Asteroid Rotation Research Articles

The dynamics of globally active triaxial comets, with applications to asteroid rotation

It is demonstrated how globally distributed outgassing activity on a triaxial comet nucleus bridges the gap between the intuitive Sekanina model, used for comet orbit solutions, and the physics of the problem. In this activity and shape limit, it is shown how a recoil force component, which originates from a day-side restricted sublimation process, is necessary to describe the comet's rotational evolution. Modifications of the non-gravitational force cosines are suggested, with a fundamentally different interpretation than before. Applications to asteroid rotation yield that the ability of specular reflection, of solar photons on an asteroid's surface, to change the asteroid's rotation period and equatorial obliquity, is not dependent on the overall shape of the asteroid.

Direct measurement of the size, shape, and pole of 511 Davida with Keck AO in a single night

Using the high-quality data set of 165 images taken at 11 epochs over the 5.13 h rotation of the large C-type Asteroid 511 Davida, we find the dimensions of its triaxial ellipsoid model to be 357 ± 2 × 294 ± 2 × 231 ± 50 km . The images were acquired with the adaptive optics system on the 10 m Keck II telescope on December 27, 2002. The a and b diameters are much better determined than previously estimated from speckle interferometry and indirect measurements, and our mean diameter, ( a b c ) 1 / 3 = 289 ± 21 km , is 19% below previous estimates. We find the pole to lie within 2° of [ RA = 295 ° ; Dec = 0 ° ] or in Ecliptic coordinates [ λ = 297 ° ; β = + 21 ° ], a significant improvement to the pole direction. Otherwise, previous determinations of the axial ratios agree with our new results. These observations illustrate that our technique of finding the dimensions and pole of an asteroid from its changing projected size and shape is very powerful because it can be done in essentially one night as opposed to decades of lightcurves. Average departures of 3% (5 km) of the asteroid's mean radius from a smooth outline are detected, with at least two local positive-relief features and at least one flat facet showing approximately 15 km deviations from the reference best-fit ellipsoid. The facet is reminiscent of large global-scale craters on Asteroid 253 Mathilde (also a C-type) when seen edge-on in close-up images from the NEAR mission flyby. We show that giant craters (up to 150 km diameter, the size of the largest facets seen on Davida) can be expected from the impactor size distribution, without likelihood of catastrophic disruption of Davida.

Acceleration of the rotation of asteroid 1862 Apollo by radiation torques

The anisotropic reflection and thermal re-emission of sunlight from an asteroid's surface acts as a propulsion engine. The net propulsion force (Yarkovsky effect) changes the orbital dynamics of the body at a rate that depends on its physical properties; for irregularly shaped bodies, the propulsion causes a net torque (the Yarkovsky-O'Keefe-Radzievskii-Paddack or YORP effect) that can change the object's rotation period and the direction of its rotation axis. The Yarkovsky effect has been observed directly, and there is also indirect evidence of its role in the orbital evolution of asteroids over long time intervals. So far, however, only indirect evidence exists for the YORP effect through the clustering of the directions of rotation axes in asteroid families. Here we report a change in the rotation rate of the asteroid 1862 Apollo, which is best explained by the YORP mechanism. The change is fairly large and clearly visible in photometric lightcurves, amounting to one extra rotation cycle in just 40 years even though Apollo's size is well over one kilometre. This confirms the prediction that the YORP effect plays a significant part in the dynamical evolution of asteroids.

Canonical rotation variables and non-Hamiltonian forces: solar radiation pressure effects on asteroid rotation

The differential equations for canonical rotation variables are formulated as functions of the torque components on the principal axes of a rigid body. The resulting structure of the equations is. then used to prove that solar photons absorbed by a body orbiting the Sun are not able to change the body's rotation state, if the absorption is uniform across its surface. Otherwise, a tendency induced by the absorbed photons could be to drive the spin axis into the body's orbit plane while the rotation period is increased, consistent with observations of Eros. The ability of this radiation pressure to change the rotational excitation could be as important as that due to inelastic energy dissipation for subkilometre asteroids.

