The asteroid ephemerides program at the U.S. Naval Observatory

The U.S. Naval Observatory has begun a program of ephemeris improvement and reference frame determination from the main belt asteroids. The program is, currently, starting out with a limited set of observations of the larger asteroids to determine the equator and equinox corrections for the USNO W1J00 transit circle observations catalog, and, if possible, improve the orbits of these asteroids based on this limited set of observations. For this project, transit circle observations of the Sun and the planets Mercury through Jupiter, are also being used to determine the equator, equinox, and ephemeris corrections, the next goal is to improve the orbits of the larger asteroids in the optical reference frame using observation series that cover a much longer period of time. This will allow the exploration of the differences between the dynamical reference frame based on radar observations of main belt asteroids and its relation with the optical reference frame. Other goals include the exploration of the mass distribution in the main asteroid belt from high precision observations, and the effect of this mass on the ephemerides of the major planets.     

Some results from the National Observatory of Turkey, Kazan State University, and Nikolaev Astronomical Observatory on small bodies of the solar system

A scientific collaboration between TÜB?TAK National Observatory (Turkey), Kazan State University (Russia) and Nikolaev Astronomical Observatory (Ukraine) involves observations of minor planets and near-Earth asteroids (NEAs) with the 1.5 m Russian-Turkish telescope (RTT150). Regular observations of selected asteroids in the range of 11-18 magnitudes began in 2004 with the view of determining masses of selected asteroids, improving the orbits of the NEAs, and studying physical characteristics of selected asteroids from photometric observations. More than 3000 positions of 53 selected asteroids and 11 NEAs have been obtained with an internal error in the range of 30-300 mas for a single determination. Photometric reductions of more than 4000 CCD frames are in progress. Masses of 21 asteroids were estimated through dynamical method using the ground-based optical observations, mainly from the RTT150 and Minor Planet Center. A comparison of the observational results from the RTT150 in 2004-2005 with observations of the same objects at other observatories allows us to conclude that RTT150 can be used for ground-based support in astrometry for the space mission GAIA.     

Spectral observations of 19 weathered and 23 fresh NEAs and their correlations with orbital parameters

Results of our visible to near-infrared spectrophotometric observations of 41 near-Earth asteroids (NEAs) are reported. These moderate-resolution spectra, along with 14 previously published spectra from our earlier survey [Hicks, M.D., Fink, U., Grundy, W.M., 1998. Icarus 133, 69-78] show a preponderance of spectra consistent with ordinary chondrites (23 NEAs with this type of spectrum, along with 19 S-types and 13 in other taxonomic groups). There exists statistically significant evidence for orbit-dependent trends in our data. While S-type NEAs from our survey reside primarily in (1) Amor orbits or (2) Aten or Apollo orbits which do not cross the asteroid main-belt, the majority of objects with spectra consistent with ordinary chondrites in our survey are in highly eccentric Apollo orbits which enter the asteroid main-belt. This trend toward fresh, relatively unweathered NEAs with ordinary chondrite type spectra in highly eccentric Apollo orbits is attributed to one or a combination of three possible causes: (1) the chaotic nature of NEA orbits can easily result in high eccentricity orbits/large aphelion distances so that they can enter the collisionally enhanced environment in the main-belt, exposing fresh surfaces, (2) they have recently been injected into such orbits after a collision in the main-belt, or (3) such objects cross the orbits of several terrestrial planets, causing tidal disruption events that expose fresh surfaces.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

Masses of the Main Asteroid Belt and the Kuiper Belt from the Motions of Planets and Spacecraft

Dynamicalmass estimates for the main asteroid belt and the trans-Neptunian Kuiper belt have been found from their gravitational influence on the motion of planets. Discrete rotating models consisting ofmovingmaterial points have been used tomodel the total attraction fromsmall or as yet undetected bodies of the belts. The masses of the model belts have been included in the set of parameters being refined and determined and have been obtained by processing more than 800 thousand modern positional observations of planets and spacecraft. We have processed the observations and determined the parameters based on the new EPM2017 version of the IAA RAS planetary ephemerides. The large observed radial extent of the belts (more than 1.2 AU for the main belt and more than 8 AU for the Kuiper belt) and the concentration of bodies in the Kuiper belt at a distance of about 44 AU found from observations have been taken into account in the discrete models. We have also used individual mass estimates for large bodies of the belts as well as for objects that spacecraft have approached and for bodies with satellites. Our mass estimate for the main asteroid belt is (4.008 ± 0.029) × 10^?4/m_⊕ (3σ). The bulk of the Kuiper belt objects are in the ring zone from 39.4 to 47.8 AU. The estimate of its total mass together with the mass of the 31 largest trans-Neptunian Kuiper belt objects is (1.97 ± 0.30) × 10^?2m_⊕ (3σ), which exceeds the mass of the main asteroid belt almost by a factor of 50. The mass of the 31 largest trans-Neptunian objects (TNOs) is only about 40% of the total one.     

