Axial rotation of near-earth asteroids: The influence of the YORP effect

The distribution of axial rotation velocities of near-Earth asteroids (NEAs) substantially differs from that of the Main-Belt asteroids by an excess of both quickly and slowly rotating objects. Among the possible causes of this difference is the influence of the solar radiation—the so-called YORP effect—that arises from the absorption of solar energy and its reemission in the thermal range by a rotating body of irregular shape. It is known that the magnitude of this effect depends on the asteroid size and the quantity of received solar energy (the insolation). Analysis of the observational data showed that the mean diameter of NEAs decreases from the middle of the distribution to the edges, i.e., the excess of both slowly (ω ≤ 2 rev/day) and quickly (ω = 8–11 rev/day) rotating objects is formed due to the asteroids with sizes smaller than those in the middle of the distribution, which agrees well with the influence of the YORP effect. Moreover, the dependence of the axial rotation velocity of NEAs on the relative insolation shows that, for the NEAs referred to, both excesses are found in orbits where, on average, they receive 8–10% more solar energy than the NEAs in the middle of the distribution. This result also agrees with the character of the influence of the YORP effect and can be considered as an additional argument in its support. Thus, the study showed that one can infer that the currently available observational data suggest the possible influence of the YORP effect on the axial rotation of the near-Earth asteroids having sizes of D ～ 2 km and less. This is the first attempt to find the influence of the YORP effect on the axial rotation of the NEA family as a whole.     

Distribution of the near-earth objects

This paper analyzes the distribution of the orbits of near-Earth minor bodies from the data on more than 7500 objects. The distribution of large near-Earth objects (NEOs) with absolute magnitudes of H < 18 is generally consistent with the earlier predictions (Bottke et al., 2002; Stuart, 2003), although we have revealed a previously undetected maximum in the distribution of perihelion distances q near q = 0.5 AU. The study of the orbital distribution for the entire sample of all detected objects has found new significant features. In particular, the distribution of perihelion longitudes seriously deviates from a homogeneous pattern; its variations are roughly 40% of its mean value. These deviations cannot be stochastic, which is confirmed by the Kolmogorov-Smirnov test with a more than 0.9999 probability. These features can be explained by the dynamic behavior of the minor bodies related to secular resonances with Jupiter. For the objects with H < 18, the variations in the perihelion longitude distribution are not so apparent. By extrapolating the orbital characteristics of the NEOs with H < 18, we have obtained longitudinal, latitudinal, and radial distributions of potentially hazardous objects in a heliocentric ecliptic coordinate frame. The differences in the orbital distributions of objects of different size appear not to be a consequence of observational selection, but could indicate different sources of the NEOs.     

Astrometry of near-earth objects using small telescopes

Currently, when a near-Earth object (NEO: any asteroid or comet approaching the terrestrial orbit about the Sun) is discovered, there is a distinct chance that it will be lost again due to the lack of suitable follow-up astrometry. The burgeoning international Spaceguard program — which has an aim of discovering and determining the orbits of all possible Earth-impactors so that calamitous collisions can be avoided-will make this problem more acute, as the discovery rate increases. When NEOs reach visual magnitudes brighter than 21, they may be observed with suitable CCD-equipped telescopes with apertures of one metre or less; in fact, even 0.25-m aperture instruments are now being employed to great effect in this regard. This means that in the present situation, countries or individuals having access to quite modest-sized and modest-priced equipment can make a real, valuable contribution to this international effort. When Spaceguard begins in earnest it will be vital that astronomers spread around the world, using small telescopes, take over the tracking of NEOs discovered by the large, expensive, search instruments. The Spaceguard project therefore represents an excellent opportunity for international collaboration, with scientists in developing nations being valuable contributors in a space program with real significance for all humankind. Presented at the UN/ESA Workshop on Basic Space Science: From Small Telescope to Space Mission, Colombo, Sri Lanka, 11–14 January 1996.

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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.     

Combined perturbation on near-earth satellite orbits

Using a semi-analytical method, we have obtained a first-order solution of the equations of motion of near-Earth satellites under the combined perturbing effect due to Earth's figure and air drag.     

