan asteroids and Jovian satellites 6 and 7

Thermal radiation has been detected from four asteroids of the Trojan group, and J6 and J7, the brightest of the outer satellites of Jupiter. The six objects all have exceedingly low geometric albedos of 0.02 or 0.03 according to calculations based on their known visual brightness and the measured thermal fluxes. 624 Hektor, the largest object studied here, has a radius of 110 ± 20 km, though the exact shape of this body is in question. While the sample observed in this work is small (the total number of Trojans larger than 0.25 km in radius is about 1000), the fact that all four studied have similarly low albedos suggests that this property is characterisic of the Trojans and at least two of the outer members of Jupiter's retinue of satellites. The low surface albedo of the Trojans may preclude the proposed origin of the Jovian group of comets among these bodies according to E. Rabe. Updated tables of the dimensions of all the Jovian satellites are given.     

Orbital evolution of asteroids with the effects of mutual gravitational attraction

The effects of the mutual gravitational attraction between asteroids were analyzed by two N-body calculations, in which N=4,516 (the Sun, the nine planets, and 4,506 asteroids). In one calculation the gravity of the asteroids was taken into account, and in the other it was ignored. These calculations were carried out for a time period of about 100 years. The largest difference in the positions of the asteroids between these two calculations is about 10^–3 AU. For the orbital elements of the semimajor axis, the eccentricity, and the inclination, the largest differences were 9 × 10^–6 AU, 4 × 10^–6, and 5 × 10^–4 degrees, respectively. It was found that the distribution of the differences of the semimajor axis between the two calculations is quite similar to the Cauchy distribution.     

Orbital evolution of asteroids with the effects of mutual gravitational attraction

The effects of the mutual gravitational attraction between asteroids were analyzed by two N-body calculations, in which N=4,516 (the Sun, the nine planets, and 4,506 asteroids). In one calculation the gravity of the asteroids was taken into account, and in the other it was ignored. These calculations were carried out for a time period of about 100 years. The largest difference in the positions of the asteroids between these two calculations is about 10^?3 AU. For the orbital elements of the semimajor axis, the eccentricity, and the inclination, the largest differences were 9 × 10^?6 AU, 4 × 10^?6, and 5 × 10^?4 degrees, respectively. It was found that the distribution of the differences of the semimajor axis between the two calculations is quite similar to the Cauchy distribution.     

Optimal configurations for dual-spin satellites subject to gravitational torques

Dual-spin or gyrostat satellites subject to gravitational torques can adopt an infinite number of possible equilibria obtained by adjusting the magnitude and direction of the rotor angular momentum within the satellite. This paper seeks to answer the question, which of these equilibria is best — and best is chosen here to mean most stable in the sense that the energy required to perturb the orientation by any prescribed amount is maximized, i.e. the smallest eigenvalue of the Hessian matrix of the dynamic potential energy is maximized. Using this criterion, it is shown that the conventional configuration for dual-spin satellites with the angular momentum of the rotor, the spacecraft principal axis of maximum moment of inertia, and the perpendicular to the orbital plane coincident is not always the best orientation. The optimal configuration is shown to have the minimum moment of inertia always aligned with the local vertical, but the principal axis of maximum moment of inertia, shifts from the perpendicular to the orbital plane to lying in-plane as the angular momentum of the rotor is increased from zero (corresponding to a rigid gravity gradient satellite) to some sufficiently large value which is determined as a function of parameters. For angular momentum greater than this value, global optimality is established analytically, and otherwise local optimality is proved analytically with global optimality demonstrated numerically.     

Can gravitational compaction explain the spin-diameter relation for the asteroids?

Dermott and Murray (1982) have found certain relations between mean spin frequency and mean diameter for asteroids. By assuming that matter gets compacted during the evolution of an asteroid, these relations may be explained by means of a spin formula for accreted bodies given by Alfvén and Arrhenius. We present a rough model for gravitational compaction of porous matter in asteroids, combine it with the spin formula, and fit the result to Dermott's and Murray's spin-diameter curves. The values obtained for the parameters (mass densities and material strengths) appear to be of a quite realistic order of magnitude.     

Significance of gravitational moments for interior structure of Jupiter and Saturn

We present the case for liquid models of Jupiter and Saturn. We then discuss the information which can be obtained about their interior structure from a knowledge of their gravitational moments, and we discuss the nature of presently available data and data which will be necessary to fully exploit future results.     

