Inelastic Dissipation in Wobbling Asteroids and Comets

Asteroids and comets dissipate energy when they rotate about the axis different from the axis of the maximal moment of inertia. We show that the most efficient internal relaxation happens at the double frequency of body's tumbling. Therefore the earlier estimates that ignore double frequency input underestimate the internal relaxation in asteroids and comets. We show that the Earth seismological data may poorly represent acoustic properties of asteroids and comet as internal relaxation increases in the presence of moisture. At the same time owing to non-linearlity of inelastic relaxation small angle nutations can persist for very long time spans, but our ability to detect such precessions is limited by the resolution of the radar-generated images. Wobbling may provide valuable information on the composition and structure of asteroids and on their recent history of external impacts.Comment: 20 pages, 1 figur

Radar Investigations of Asteroids

Radar investigations of asteroids, including observations during 1984 to 1985 of at least 8 potential targets and continued analyses of radar data obtained during 1980 to 1984 for 30 other asteroids is proposed. The primary scientific objectives include estimation of echo strength, polarization, spectral shape, spectral bandwidth, and Doppler shift. These measurements yield estimates of target size, shape, and spin vector; place constraints on topography, morphology, density, and composition of the planetary surface; yield refined estimates of target orbital parameters; and reveals the presence of asteroidal satellites

Radar investigation of asteroids

The dual polarization CW radar system which permits simultaneous reception in the same rotational sense of circular polarization as transmitted (i.e., the "SC" sense) and in the opposite ("OC") sense, was used to observe five previously unobserved asteroids: 2 Pallas, 8 Flora, 22 Kalliope, 132 Aethra, and 471 Papagena. Echoes from Pallas and Flora were easily detected in the OC sense on each of several nights. Weighted mean echo power spectra also show marginally significant responses in the SC sense. An approximately 4.5 standard deviation signal was obtained for Aethra. The Doppler shift of the peak is about 10 Hz higher than that predicted from the a priori trial ephemeris. Calculations are performed to determine whether this frequency offset can be reconciled dynamically with optical positions reported for Aethra

Radar investigation of asteroids and planetary satellites

The aim is to make radar reconnaissance of near-Earth asteroids, mainbelt ateroids, the Galilean satellites, the Martian satellites, and the largest Saturnian satellites, using the Arecibo 13-cm and the Goldstone 3.5-cm systems. Measurements of echo strength, polarization, and delay/Doppler distribution of echo power provide information about dimensions, spin vector, large-scale topography, cm-to-m-scale morphology, and surface bulk density. The observations also yield refined estimates of target orbital elements. Radar signatures were measured for 31 mainbelt asteroids and 16 near-Earth asteroids since this task began eight years ago. The dispersion in asteroid radar albedoes and circular polarization ratios is extreme, revealing huge differences in surface morphologies, bulk densities, and metal concentration. For the most part, correction between radar signature and VIS/IR class is not high. Many near-Earth asteroids have extremely irregular, nonconvex shapes, but some have polar silhouettes that appear only slightly noncircular. The signatures of 1627 Ivar, 1986 DA, and the approximately 180-km mainbelt asteroid 216 Kleopatra suggest bifurcated shapes. Observational milestones during 1987 and 1988 are noted

Asteroid lightcurve inversion

One of the most fundamental physical properties of any asteroid is its shape. Lightcurves provide the only source of shape information for most asteroids. Unfortunately, the functional form of a lightcurve is determined by the viewing/illumination geometry and the asteroid's light scattering characteristics as well as its shape, and in general it is impossible to determine an asteroid's shape from lightcurves. A technique called convex-profile inversion (CPI) that obtains a convex profile, P, from any lightcurve is introduced. If certain ideal conditions are satisfied, then P is an estimator for the asteroid's mean cross section, C, a convex set defined as the average of all cross sections C(z) cut by planes a distance z above the asteroids's equatorial plane. C is therefore a 2-D average of the asteroid's 3-D shape

Bose Condensation and Temperature

A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity.Comment: 4 pages, 5 figure

The shape of asteroid 1917 Cuyo

Lightcurves obtained for 1917 Cuyo at solar phase angles near 54 degrees have an amplitude delta m = 0.44 mag. However, convex-profile inversion of the lightcurves yields an estimate of the asteroid's mean cross section (C, a 2-D average of the 3-D shape) that is only slightly noncircular, with an elongation approximately 1.15. The estimate of C undoubtedly contains systematic errors, the most severe of which could arise from non-equatorial viewing/illumination geometry. However, Cuyo's radar echo shows very little variation in bandwidth vs. rotation phase, supporting the hypothesis that this asteroid's elongation is rather modest

Relaxation of Wobbling Asteroids and Comets. Theoretical Problems. Perspectives of Experimental Observation

A body dissipates energy when it freely rotates about any axis different from principal. This entails relaxation, i.e., decrease of the rotational energy, with the angular momentum preserved. The spin about the major-inertia axis corresponds to the minimal kinetic energy, for a fixed angular momentum. Thence one may expect comets and asteroids (as well as spacecraft or cosmic-dust granules) stay in this, so-called principal, state of rotation, unless they are forced out of this state by a collision, or a tidal interaction, or cometary jetting, or by whatever other reason. As is well known, comet P/Halley, asteroid 4179 Toutatis, and some other small bodies exhibit very complex rotational motions attributed to these objects being in non-principal states of spin. Most probably, the asteroid and cometary wobble is quite a generic phenomenon. The theory of wobble with internal dissipation has not been fully developed as yet. In this article we demonstrate that in some spin states the effectiveness of the inelastic-dissipation process is several orders of magnitude higher than believed previously, and can be measured, by the presently available observational instruments, within approximately a year span. We also show that in some other spin states both the precession and precession-relaxation processes slow down considerably. (We call it near-separatrix lingering effect.) Such spin states may evolve so slowly that they can mimic the principal-rotation state.Comment: 2 figure

Precession of a Freely Rotating Rigid Body. Inelastic Relaxation in the Vicinity of Poles

When a solid body is freely rotating at an angular velocity ${\bf \Omega}$, the ellipsoid of constant angular momentum, in the space $\Omega_1, \Omega_2, \Omega_3$, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behaviour, because an infinitesimally small deviation of the body's shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body's precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed.Comment: 47 pages, 1 figur