Model orbits of asteroid 3040 Kozai

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.     

近地小行星轨道演化的研究

主要阐述近年来在近地小行星轨道演化研究工作中所获得的一些基本结果，即合理的力学模型和相应的有效算法，并以实际预报算例（近地小行星与地球的交会状态）与有关权威性的结果作了比较，证实这些研究结果确实是可信的。在给出的力学模型中，考虑了所有可能影响近地小行星运动的力学因素，包括各大天体和较大的主带小行星的引力作用、有关天体的扁率影响以及源于太阳引力的后牛顿效应。而在计算方法中，合理地处理了变步长问题和月球位置量这种相对而言的快变化问题，使得数值求解一个高维方程组时，对各天体而言，可采用同一步长进行 积分，避免了求解过程中的复杂性。     

Planets in the asteroid belt

Abstract— The main asteroid belt has lost >99.9% of its solid mass since the time at which the planets were forming, according to models for the protoplanetary nebula. Here we show that the primordial asteroid belt could have been cleared efficiently if much of the original mass accreted to form planetsized bodies, which were capable of perturbing one another into unstable orbits. We provide results from 25 N‐body integrations of up to 200 planets in the asteroid belt, with individual masses in the range 0.017–0.33 Earth masses. In the simulations, these bodies undergo repeated close encounters which scatter one another into unstable resonances with the giant planets, leading to collision with the Sun or ejection from the solar system. In response, the giant planets' orbits migrate radially and become more circular. This reduces the size of the main‐belt resonances and the clearing rate, although clearing continues. If ～3 Earth masses of material was removed from the belt this way, Jupiter and Saturn would initially have had orbital eccentricities almost twice their current values. Such orbits would have made Jupiter and Saturn 10–100x more effective at clearing material from the belt than they are on their current orbits. The time required to remove 90% of the initial mass from the belt depends sensitively on the giant planets' orbits, and weakly on the masses of the asteroidal planets. 18 of the 25 simulations end with no planets left in the belt, and the clearing takes up to several hundred million years. Typically, the last one or two asteroidal planets are removed by interactions with planets in the terrestrial region     

Observations of minor planets with the very large array

The weak thermal emission from the largest minor planets can be detected and measured at all points around their orbits at microwave frequencies using the Very Large Array (VLA). Position determinations of astrometric quality have been obtained, and flux measurements have provided size estimates. When enough precise positional observations have been accumulated, the orbits of the minor planets and the Earth can be determined. This will allow the equinox to be located within the radio reference frame, providing a truly fundamental coordinate system for radio source positions. It will also provide a means of relating the optical and radio (quasar) coordinate systems.The National Radio Astronomy Observatory is operated by Associated Universities, Incorporated, under contract with the National Science Foundation.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

The dynamical architecture and habitable zones of the quintuplet planetary system 55 Cancri

We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this sys-tem can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790 AU ≤ a ≤ 5.900 AU to examine the existence of potential asteroid structure and Habitable Zones (HZs). We show that there are unstable regions for orbits about 4:1, 3:1 and 5:2 mean motion resonances (MMRs) of the outermost planet in the system, and sev-eral stable orbits can remain at 3:2 and 1:1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.     

