Orbit determination by four observations

An elliptic orbit is determined from two short-arc pairs of observations at different oppositions by the angular momentum integral. Other methods for initial orbit determination than the classical do exist.     

The pole of (51) Nemausa

The complex lightcurves make (51) Nemausa a good case for the study of general methods for pole determination. From six lightcurves the pole is determined to 20^h24^m; +53° (1950); the rotation is retrograde with period 7^h.782936 ± 0^h.000005. Presence of nongeometric scattering is proved by a significant 0.008 mag amplitude. Formulae and photometric elements are given for predictions of the shapes of lightcurves in future oppositions. The precision of the Fourier coefficients may be reduced below the present ±0.003 mag level by avoiding the systematic errors in the observations due to phase factor variations and discontinuities when changing comparison stars.     

Flora小行星族自转特性研究

小行星族作为灾变碰撞的残留物,其基础物理性质提供了其母体以及后续演化信息.其中轨道以及自转特性分别反映了Yarkovsky效应以及Yarkovsky-O’Keefe-Radzievskii-Paddack效应(YORP效应)对于小行星族演化的影响.基于小行星光变数据库(Asteroid Lightcurve Database),通过对Flora小行星族自转速率分布进行研究,发现随着直径减小,族成员自转速率倾向于主要集中在3–5 d^-1的范围内.同时,可以注意到Flora小行星族整体表现出更倾向于顺行自转状态的现象,但对于轨道半长轴小于2.2au的成员来说,其顺行自转与逆行自转状态成员数目比接近于近地小行星中顺逆行自转状态源1:3的比例;此外,对于轨道半长轴大于2.2 au且具有顺行自转状态的部分族成员,在轨道半长轴-绝对星等分布中表现出聚集现象,并在聚集区域中有9颗成员展现出类似Slivan状态特征.     

Neptune Trojans: a Revisit and a New Membertwo

Up to now, 17 Neptune Trojan asteroids have been detected with their orbits being well determined by continuous observations. This paper analyzes systematically their orbital dynamics. Our results show that except for two temporary members with relatively short lifespans on Trojan orbits, the vast majority of Neptune Trojans located within their orbital uncertainties may survive in the solar system age. The escaping probability of Neptune Trojans, through slow diffusion in the orbital element space in 4.5 billion years, is estimated to be ～50%. The asteroid 2012 UW177 classified as a Centaur asteroid by the IAU Minor Planet Center currently is in fact a Neptune Trojan. Numerical simulations indicate that it is librating on the tadpole-shaped orbit around the Neptune's L₄ point. It was captured into the current orbit approximately 0.23 million years ago, and will stay there for at least another 1.3 million years in the future. Its high inclination of i ≈ 54^° not only makes it the most inclined Neptune Trojan, but also makes it exhibit the complicated and interesting co-orbital transitions between the leading and trailing Trojans via the quasi-satellite orbit phase.     

Radar Observations of Asteroid 3908 Nyx

We report Doppler-only (cw) radar observations of basaltic near-Earth asteroid 3908 Nyx obtained at Arecibo and Goldstone in September and October of 1988. The circular polarization ratio of 0.75±0.03 exceeds ∼90% of those reported among radar-detected near-Earth asteroids and it implies an extremely rough near-surface at centimeter-to-decimeter spatial scales. Echo power spectra over narrow longitudinal intervals show a central dip indicative of at least one significant concavity. Inversion of cw spectra yields two statistically indistinguishable shape models that have similar shapes and dimensions but pole directions that differ by ∼100°. We adopt one as our working model and explore its implications. It has an effective diameter of 1.0±0.15 km and radar and visual geometric albedos of 0.15±0.075 and 0.16^+0.08_−0.05. The visual albedo supports the interpretation by D. P. Cruikshank et al. (1991, Icarus89, 1-13) that Nyx has a thermal inertia consistent with that of bare rock. The model is irregular, modestly asymmetric, and topographically rugged.     

Inflight Calibration of the NEAR Multispectral Imager: II. Results from Eros Approach and Orbit

During the Near-Earth Asteroid Rendezvous (NEAR) spacecraft's investigation of asteroid 433 Eros, inflight calibration measurements from the multispectral imager (MSI) have provided refined knowledge of the camera's radiometric performance, pointing, and light-scattering characteristics. Measurements while at Eros corroborate most earlier calibration results, although there appears to be a small, gradual change in instrument dark current and flat field due to effects of aging in the space environment. The most pronounced change in instrument behavior, however, is a dramatic increase in scattered light due to contaminants accumulated on the optics during unscheduled fuel usage in December 1998. Procedures to accurately quantify and to remediate the scattered light are described in a companion paper (Li et al. 2002, Icarus155, 00-00). Acquisition of Eros measurements has clarified the relative, filter-to-filter, radiometric performance of the MSI. Absolute radiometric calibration appears very well constrained from flight measurements, with an accuracy of ∼5%. Pointing relative to the spacecraft coordinate system can be determined from the temperature of the spacecraft deck with an accuracy of ∼1 pixel.     