Kharkiv study of near-Earth asteroids

AbstractThe regular CCD observations of near-Earth asteroids (NEAs) in the Institute of Astronomy of Kharkiv National University were initiated in 1995 within the framework of asteroid hazard problem in collaboration with the DLR, Institute of Planetary Research (Berlin). The main aim of the study is a determination of rotation periods and shapes of NEAs as well as astrometry of newly discovered objects. We also carry out the absolute photometry of NEAs inBVRIbands in order to put constraints on surface properties and to estimate their diameters. The observations are carried out with 0.7-m telescope of the Institute of Astronomy (Kharkiv) and with 1-m telescope of the Crimean Astrophysical Observatory (Simeiz) in the standard Johnson-Cousins photometric system. Some observations were made as an optical support of radar observation of NEAs. We present the results of photometric observations of 21 NEAs obtained in 2004-2006 which include asteroid rotation properties, diameters and shapes.

Tidal encounters of ellipsoidal granular asteroids with planets

We investigate planetary fly-bys of asteroids using an approximate volume-averaged method that offers a relatively simple, but very flexible, approach to study the rotational dynamics of ellipsoids. The asteroid is considered to be a deformable, prolate ellipsoid, with its interior being modeled as a rigid-granular material. Effects due to the asteroid's rotation, its self-gravity and gravitational interaction with the planet are included. Using a simplified approach allows us to explore in detail the mechanics of asteroid's deformations and disruptions during planetary encounters. We also compare our results with those obtained by Richardson et al. [Richardson, D.C., Bottke Jr., W.F., Love, S.G., 1998. Icarus 134, 47–76] who used a large numerical code. We find that many of the features reported by them can indeed be captured by our rather simple methodology, and we discuss the reasons why some of our results differ from theirs.

Physical properties of Asteroid (25143) Itokawa—Target of the Hayabusa sample return mission

We present results of a ground-based observational study of the Hayabusa mission target near-Earth Asteroid (25143) Itokawa. Our data consist of BVRI-filter CCD photometry and low resolution CCD spectroscopy, from which the asteroid's rotation period, axial ratio, broadband colors, and taxonomic classification are derived. Analysis of the R-filter lightcurve data shows a synodic rotation period of 12.12 ± 0.02 h , consistent with results from other observers. We observed a maximum peak-to-peak amplitude of 1.05 magnitudes, which—depending on the taxonomic class assumed when correcting for phase angle effects—implies a minimum axial ratio of 2.14. The shape of the rotation lightcurves varies considerably between data sets due to the changing viewing geometry. The lightcurve data from this study has been included in the shape model analysis of Kaasalainen et al. (2003 Astron. Astrophys, 405, L29–L32) and the Hapke analysis of Lederer et al. (2005 Icarus 173,153–165). Color variations were also observed, with the interpolated color indices at lightcurve midpoint being: ( B–V ) = 0.94 ± 0.05 , ( V–R ) = 0.40 ± 0.06 , and ( V–I ) = 0.74 ± 0.07 . Our low resolution Palomar spectra from March 2001 covered a wavelength range of 0.3–1.0 μm. We measured a spectral slope of 9.3 ± 0.3 % / 100 nm between 0.55–0.70 μm and a deep 1 μm absorption (equivalent ECAS color: w – x = − 0.111 ± 0.003 , v – x = 0.031 ± 0.003 ). Comparison of our spectra with published ECAS data from Zellner et al. (1985 Icarus 61, 355–416) indicates that this object is most likely of Q- or S-type, similar to ordinary chondrite meteorites. Our data are more consistent with a Q-type body when both the spectroscopic data and the available BVRI photometry are taken into account.

Geometric mechanics and the dynamics of asteroid pairs.

The purpose of this paper is to describe the general setting for the application of techniques from geometric mechanics and dynamical systems to the problem of asteroid pairs. The paper also gives some preliminary results on transport calculations and the associated problem of calculating binary asteroid escape rates. The dynamics of an asteroid pair, consisting of two irregularly shaped asteroids interacting through their gravitational potential is an example of a full-body problem or FBP in which two or more extended bodies interact. One of the interesting features of the binary asteroid problem is that there is coupling between their translational and rotational degrees of freedom. General FBPs have a wide range of other interesting aspects as well, including the 6-DOF guidance, control, and dynamics of vehicles, the dynamics of interacting or ionizing molecules, the evolution of small body, planetary, or stellar systems, and almost any other problem in which distributed bodies interact with each other or with an external field. This paper focuses on the specific case of asteroid pairs using techniques that are generally applicable to many other FBPs. This particular full two-body problem (F2BP) concerns the dynamical evolution of two rigid bodies mutually interacting via a gravitational field. Motivation comes from planetary science, where these interactions play a key role in the evolution of asteroid rotation states and binary asteroid systems. The techniques that are applied to this problem fall into two main categories. The first is the use of geometric mechanics to obtain a description of the reduced phase space, which opens the door to a number of powerful techniques, such as the energy-momentum method for determining the stability of equilibria and the use of variational integrators for greater accuracy in simulation. Second, techniques from computational dynamic systems are used to determine phase space structures that are important for transport phenomena and dynamic evolution.

