Some specific features of light curves of (39) Laetitia, (87) Sylvia, (90) Antiopa,and 2006 VV2 asteroids

The results of photometric observations of (87) Sylvia, 2006 VV2, (90) Antiopa, and (39) Laetitia asteroids in 2006–2008 are presented. The specific features of light curves are considered for each object. In particular, for asteroid (87) Sylvia, possible mutual phenomena in this triple system are identified. Asteroid 2006 VV2 manifests a strong dependence of the light curve on the filter color, which testifies to the presence of inhomogeneities on its surface. The previously unknown brightness variation period with a duration of about three days was obtained for this asteroid. For binary asteroid (90) Antiopa, the strong dependence of its brightness on the phase angle was noticed; this may testify to the very flattened shape of its components. Considerable time variations of the shape of the light curve for asteroid (39) Laetitia may testify either to its complex shape or to its binary character.     

Radar observations of the asteroid 2011 UW158

In July 2015 intercontinental bistatic radar observations of the potentially dangerous asteroid 2011 UW158 during its close approach to the Earth were carried out. The asteroid was illuminated at a frequency of 8.4 GHz with the 70-m DSS-14 antenna of the Goldstone Deep Space Communications Complex, while the signal reflected from the asteroid was received with the 32-m radio telescopes of the Quasar VLBI network at the Zelenchukskaya and Badary Observatories. The spectra of the reflected radio signals were obtained. The sizes and rotation period of the asteroid consistent with photometric observations and the ratio of the powers of the reflected signals with left- and right-hand circular polarizations were determined. The derived values suggest that the asteroid has an inhomogeneous surface and a prolate shape. The observations of the Doppler shift of the reflected signal frequency were obtained, which allowed the orbital parameters of the asteroid to be improved.     

The shape of asteroids: Theoretical considerations

Theoretical consideration and observations by other authors indicate that small asteroids are capable of maintaining irregular shapes, notably the shape of a cigar and even of a dumb-bell. This paper presents a model which describes the changes in the shape of an asteroid due to collisions of smaller objects (meteoroids) with the asteroid. The following assumptions must be approximately valid: (1) collisions are not uncommon; (2) collisions between a (relatively) large asteroid and small objects (meteroids) are more common than collisions between asteroids; (3) the cumulative probability of the collision of a meteoroid on a point on the surface of an asteroid is proportional to the zenith angle of the horizon as seen by that point; (4) obliquities of all but the major asteroids are random, so that there is not a preferred side on which collisions occur; (5) a considerable percentage of collision ejecta achieves escape velocity; and (6) the rate of erosion of each point on the surface of an asteroid is proportional to the cumulative probability of collision.Generalized conclusions that are obtained from the computer running of the model indicate that both cigars and dumb-bells are possible outcomes. Sharp corners are smoothed away, the radius of curvature of rounded surfaces increases to the point of going from convexity to concavity, and flat surfaces develop into gentle concavities.Collisions of an asteroid with an object of sufficient size such that the impact causes the breakage of the asteroid or the formation of a large crater, are not discussed in this paper. Previous work, however, suggests that the crater will undergo geomorphological changes of different geometry than a similar crater on the Moon.     

Combining asteroid models derived by lightcurve inversion with asteroidal occultation silhouettes

Asteroid sizes can be directly measured by observing occultations of stars by asteroids. When there are enough observations across the path of the shadow, the asteroid’s projected silhouette can be reconstructed. Asteroid shape models derived from photometry by the lightcurve inversion method enable us to predict the orientation of an asteroid for the time of occultation. By scaling the shape model to fit the occultation chords, we can determine the asteroid size with a relative accuracy of typically ∼10%. We combine shape and spin state models of 44 asteroids (14 of them are new or updated models) with the available occultation data to derive asteroid effective diameters. In many cases, occultations allow us to reject one of two possible pole solutions that were derived from photometry. We show that by combining results obtained from lightcurve inversion with occultation timings, we can obtain unique physical models of asteroids.     

Asteroid lightcurve phase shift from rough‐surface shadowing

We have simulated asteroid lightcurves for simple shape models using a realistic surface scattering law. The scattering law includes a shadowing function computed with numerical ray‐tracing. We computed lightcurves in a variety of illumination geometries for both the traditional Lommel–Seeliger law and our seminumerical law. We observe a shift in the rotational phase of the lightcurves, which depends on the parameters of the scattering law as well as the illumination geometry and the direction of the spin axis of the asteroid. This phase shift is always zero at opposition, and can be as large as 10° for illumination geometries typical for Main Belt asteroids. The phase shift has implications on the accuracy of other results which are based on asteroid lightcurve analysis, such as spin‐state or shape determination.     