Hidden Mass in the Asteroid Belt

The total mass of the asteroid belt is estimated from an analysis of the motions of the major planets by processing high precision measurements of ranging to the landers Viking-1, Viking-2, and Pathfinder (1976-1997). Modeling of the perturbing accelerations of the major planets accounts for individual contributions of 300 minor planets; the total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Mass M_ring of the ring and its radius R are considered as solve-for parameters. Masses of the 300 perturbing asteroids have been derived from their published radii based mainly on measured fluxes of radiation, making use of the corresponding densities. This set of asteroids is grouped into three classes in accordance with physical properties and then corrections to the mean density for each class are estimated in the process of treating the observations. In this way an improved system of masses of the perturbing asteroids has been derived.The estimate M_ring≈(5±1)×10⁻¹⁰M_⊙ is obtained (M_⊙ is the solar mass) whose value is about one mass of Ceres. For the mean radius of the ring we have R≈2.80 AU with 3% uncertainty. Then the total mass M_belt of the main asteroid belt (including the 300 asteroids mentioned above) may be derived: M_belt≈(18±2)×10⁻¹⁰M_⊙. The value M_belt includes masses of the asteroids which are already discovered, and the total mass of a large number of small asteroids—most of which cannot be observed from the Earth. The second component M_ring is the hidden mass in the asteroid belt as evaluated from its dynamical impact onto the motion of the major planets.Two parameters of a theoretical distribution of the number of asteroids over their masses are evaluated by fitting to the improved set of masses of the 300 asteroids (assuming that there is no observational selection effect in this set). This distribution is extrapolated to the whole interval of asteroid masses and as a result the independent estimate M_belt≈18×10⁻¹⁰M_⊙ is obtained which is in excellent agreement with the dynamical finding given above.These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H. Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H<14 have been discovered (according to the derived distribution, about 130,000 such asteroids are expected to exist).     

Lightcurve Analysis of Four New Monolithic Fast-Rotating Asteroids

We present lightcurves and analysis for four new monolithic fast-rotating asteroids: 2000 AG₆, 2000 DO₈, 2000 EB₁₄, and 2000 HB₂₄. Their rotation periods of 4.60, 1.30, 107.47, and 13.05 min place them well below the critical threshold for the rotation rate of strengthless prolate ellipsoids, as we demonstrate. These four objects join the five previously identified fast-rotating asteroids. The sharp segregation in spin rates between these nine objects and asteroids with more typical spin rates is somewhat puzzling. No observed objects larger than about 200 m spin with rates faster than the critical rate for strengthless prolate ellipsoids, while no objects smaller than 200 m have shown spin rates slower than this critical limit. We hypothesize that these small, fast-rotating objects are representative of the building blocks of the “rubble pile” asteroids and are in fact derived from impacts into already existing “rubble piles.”     

From Magnitudes to Diameters: The Albedo Distribution of Near Earth Objects and the Earth Collision Hazard

A recently published model of the Near Earth Object (NEO) orbital-magnitude distribution (Bottke et al., 2002, Icarus156, 399-433.) relies on five intermediate sources for the NEO population: the ν₆ resonance, the 3:1 resonance, the outer portion of the main belt (i.e., 2.8-3.5 AU), the Mars-crossing population adjacent to the main belt, and the Jupiter family comet population. The model establishes the relative contribution of these sources to the NEO population. By computing the albedo distribution of the bodies in and/or near each of the five sources, we can deduce the albedo distribution of the NEO population as a function of semimajor axis, eccentricity, and inclination. A problem with this strategy, however, is that we do not know a priori the albedo distribution of main belt asteroids over the same size range as observed NEOs (diameter D<10 km). To overcome this problem, we determined the albedo distribution of large asteroids in and/or near each NEO source region and used these results to deduce the albedo distribution of smaller asteroids in the same regions. This method requires that we make some assumptions about the absolute magnitude distributions of both asteroid families and background asteroids. Our solution was to extrapolate the observed absolute magnitude distributions of the families up to some threshold value H_thr, beyond which we assumed that the families' absolute magnitude distributions were background-like.We found that H_thr=14.5 provides the best match to the color vs heliocentric distance distribution observed by the Sloan Digital Sky Survey. With this value of H_thr our model predicts that the debiased ratio between dark and bright (albedo smaller or larger than 0.089) objects in any absolute-magnitude-limited sample of the NEO population is 0.25±0.02. Once the observational biases are properly taken into account, this agrees very well with the observed C/S ratio (0.165 for H<20). The dark/bright ratio of NEOs increases to 0.87±0.05 if a size-limited sample is considered. We estimate that the total number of NEOs larger than a kilometer is 855±110, which, compared to the total number of NEOs with H<18 (963±120), shows that the usually assumed conversion H=18?D=1 km slightly overestimates the number of kilometer-size objects.Combining our orbital distribution model with the new albedo distribution model, and assuming that the density of bright and dark bodies is 2.7 and 1.3 g/cm³, respectively, we estimate that the Earth should undergo a 1000 megaton collision every 63,000±8000 years. On average, the bodies capable of producing 1000 megaton of impact energy are those with H<20.6. The NEOs discovered so far carry only 18±2% of this collision probability.     

Dynamical behaviour of the primitive asteroid belt

In this paper we consider the dynamical evolution and orbital stability of objects in the asteroid belt. A simple physical model, including full gravitational perturbations from both giant planets, is used to compute the dynamical evolution of 1000 test particles simulating the primitive asteroids. The criterion of planet crossing (or close approach in the case of resonant objects) is used to reject particles from the simulation. 44 per cent of the particles survived for the whole time-span covered by the numerical integration (∼10⁹ yr).
The 4:1, 3:1 and to a lesser extent the 2:1 Kirkwood gaps are formed in ∼10⁷ yr of evolution, representing direct numerical evidence about their gravitational origin.
We found that the rms eccentricity and inclination of the sample experience a fast increase during the first 10⁶ yr. The final rms eccentricity is 0.11, ∼60 per cent smaller than the present rms eccentricity (0.17). Nevertheless, the gravitational action of the giant planets suffices to prevent the formation of large objects, allowing catastrophic collisions and the subsequent depletion of material from this zone of the Solar system. The excited eccentricity by Jupiter and Saturn may favour mutual encounters and the further increase of the relative velocities up to their present values.