The vector alignments of asteroid spins by thermal torques.

Collisions have been thought to be the dominant process altering asteroid rotations, but recent observations of the Koronis family of asteroids suggest that this may be incorrect. This group of asteroids was formed in a catastrophic collision several billion years ago; in the intervening period their rotational axes should have become nearly random because of subsequent collisions, with spin rates that follow a maxwellian distribution. What is seen, however, is that the observed family members with prograde spins have nearly identical periods (7.5-9.5 h) and obliquities between 42 and 50 degrees, while those with retrograde spins have obliquities between 154 and 169 degrees with periods either <5 h or >13 h. Here we show that these non-random orientations and spin rates can be explained by 'thermal torques' (arising from differential solar heating), which modify the spin states over time. In some cases, the asteroids become trapped in spin-orbit resonances. Our results suggest that thermal torques may be more important than collisions in changing the spin states (and possibly shapes) of asteroids with diameters <40 km.

Rotation and photometric properties of E-type asteroids

The results of photometric observations of seven E-type asteroids 64 Angelina, 214 Aschera, 1025 Riema, 1103 Sequoia, 1251 Hedera, 2035 Stearns, and 2248 Dwornik are presented. New rotation periods have been determined for asteroids 1025 Riema (6.557±0.001 h) , 1251 Hedera (15.015±0.010 h) , 2035 Stearns (85.0±0.1 h ), and 2048 Dwornik (3.664±0.001 h) . Two new poles have been estimated for 214 Aschera (274±8°; 64±4°) and 1025 Riema (141±10°, 11±6°) and pole has been redefined for 64 Angelina (138±10°, 31±5°). Using all available data on rotation periods, the spin rates of E-type asteroids have been analyzed. The distribution of the spin rates has maximum corresponding to the period of about 6.2 h . The shapes of E-asteroids are more elongated than the shapes of small-size S-asteroids. The average values of color indexes, albedo and G parameter for E-type asteroids have also been determined.

The effect of falling particles on the shape and spin rate of an asteroid

This simulation is focused on the specific influence of the gravitational field of a very elongated rotating asteroid on the location of zones of the most intensive bombardment by falling particles. It is assumed that the particles are distributed uniformly in the space surrounding the asteroid. The asteroid shape is approximated by a triaxial ellipsoid with semiaxes 28,12,10.5 (equal to those of asteroid 243 Ida) and by a dumb-bell of the same mass. The computations and appropriate figures show that at a rotation period faster than approximately 9.1 hours for the triaxial ellipsoid model and 3.3 hours for the dumb-bell one the leading sides of the asteroid receive a higher flux of impacting particles than the trailing sides while at slower periods the situation is the opposite. The zones of possible erosion are computed depending on the asteroid rotation period and on the ratio of impact and rebound velocities of particles. The contribution of all impacting particles to the angular momentum of the asteroid is computed, which leads to the conclusion that falling out of particles damps the asteroid rotation at any spin period.

Statistical evidence for fast and slow asteroid rotations using Bayesian methods

Asteroid rotation rates have been analysed by many authors in the past. The statistical results and physical interpretations of the models have varied widely. Bayesian statistics are used here to analyse the rotation rates of 749 asteroids. The larger asteroids are best fitted with a single Maxwellian distribution while the smaller asteroids are fitted by a mixture of Maxwellian distributions. The optimal separation point, determined by the data fit, occurred around 33 km. The smaller asteroids are composed of a mixture of four Maxwellians corresponding to populations of slow rotators, fast rotators and a population identical to the larger asteroids.

Energy and Stress Distributions in Ellipsoids

A closed form solution for a uniform, isotropic, homogenous, rotating, and self-gravitating solid ellipsoid is analyzed as a function of its material properties and angular momentum. This solution recovers the classical results for an incompressible material, namely that Maclaurin and Jacobi ellipsoids minimize the total strain energy of an ellipsoid. As the solid becomes compressible we find that Maclaurin-type spheroids are energetically preferred over all relevant values of angular momentum, although the gradient toward these spheroids is weak, at best. Compressibility allows the weak minima to encompass most observed asteroid shapes. Using this solution, a simple failure criterion of maximum principal stress is examined. Under this failure criterion, an ellipsoid rotating at a sufficiently rapid rate can have positive stress on the periphery and in the polar regions. Contours for this failure theory are compared with estimated asteroid rotation rates and ellipsoidal shape estimates. For compressible materials there is surprisingly good correspondence for such a simple theory and criterion, with the failure curve delimiting a demarcation that few observed asteroids cross. This research has implications for the shapes and distortions of rubble pile asteroids. In particular, the theory gives insight into the internal stress field and the effects of energy dissipation in an asteroid after it has been boosted into a nonminimum energy configuration due to an impact event or a close flyby with a planet. Internally there are double-lobed compressive stress regions reminiscent of the external shape of Kleopatra.