A Research on the Imaging Strategy and Imaging Simulation of Toutatis in the Chang’e-2 Flyby Mission

For the Chang’e-2 extended mission of asteroid exploration, the illumination conditions for imaging the asteroid Toutatis are calculated in this paper according to the orbital parameters of both the Chang’e-2 detector and the asteroid, as well as the incident angles of sunlight. On this basis, it is suggested to take photographs after flyby, and the orientation of the camera's optical axis in the coordinate system deflned by Earth's mean equator and equinox at J2000.0 is proposed to be (118.02°, 22.03°). Based on the shape model of Toutatis determined by the foreign radar data, the orientation of the asteroid in the inertial space is calculated at the rendezvous time. Using the Oren-Nayar diffuse-reflection model and the relative positions among the sun, the asteroid, and the detector, together with the cameras orientation, the imaging simulations are performed on the starry sky background respectively at the distances of 300 km, 500 km, and 1000 km from the asteroid after flyby. The results of simulations are verified further by the optical images of Toutatis obtained in the mission.     

Observations of asteroid occultations by the trailed-image method

The method of trailed CCD images for observations of asteroid occultations is described. This method was used to observe 9 asteroid occupations at the Lisnyky observational station in 2006 with the telescope AZT-8 (D= 0.7m and F= 2.8m) equipped by the CCD ST-8 XME. In the case of occultation of the star TYC 0587-00209-1U by the asteroid 76 Freia in November 4, 2006, the distance between the asteroid center and the star, as well as the time of asteroid occultation were determined. The size of asteroid 76 Freia is determined assuming that its shape is spherically symmetric. In other cases, the minimal distances between the asteroid center and the star are determined. The method makes it possible to observe asteroid occultations with high time resolution.     

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.     

A Review for the Thermophysics and the Yarkovsky and YORP Effects of Asteroidstwo

The thermophysics of asteroids has become an important frontier for the research of asteroids in recent years. In this paper, we have introduced the thermophysical models commonly used in this field, by using these thermophysical models and combining with the data observed by the space or ground-based IR telescopes, some thermophysical parameters of asteroids, such as the thermal inertia, geometric albedo, effective diameter, surface roughness, and surface temperature, etc., can be derived. We have mentioned also the shape model and IR observation of asteroids, as well as the obtained thermophysical parameters for a part of asteroids. These thermophysical parameters can be further applied to studying the asteroids’ Yarkovsky effect, YORP effect, and so on, even can provide the relevant information for the spacecraft landing on the asteroid surface and the return mission of a spacecraft after the asteroid sampling.     

Photometry of asteroids

Photometry is one of the most efficient investigation techniques. It provided a large body of data on albedos, sizes, shapes, rotation, optical properties, and structural characteristics of asteroids and other minor bodies of the solar system. The contribution of photometry to the determination of asteroid parameters was most crucial. This review summarizes main results of asteroid studies in three most important areas: i) determination of the shape and rotation parameters of asteroids, ii) investigation of optical properties of asteroid surfaces, and iii) detection and investigation of binary asteroid systems.     

Observation Plan for Refining Shape Model of (6) HEBE

As the number of observatories located on the surface of Earth is increasing largely in decades more and more photometric data of asteroids is observed to make the research about their various physical and chemical characteristics. Compared with hundreds of thousands of asteroids found up to now, rare hundreds of three-dimensional shape models of asteroids have been built from the tremendous photometric data with incessant observations, i.e. lightcurves. For some specific asteroid already with many observed lightcurves, the unceasing observation is not too much valuable, nevertheless an additional lightcurve observed in a request viewing aspect can refine the shape model and other related parameters. This article taking the asteroid (6) HEBE for example, attempts to introduce a method to make the observation plan by combining the request of the shape model and the orbital limitation of asteroids. Through analyzing the distribution of lightcurves of (6) HEBE, small cabins without any lightcurve data are found, which can be filled by new observations at some specified dates when the positions of Asteroid, Sun, Earth are limited as the request geometry.     

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.     

Stability of Surface Motion on a Rotating Ellipsoid

The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid.     

Asteroid rotation and shapes from numerical simulations of gravitational re-accumulation

We present simulations of the gravitational collapse of a mono-disperse set of spherical particles for studying shape and spin properties of re-accumulated members of asteroid families. Previous numerical studies have shown that these “gravitational aggregates” exhibit properties similar to granular continuum models described by Mohr-Coulomb theory. A large variety of shapes is thus possible, in principle consistent with the observed population of asteroid shapes.However, it remains to be verified that the re-accumulation following a catastrophic disruption is capable of naturally producing those shapes. Conversely, we find that fluid equilibrium shapes (flattened two-axis spheroids, in particular) are preferentially created by re-accumulation. This is rather unexpected, since the dynamical system used could allow for other stable configurations. Jacobi three-axial ellipsoids can also be created, but this seems to be a less common outcome.The results obtained so far seem to underline the importance of other non-disruptive shaping factors during the lifetime of rubble-pile asteroids.     