Tumbling asteroids

We present both a review of earlier data and new results on non-principal axis rotators (tumblers) among asteroids. Among new tumblers found, the best data we have are for 2002 TD₆₀, 2000 WL₁₀₇, and (54789) 2001 MZ₇—each of them shows a lightcurve with two frequencies (full terms with linear combinations of the two frequencies are present in the lightcurve). For 2002 TD₆₀, we have constructed a physical model of the NPA rotation. Other recent objects which have been found to be likely tumblers based on their lightcurves that do not fit with a single periodicity are 2002 NY₄₀, (16067) 1999 RH₂₇, and (5645) 1990 SP. We have done a statistical analysis of the present sample of the population of NPA rotators. It appears that most asteroids larger than ∼0.4 km with estimated damping timescales (Harris, 1994, Icarus 107, 209) of 4.5 byr and longer are NPA rotators. The statistic of two short-period tumblers (D=0.04 and 0.4 km) with non-zero tensile strength suggests that for them the quantity μQ/T, where μ is the mechanical rigidity, Q is the elastic dissipation factor, and T is a spin excitation age (i.e., a time elapsed since the last significant spin excitation event), is greater by two to four orders of magnitude than the larger, likely rubble-pile tumblers. Among observational conditions and selection effects affecting detections of NPA rotations, there is a bias against detection of low-amplitude (small elongation) tumblers.     

Near-Sun asteroids

As follows from dynamical studies, in the course of evolution, most near-Earth objects reach orbits with small perihelion distances. Changes of the asteroids in the vicinity of the Sun should play a key role in forming the physical properties, size distribution, and dynamical features of the near-Earth objects. Only seven of the discovered asteroids are currently moving along orbits with perihelion distances q < 0.1 AU. However, due to the Kozai–Lidov secular perturbations, the asteroids, having recently passed near the Sun, could by now have moved to orbits farther from the Sun. In this study, we found asteroids that have been recently orbiting with perihelion distances q < 0.1 AU. Asteroids may be on such orbits for hundreds to tens of thousands of years. To carry out astrophysical observations of such objects is a high priority.     

Taxonomy of asteroids

A taxonomic system was introduced by C. R. Chapman, D. Morrison, and B. Zellner [Icarus25, 104–130 (1975)], in which minor planets are classified according to a few readily observable optical properties, independent of specific mineralogical interpretations. That taxonomy is here augmented to five classes, now precisely defined in terms of seven parameters obtained from polarimetry, spectrophotometry, radiometry, and UBV photometry of 523 objects. We classify 190 asteroids as type C, 141 as type S, 13 as type M, 3 as type E, and 3 as type R; 55 objects are shown to fall outside these five classes and are designated U (unclassifiable). For the remaining 118, the data exclude two or more types but are insufficient for unambiguous classification. Reliable diameters, from radiometry or polarimetry or else from albedos adopted as typical of the types, are listed for 396 objects. We also compare our taxonomy with other ones and discuss how classification efforts are related to the interpretation of asteroid mineralogies.     

Relativistic effects for near-earth satellite orbit determination

The relativistic formulations for the equations which describe the motion of a near-Earth satellite are compared for two commonly used coordinate reference systems (RS). The discussion describes the transformation between the solar system barycentric RS and both the non-inertial and inertial geocentric RSs. A relativistic correction for the Earth's geopotential expressed in the solar system barycentric RS and the effect of geodesic precession on the satellite orbit in the geocentric RS are derived in detail. The effect of the definition of coordinate time on scale is also examined. A long-arc solution using 3 years of laser range measurements of the motion of the Lageos satellite is used to demonstrate that the effects of relativity formulated in the geocentric RS and in the solar system barycentric RS are equivalent to a high degree of accuracy.     

Express identification of asteroids

A technique for the fast identification of detected asteroids directly after terminating their observations on a short topocentric arch is briefly described.     

Stability of binary asteroids

The restricted problem of 2+2 bodies is applied to the study of the stability and dynamics of binary asteroids in the solar system. Numerical investigation of the behavior of the orbital elements and the maximal Lyapunov characteristic number of binary asteroids reveal extensive regions where bounded quasiperiodic motion is possible. These regions are compared to the bounded regions which are predicted by the classical restricted problem of three bodies. Regions of bounded chaotic solutions are also found.     

Transient co-orbital asteroids

We analyze the orbital behavior of four new co-orbital NEOs and the Earth horseshoe object 2002 AA29. The new objects are 2001 CK32, a 3753 Cruithne-like co-orbital of Venus, 2001 GO2 and 2003 YN107, two objects with motion similar to 2002 AA29. 2001 CK32 is on a compound orbit. The asteroid reverses its path when the mean longitude difference is −50°. Its motion is chaotic. 2001 GO2 is an Earth HS orbiter with repeated transitions to the QS phase, the next occurring 200 years from now. The HS libration period is 190 years and the QS phases last 45 years. For 2002 AA29, our simulations permit us to find useful theoretical insights into the HS-QS transitions. Its orbit can be simulated with adequate accuracy for 4400 years into the future and 1483 years into the past. The new co-orbital 2003 YN107 is at present an Earth QS. It has entered this phase in 1997 and will leave it again in 2006, completing one QS cycle. Like 2002 AA29, it has frequent transitions between HS and QS. One HS cycle takes 133 years.     