Determination of the masses of planetary satellites from their mutual gravitational perturbations

We analyze the possibility of determining the masses of outer planetary satellites from their mutual gravitational perturbations via ground-based observations. Such a technique has been applied in (Emelyanov, 2005b) to determine the mass of the Jovian satellite Himalia. In this paper, we use the least-squares method to compute the errors of satellite masses inferred from simulated observations. We analyze several of the most suitable variants of groups of outer satellites of planets with maximum mutual attraction. We found that the mass of the Satumian satellite Phoebe (S9) can be refined by continuing observations of the satellite S25 Mundilfari until 2027. We show that the masses of other known outer planetary satellites cannot be determined from ground-based observations.     

Attitude equilibria of dual spin satellites subject to gravitational torques ofn bodies

We consider the motion of a dual spin satellite placed in the gravitational field of n material points, assuming that the satellite has no influence on the motion of these points. The main bodies are located at the libration points of the classical n bodies problem. We investigate the set of relative equilibria of the satellite. As in the elementary case of a gyrostat attracted by a single point, we show that this problem is equivalent to find the extremum of a quadratic function. We obtain all possible equilibria of the satellite by solving two algebraic equations. Sufficient conditions of stability of these relative equilibria are given.     

New values of gravitational moments J 2 and J 4 deduced from helioseismology

By applying the theory of slowly rotating stars to the Sun, the solar quadrupole and octopole moments J ₂ and J ₄ were computed using a solar model obtained from CESAM stellar evolution code (Morel, 1997) combined with a recent model of solar differential rotation deduced from helioseismology (Corbard et al., 2002). This model takes into account a near-surface radial gradient of rotation which was inferred and quantified from MDI f-mode observations by Corbard and Thompson (2002). The effect of this observational near-surface gradient on the theoretical values of the surface parameters J ₂, J ₄ is investigated. The results show that the octopole moment J ₄ is much more sensitive than the quadrupole moment J ₂ to the subsurface radial gradient of rotation.     

Stabilization due to gyroscopic coupling in dual-spin satellites subject to gravitational torques

The stability of attitude equilibria relative to gravitational torques for a rigid satellite in a circular orbit has been divided into three inertia regions, the Lagrange region of assured Liapunov stability, the Beletskii-Delp region which is often described as stabilized due to gyroscopic coupling, and an assured instability region. The generalization of these regions to the case of dual-spin or gyrostat satellites whose internal spin momentum is along a principal axis is treated here. The stability boundaries are obtained for all possible equilibrium orientations for such vehicles, and the variations of these boundaries corresponding to changes in the internal momentum magnitude, or to aligning the momentum with a different principal axis, are determined.Alexander von Humboldt Research Fellow at the Institut für Mechanik; on sabbatical leave from Columbia University, New York, U.S.A.     

Prediction of satellites in Earth's gravitational field with axial symmetry using Burdet's regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36.A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.Dept. of Astronomy, KAU     

Ejecta exchange and satellite color evolution in the Pluto system, with implications for KBOs and asteroids with satellites

In this Note, I present first-order scaling calculations to examine the efficacy of impacts by Kuiper Belt debris in causing regolith exchange between objects in the Pluto system. It is found that ejecta can escape Nix and Hydra with sufficient velocity to reach one another, as well as Charon, and even Pluto. The degree of ejecta exchanged between Nix and Hydra is sufficient to cover these bodies with much more material than is required for photometrically change. In specific, Nix and Hydra may have exchanged as up to 10s of meters of regolith, and may have covered Charon to depths up to 14 cm with their ejecta. Pluto is likely unaffected by most Nix and Hydra ejecta by virtue of a combination of dynamical shielding from Charon and Pluto's own annual atmospheric frost deposition cycle. As a result of ejecta exchange between Nix, Hydra, and Charon, these bodies are expected to evolve their colors, albedos, and other photometric properties to be self similar. These are testable predictions of this model, as is the prediction that Nix and Hydra will have diameters near 50 km, owing to having a Charon-like albedo induced by ejecta exchange. As I discuss, this ejecta exchange process can also be effective in many KBOs and asteroids with satellites, and may be the reason that very many KBO and asteroid satellite systems have like colors.