Capillary action in a crack on the surface of asteroids with an application to 433 Eros

Some asteroids contain water ice, and a space mission landing on an asteroid may take liquid to the surface of the asteroid. Gas pressure is very weak on the surface of asteroids. Here we consider the capillary action in a crack on the surface of irregular asteroids. The crack is modeled as a capillary which has a fixed radius. An asteroid's irregular gravitational potential influences the height of the liquid in the capillary. The height of the liquid in the capillary on the surface of such asteroids is derived from the asteroid's irregular gravitational potential. Capillary mechanisms are expected to produce an inhomogeneaous distribution of emergent liquid on the surface. This result is applied to asteroid 433 Eros, which has an irregular, elongated, and concave shape. Two cases are considered: (1) we calculate the height of the liquid in the capillary when the direction of the capillary is perpendicular to the local surface of the asteroid; (2) we calculate the height of the liquid in the capillary when the direction of the capillary is parallel to the vector from the center of mass to the surface position. The projected height in the capillary on the local surface of the asteroid seems to depend on the assumed direction of the capillary.     

Dynamical parameters of spacecraft motion near small celestial body

The paper considers how a spacecraft can be put into orbit around a small asteroid to function as its artificial moon. We study the general behavior of perturbations that affect the current coordinates of an orbiting spacecraft and estimate the perturbations caused by the main perturbing factors, i.e., (1) the irregular shape of an asteroid and (2) celestial bodies of the Solar System. With specific orbital parameters, a long-term targeted operation of a spacecraft can be actualized in a mission to the asteroid Apophis where the spacecraft will carry a radio beacon transponder.     

Photometric observations of Earth‐impacting asteroid 2008 TC3

Abstract– A calibrated lightcurve is presented of the near‐Earth asteroid 2008 TC₃, obtained before it impacted Earth on October 7, 2008. The asteroid was observed in unfiltered images from the end of astronomical twilight until the object entered Earth’s shadow about 2 h later. The observations covered a wide range of phase angles from 14.79° to 2.93°, during which the asteroid ranged from 82,000 km to 29,000 km distance from the observer. A method is presented for obtaining photometrically filtered brightness values for the asteroid using unfiltered imaging techniques. Over 1,700 images of the asteroid produce a lightcurve with a peak‐to‐peak variation in V of 0.76 magnitude. Analysis of the lightcurve yields values for H = 30.86 ± 0.01 and G = 0.33 ± 0.03. Combined with other constraints on the kinetic energy and diameter of the asteroid, which suggest a low 1.8 g cm^?3 density and albedo 0.05 ± 0.01, the value of H implies an asteroid of about 4.1 m in diameter, 28 m³ in volume, and 51,000 kg in mass. The determined value of G is out of range for normal, larger asteroids of albedo 0.05–0.15.     

Photometric and Colorimetric Observations of Asteroid 423 Diotima and Their Analysis

Series of photometric and colorimetric observations of the Main-Belt asteroid 423 Diotima during its five oppositions were obtained at the Crimean Astrophysical Observatory. It was concluded, based on the results of a frequency analysis of the V-band photometry obtained in 1990, that the asteroid is a binary system: the rotation period of the primary component is equal to 4_. ^h56, and the period of rotation and the orbital period of the satellite are equal to 14_. ^h90. An analysis of simultaneous BV and BVR observations made in 1993 and 1998–1999 yielded a rotation period of 4_. ^h54 ± 0_. ^h01 for the primary component. An analysis of the sets of V-band observations of the asteroid made from 1982 through 2000 allowed us to find the period of forced precession, which was equal to 113^d (or 226^d). It was suggested that the axis of the primary component of the binary asteroid precesses and the large amplitude of brightness variations (about 1 ^m ) is due to its lenticular shape.     

Opposition polarimetry and photometry of S- and E-type asteroids

The first results of the observational program devoted to simultaneous investigation of asteroid polarimetric and photometric opposition phenomena are presented. UBVRI polarimetric and V-band photometric observations of the S-type Asteroid 20 Massalia and the E-type Asteroids 214 Aschera and 620 Drakonia were carried out in 1996-1999 down to phase angles of 0.08°, 0.7°, and 1.2°, correspondingly. The S-type Asteroid 20 Massalia is characterized by the pronounced brightness opposition surge with an amplitude larger than that observed for the E-type asteroids. A sharp peak of negative polarization at small phase angles was not observed for this asteroid. The value of polarization degree at phase angle α<1° is less than 0.5% for both S and E types. The negative polarization branches of S and especially E-asteroids have an asymmetrical shape. The phase angle at which the polarization minimum occurs is close to the angle at which non-linear increase begins in the asteroid magnitude phase curves. A relation of the observed effects to the mechanism of coherent backscattering is discussed.