Mineralogies and source regions of near-Earth asteroids

Near-Earth Asteroids (NEAs) offer insight into a size range of objects that are not easily observed in the main asteroid belt. Previous studies on the diversity of the NEA population have relied primarily on modeling and statistical analysis to determine asteroid compositions. Olivine and pyroxene, the dominant minerals in most asteroids, have characteristic absorption features in the visible and near-infrared (VISNIR) wavelengths that can be used to determine their compositions and abundances. However, formulas previously used for deriving compositions do not work very well for ordinary chondrite assemblages. Because two-thirds of NEAs have ordinary chondrite-like spectral parameters, it is essential to determine accurate mineralogies. Here we determine the band area ratios and Band I centers of 72 NEAs with visible and near-infrared spectra and use new calibrations to derive the mineralogies 47 of these NEAs with ordinary chondrite-like spectral parameters. Our results indicate that the majority of NEAs have LL-chondrite mineralogies. This is consistent with results from previous studies but continues to be in conflict with the population of recovered ordinary chondrites, of which H chondrites are the most abundant. To look for potential correlations between asteroid size, composition, and source region, we use a dynamical model to determine the most probable source region of each NEA. Model results indicate that NEAs with LL chondrite mineralogies appear to be preferentially derived from the ν₆ secular resonance. This supports the hypothesis that the Flora family, which lies near the ν₆ resonance, is the source of the LL chondrites. With the exception of basaltic achondrites, NEAs with non-chondrite spectral parameters are slightly less likely to be derived from the ν₆ resonance than NEAs with chondrite-like mineralogies. The population of NEAs with H, L, and LL chondrite mineralogies does not appear to be influenced by size, which would suggest that ordinary chondrites are not preferentially sourced from meter-sized objects due to Yarkovsky effect.     

Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect

Thermal inertia determines the temperature distribution over the surface of an asteroid and therefore governs the magnitude the Yarkovsky effect. The latter causes gradual drifting of the orbits of km-sized asteroids and plays an important role in the delivery of near-Earth asteroids (NEAs) from the main belt and in the dynamical spreading of asteroid families. At present, very little is known about the thermal inertia of asteroids in the km size range. Here we show that the average thermal inertia of a sample of NEAs in the km-size range is . Furthermore, we identify a trend of increasing thermal inertia with decreasing asteroid diameter, D. This indicates that the dependence of the drift rate of the orbital semimajor axis on the size of asteroids due to the Yarkovsky effect is a more complex function than the generally adopted D⁻¹ dependence, and that the size distribution of objects injected by Yarkovsky-driven orbital mobility into the NEA source regions is less skewed to smaller sizes than generally assumed. We discuss how this fact may help to explain the small difference in the slope of the size distribution of km-sized NEAs and main-belt asteroids.     

Dynamics of Small Earth-Approachers on Low-Eccentricity Orbits and Implications for Their Origins

The population of Near-Earth Asteroids (NEAs) appears to be overabundant at sizes smaller than 50m, compared to a power-law extrapolation from kilometer-sized objects. Several of these small NEAs are also concentrated on low-eccentricity orbits, where a few larger Earth-crossers are observed, and are called Small Earth-Approachers (SEAs). Their source region as well as the dynamical mechanisms involved in their transport close to the Earth on low-eccentricity orbits have not yet been determined. In this paper, we present our numerical and statistical study of the production and dynamical evolution of these SEAs. We first show that three main sources of Earth-crossers which are, according to recent simulations, the 3/1 and ₆ resonances in the main belt, and the Mars-crosser population, are not able to produce as many bodies on SEAs-like orbits compared to other Earth-crossing orbits as has been inferred from observations. From these sources, SEAs-like orbits are reached through the interplay of two required mechanisms: secular resonances and planetary close approaches. However, the time spent on these orbits remains smaller than 1 Myr as confirmed by the study of the evolutions of 11 observed SEAs which also reveal the action of various mechanisms such as close approaches to planets and/or secular resonances. Therefore, our results present some mechanisms which can be responsible for their production but none that would preserve the lifetime of the SEAs sufficiently to enhance their abundance relative to other Earth-crossing orbits at the level observed. The overabundance of the SEA population, if real, remains a problem and could be related to the influence of collisional disruption and tidal splitting of Earth-crossers, as well as to observational biases that might account for a discrepancy between theory and observation.     

International program of observations of selected minor planets: first results

International programs of observations of selected minor planets have lasted about 50 years and the last one comes to the end in 2000. The main aim of these observational programs consists in obtaining the orientation of the stellar reference frame with respect to the dynamical one using observations of the bright minor planets. The observations are also useful for the orbital improvements of the asteroids themselves. They are available from the author via e-mail at the address .During the above mentioned period more than 23 000 observations of minor planets, referred to different reference star catalogues, have been obtained. The reduction procedure of observations to the PPM star catalogue is described. The orientation parameters are given and discussed.     