Spin rates of asteroids

The Asteroid Photometric Catalogue was used to redetermine the rotation periods of all asteroids with data in the catalogue. The quality of the period determinations was divided into five groups. The total number of asteroids studied were 710 and 225 of these were considered not to be observed enough to yield any rotation period (code 0). For 121 asteroids the uncertainty was several hours (code d) and for 180 the uncertainty was less than one hour (code c). Code a was used for asteroids with reliable pole determinations (47 asteroids) and code b was used for asteroids with very reliable synodic rotation periods (137 asteroids). Some statistic properties of the rotation periods of asteroids are presented.     

Physical study of asteroids: Ligthcurves and rotational periods of six asteroids

V band photoelectric lightcurves and rotational periods are presented for six asteroids: 150 Nuwa, 203 Pompeja, 336 Lacaderia, 545 Messalina, 984 Gretia, and 1240 Fantasia. Except for 984 Gretia, none of these asteroids has been previously observed. The observations were obtained during September 1983 at the Astrophysical Observatory of Catania and are part of a program devoted to increase the present data set of asteroids' rotational properties. For 336 Lacaderia and 984 Gretia the magnitude-phase relations, in terms ofQ_v and β_v, were also obtained.     

Spacecraft exploration of asteroids

The past, current, and planned space missions for asteroid exploration are reviewed. The main results based on observations performed with satellites in near-Earth orbits (OAO-2, IUE, FIRSSE, IRAS, HST, Hipparcos, ISO, MSX) and space probes sent to particular objects (Galileo, NEAR, DS1, Stardust) are reported. Future space missions (MUSES-C, Rosetta, DOWN, etc.) and their main goals in asteroid study are considered. The feasibility of using spacecraft for minor-body exploration is discussed.Translated from Astronomicheskii Vestnik, Vol. 39, No. 1, 2005, pp. 81–90. Original Russian Text Copyright © 2005 by Shevchenko, Mohamed.     

Opposition effect of Trojan asteroids

CCD-photometry of three Jupiter Trojan asteroids were carried out to study their opposition effect. We obtained well-sampled magnitude–phase curves for (588) Achilles, (884) Priamus, and (1143) Odysseus in the maximal attainable phase angle range down to 0.1–0.2°. The magnitude–phase relations have a linear behavior in all observed range of phase angles and do not show any non-linear opposition brightening. We have not found any confident differences between phase slopes measured in B, V and R bands. The values of the measured phase slopes of Trojans are different from available data for Centaurs. They are within the range of phase slopes measured for some low-albedo main belt asteroids, also exhibit a linear behavior down to small phase angles. An absence of non-linear opposition brightening puts constraints on the surface properties of the studied objects, assuming very dark surfaces where single scattering plays dominating role.We also determined the rotation periods, amplitudes, the values of color indexes B–V and V–R, and the absolute magnitudes of these asteroids.     

Photoelectric photometry of 21 asteroids

Photoelectric lightcurves of 21 asteroids are presented. The observations were carried out from 1978 to 1982 at the Astronomical Observatory of Torino (at the Astrophysical Observatory of Catania for 137 Meliboea). For 10 objects a reliable rotation period has been obtained, while for two others a rough estimate is given. In several cases the analysis of the observed amplitudes versus the ecliptic longitudes indicates the most favorable future oppositions for period and/or pole determination. For some asteroids transformations to UBV Standard System were performed.     

The R asteroids reconsidered

JHK infrared photometry shows that R asteroids have two distinct infrared color domains. Most R asteroids have JHK and visual colors and albedos that fall amongst those observed for S asteroids, but a small subset is clearly different. These are designated as a new A class of asteroids.     

Photoelectric photometry of 17 asteroids

Seventeen asteroids were observed photoelectrically in the V band at the Torino Observatory in 1983–1984 as part of the coordinated campaign for pole determinations. The obtained lightcurves allowed us to deduce new pole coordinates of four objects, while for the other three a check of previous results was possible. Additionally, the ambiguity for the rotation period of 776 Berbericia was solved in favor of a shorter value, and the importance of this problem was evidenced once more after analyzing the lightcurves of 69 Hesperia and 349 Dembowska. A new possible value of the period of 121 Hermione was also suggested.     

Critical inclination of Trojan asteroids

The author's earlier solution for Trojan asteroids is developed further. It is shown that depending on the amplitude of libration around the Lagrangian point L₄, there is a critical inclination which determines the sign of the variation of the ascending node. If the orbital inclination of a Trojan is smaller than the critical one, then the ascending node decreases and otherwise it increases. The variation of the eccentricity and of the longitude of the perihelion has also a dependence on the critical inclination.