Spacecraft Motion About Slowly Rotating Asteroids

Spacecraft motion about an arbitrary second-degree and second-order gravity eeld is investigated. We assume thatthegravityeeldisinuniformrotation aboutanaxisofitsmaximummomentofinertiaandthatitrotatesslowly as compared to the spacecraft orbit period. We derive the averaged Lagrange planetary equations for this system and use them, in conjunction with the Jacobi integral, to give a complete description of orbital motion. We show that, under the averaging assumptions, the problem is completely integrable and can be reduced to quadratures. For the case of no rotation, these quadratures can be expressed in terms of elliptic functions and integrals. For this problem, the orbit plane will experience nutation in addition to the precession that is found for orbital motion about an oblate body. It is possible for the orbit plane to be trapped in a 1:1 resonance with the rotating body, the plane essentially being dragged by the rotating asteroid. As the asteroid rotation rate is increased, this resonant motion disappears for rotation rates greater than a speciec value. Finally, we validate our analysis with numerical integrations of cases of interest, showing that the averaging assumptions apply and give a correct prediction of motion in this system. These results are applicable to understanding spacecraft and particle motion about slowly rotating asteroids. I. Introduction T HIS paper studies the orbital motion of a spacecraft about slowly rotating asteroids. The asteroid gravity e eld is represented by the second-degree and second-order gravity coefecients C20 and C22. The asteroid itself is assumed to be uniformly rotating about the axis of its major moment of inertia. When the asteroid is slowly rotating, we can apply averaging techniques to the Lagrange planetary equations to derive a simplie edset of equations that describe a spacecraft’s orbit. Also, because this is a uniformly rotatinggravitye eld,the Jacobiintegralthatistraditionally used for restricted three-body problems is deened for this problem. 1 Using the Jacobi integral in conjunction with the averaged equations, we can show that the problem can be reduced to quadratures, that is, the problem is integrable. This is an extension of the results that show that the averaged problem is integrable in terms of elliptic, hyperbolic, and trigonometric functions ifthe central body does not rotate. 2 ByproperinterpretationoftheJacobiintegral,wecanderive

Orbital dynamics about a slowly rotating asteroid

We analyze orbital stability of satellites (moonlet, spacecraft) near a slowly rotating axisymmetric asteroid. Using simple point mass models as a guide, we discover an unstable region near the equatorial plane of an indented asteroid. The existence of stable/unstable regions is confirmed numerically for a realistic “peanut” model asteroid. The stable region is found to survive small asteroidal rotation about an axis of maximum moment of inertia. A simple semi‐empirical formula is found for the orbital tilt angle as a function of asteroid rotation speed. Implications for motion about realistic asteroids are discussed.

On the Slow Rotation of Asteroids

Asteroids with very slow rotation rates, up to 100 times slower than the mean for ordinary asteroids, are clearly a statistically distinct population from the rest. The cause of such slow rotation has remained a mystery since the discovery of the population about 20 years ago. The expected distribution of slow rotations for three-dimensional rotation vectors f → if uniform near the origin (e.g., a three-dimensional Maxwellian distribution) would be N (< f)∝ f 3, where f is the rotation frequency (inverse period of rotation) and N (< f) is the cumulative number of asteroids with spin rate less than f. In this paper I show that the statistics of the slow-rotation population as currently known is well fit as a uniform distribution of the one-dimensional parameter f, that is N (< f)∝ f. I offer as a possible explanation for slow rotations that they result from disintegration of high mass ratio (∼1:5) binaries through the rapid transfer of rotational energy of the primary into the orbit of the secondary due to the irregular gravity field of the primary. A troubling aspect of this hypothesis is that it would seem to predict a distribution of residual spins of the approximate form N (< f)∝ f 2, which does not fit the available data.