Problems of asteroid–comet hazard

The most relevant tasks associated with the problem of asteroid–comet hazard are discussed. A review is given of the respective research at the Institute of Applied Astronomy. The institute is currently implementing a project to create an information center whose tasks include the collection and processing of optical and radar observations of small solar system bodies, determination of their orbits, and assessment of the impact hazard of the newly discovered small bodies with respect to the earth, moon, and the other major planets and their satellites.     

Fuzzy characterization of near-earth-asteroids

Due to close encounters with the inner planets, Near-Earth-Asteroids (NEAs) can have very chaotic orbits. Because of this chaoticity, a statistical treatment of the dynamical properties of NEAs becomes difficult or even impossible. We propose a new way to classify NEAs by using methods from Fuzzy Logic. We demonstrate how a fuzzy characterization of NEAs can be obtained and how a subsequent analysis can deliver valid and quantitative results concerning the long-term dynamics of NEAs.     

Yarkovsky origin of the unstable asteroids in the 2/1 mean motion resonance with Jupiter

The 2/1 mean motion resonance with Jupiter, intersecting the main asteroid belt at ≈3.27  au, contains a small population of objects. Numerical investigations have classified three groups within this population: asteroids residing on stable orbits (i.e. Zhongguos), those on marginally stable orbits with dynamical lifetimes of the order of 100 Myr (i.e. Griquas), and those on unstable orbits. In this paper, we reexamine the origin, evolution and survivability of objects in the 2/1 population. Using recent asteroid survey data, we have identified 100 new members since the last search, which increases the resonant population to 153. The most interesting new asteroids are those located in the theoretically predicted stable island A, which until now had been thought to be empty. We also investigate whether the population of objects residing on the unstable orbits could be resupplied by material from the edges of the 2/1 resonance by the thermal drag force known as the Yarkovsky effect (and by the YORP effect, which is related to the rotational dynamics). Using N -body simulations, we show that test particles pushed into the 2/1 resonance by the Yarkovsky effect visit the regions occupied by the unstable asteroids. We also find that our test bodies have dynamical lifetimes consistent with the integrated orbits of the unstable population. Using a semi-analytical Monte Carlo model, we compute the steady-state size distribution of magnitude   H < 14  asteroids on unstable orbits within the resonance. Our results provide a good match with the available observational data. Finally, we discuss whether some 2/1 objects may be temporarily captured Jupiter-family comets or near-Earth asteroids.     

Generalized Averaging Principle and the Secular Evolution of Planet Crossing Orbits

Planet crossing orbits give rise to mathematical singularities that make it not possible to apply the classical averaging principle to study the qualitative evolution of Near Earth Asteroids (NEAs). Recently this principle has been generalized to deal with crossings in a mathematical model with the planets on circular coplanar orbits. More accuracy is needed to compute the averaged evolution of planet crossing orbits for different purposes: computing reliable crossing times for the averaged motion, writing more precise proper elements and frequencies for NEAs, etc. In this paper we present the generalization of the averaging principle using a model where the eccentricity and the inclination of the planets are taken into account.     

New findings on asteroid spin-vector distributions

The number of known spin vectors of main belt and near-Earth asteroids is regularly growing, including new objects, and updating the estimates concerning known cases, with the aid of new observations and of improved observational techniques. A reliable statistical analysis of the spin vectors is now possible. In general the poles (both for MB bodies and for NEAs) are not isotropically distributed, as some general theoretical considerations may predict. Main belt asteroids show a lack of poles close to the ecliptic plane. There is a marginally significant excess of prograde spinners in the 100-150 km size range, but interestingly there is not a statistically significant excess in the larger size range. Among NEAs, there is an excess of retrograde rotations. The distributions of longitudes of poles of both groups do not show statistically significant deviations from random. We discuss the possible physical implications of the various resulting pole anisotropies in terms of dynamical—mainly non-gravitational—effects, and point out the importance of new observational campaigns, mainly devoted to compute the poles of small bodies and of the members of asteroid dynamical families.