Asteroid 1620 Geographos: I. Rotation

This study is part of a wide investigation, the goal of which is to find out whether meteor streams genetically related to asteroid 1620 Geographos exist and when and how they were formed. One of the possible mechanisms of the particles' removal from the asteroid's surface is their throw-off caused by rotational forces. The asteroid-rotation parameters were defined using the sidereal rotation period and another period of 0.8 days, which was obtained from observations and identified as nutational. Small oscillations of the asteroid's rotation axis were revealed. It was also found that the rotary acceleration does not exceed the gravitational one for all possible modes of the asteroid's rotation. The gravitational-force moment caused by the Sun's attraction and the light-pressure torque have a weak influence on the rotational motion; they have not essentially changed the rotation-pole position over the past 30 orbital periods.

A Model for Rotation and Shape of Asteroid 9969 Braille from Ground-Based Observations and Images Obtained during the Deep Space 1 (DS1) Flyby

Image data from the DS1 encounter with Asteroid 9969 Braille and data from a coordinated ground-based photometric observing campaign are combined to study the physical properties of this small Mars crosser. From telescope data the object's brightness was found to vary by up to 0.5 mag from night to night, with the most probable synodic rotational period being 226.4±1.3 h (9.4 days) and a mean lightcurve magnitude R(1, α=24°) =17.04±0.10. During the flyby of the spacecraft, two frame images from a range of approximately 13,500 km and phase angle 82.4°, which impose strong constraints on size, shape, and albedo of the object, were obtained. Using telescope and flyby data in combination, the asteroid is estimated to have a size of 2.1×1×1 km 3 and shown to have photometric properties similar to the asteroid 4 Vesta, notably a comparably high albedo. The high albedo supports the notion (L. Soderblom et al. 1999, Bull. Am. Astron. Soc. 31,) that Braille is of the V or Q taxonomic type.

Fast and Slow Rotation of Asteroids

We present an analysis of the distribution of asteroid spin rates vs. size. The existence of significant populations of both slow and fast rotators among asteroids smaller than D=40 km, and especially below 10 km (where our sample is mostly near-Earth asteroids), is shown. We have found that the excess of slow rotators is present at spin rates below ≈0.8 rev/day, and the group of fast rotators occupies the range of spin rates >7 rev/day. The fast rotators show interesting characteristics: The lack of objects rotating faster than 2.2 h period among asteroids with absolute magnitude H<22, as well as the tendency to spheroidal shapes of fast rotators, is evidence that asteroids larger than a few hundred meters are mostly loosely bound, gravity-dominated aggregates with negligible tensile strength (“rubble piles”), while monoliths may be abundant among smaller objects. A large fraction (about half) of near-Earth fast-rotating asteroids appear to be binary systems, probably created by tidal disruptions during close encounters with the terrestrial planets.

Observations of Polarization and Brightness Variations with the Rotation for Asteroids 9 Metis, 52 Europa, and 1036 Ganymed

We present the results of photo-polarimetric observations for asteroids 9 Metis (S-type, main belt asteroid (MBA)), 52 Europa (C-type, MBA), and 1036 Ganymed (S-type, near-Earth asteroid), obtained at six wavelength bands. It is found, combining our new data with previous observations, that (1) larger maximum value of negative polarization P min=−1.37% and higher polarization slope h=0.27% deg −1 occur in 52 Europa, while smaller P min and lower h appear, i.e., −0.84%, 0.11% deg −1 for 9 Metis and −0.57%, 0.095% deg −1 for 1036 Ganymed. These results confirm the general trend of polarization-phase angle curves found previously between C- and S-type asteroids (see B. Goidet-Devel et al. 1995, Planet Space Sci. 43, 779–786). (2) An increase of polarization with wavelength from 0.42 to 0.76 μm is found from the data with their root-mean-square errors in 9 Metis and 1036 Ganymed, in contrast with vice versa dependence in 52 Europa. (3) A relation of P min and geometric albedo A, presented in D. F. Lupishko and R. A. Mohamed (1996, Planet Space Sci. 46, 47–74), leads to the resulting values of A for 0.15, 0.082, and 0.24 for 9 Metis, 52 Europa, and 1036 Ganymed, respectively. (4) The polarization observed for 9 Metis shows a significant time variation modified with the rotation of asteroid, but no clear relation between lightcurve and polarization curve appears. For 52 Europa and 1036 Ganymed, the observed time variation of polarization is weak. (5) A comparison of model simulation to the observations of lightcurve and geometric albedo A variation for 9 Metis suggests the existence of inhomogeneous albedo features on its surface, where the albedo was derived from the relation of P min and A.