Asteroids on Earth-like orbits and their origin

The orbit of 1991 VG and a set of other asteroids whose orbits are very similar to that of the Earth have been examined. Its origin has been speculated to be a returning spacecraft, lunar ejecta or a low-inclination Amor- or Apollo-class object. The latter is arguably the more likely source, which has been investigated here. The impact probability for these objects has been calculated, and while it is larger than that of a typical near-Earth asteroid (NEA), it is still less than 1:200 000 over the next 5000 yr. In addition, the probability of an NEA ever ending up on an Earth-like orbit has been obtained from numerical simulations and turned out to be about 1:20 000, making this a rare class of objects. The typical time spent in this state is about 10 000 yr, much less than the typical NEA lifetime of 10 Myr.     

Long-Lived Near-Earth Asteroid 2013 RB6

The search for asteroids that maintain stable motion in the zone between the Earth and Mars has been performed. The near-Earth object 2013 RB6, which has avoided close encounters with the planets for a long period of time, has been found. Integration of the equations of motion of the object shows that its dynamical lifetime in the zone between the Earth and Mars significantly exceeds 100 Myr. 2013 RB6 moves away from orbital resonances with the planets, but is in the secular resonance ν₅. Solving the question of its origin requires further observations.     

关于章动序列计算中的地球动力学扁率的取值

刚体地球章动序列和非刚体地球章动的转换函数都和地球动力学扁率有关。ＩＡＵ１９８０章动理论中采用了一个不一致的地球动力学扁率值,从而影响了章动振幅的计算。本文介绍了章动序列计算中地球动力学扁率的取值。由地球模型１０６６Ａ或ＰＲＥＭ得到的地球动力学扁率值比由岁差观测得到的约小１％,并且不可靠。当考虑体静力学平衡被破坏时新的地球物理模型,可得到与岁差常数相一致的地球动力学扁率值。地球动力学扁率值Ｈ＝０．     

The OSIRIS‐REx target asteroid (101955) Bennu: Constraints on its physical,geological, and dynamical nature from astronomical observations

We review the results of an extensive campaign to determine the physical, geological, and dynamical properties of asteroid (101955) Bennu. This investigation provides information on the orbit, shape, mass, rotation state, radar response, photometric, spectroscopic, thermal, regolith, and environmental properties of Bennu. We combine these data with cosmochemical and dynamical models to develop a hypothetical timeline for Bennu's formation and evolution. We infer that Bennu is an ancient object that has witnessed over 4.5 Gyr of solar system history. Its chemistry and mineralogy were established within the first 10 Myr of the solar system. It likely originated as a discrete asteroid in the inner Main Belt approximately 0.7–2 Gyr ago as a fragment from the catastrophic disruption of a large (approximately 100‐km), carbonaceous asteroid. It was delivered to near‐Earth space via a combination of Yarkovsky‐induced drift and interaction with giant‐planet resonances. During its journey, YORP processes and planetary close encounters modified Bennu's spin state, potentially reshaping and resurfacing the asteroid. We also review work on Bennu's future dynamical evolution and constrain its ultimate fate. It is one of the most Potentially Hazardous Asteroids with an approximately 1‐in‐2700 chance of impacting the Earth in the late 22nd century. It will most likely end its dynamical life by falling into the Sun. The highest probability for a planetary impact is with Venus, followed by the Earth. There is a chance that Bennu will be ejected from the inner solar system after a close encounter with Jupiter. OSIRIS‐REx will return samples from the surface of this intriguing asteroid in September 2023.     

Orbit Determination of the Asteroid (469219) Kamoòalewa and Its Error Analysis

As an Earth co-orbital asteroid, (469219) Kamoòalewa is a near earth object (NEO) with high value of research, and one of the targets explored by the first Chinese asteroid exploration mission. Given its orbit characteristics, we build a refined dynamical model for this asteroid, in which the effects induced by nonspherical gravitational fields of the Sun, the Earth, and the Moon are combined. On the basis of the dynamical model of the asteroid (469219) Kamoòalewa, its orbit is determined with optical data from 2004 to 2018 available on the Minor Planet Center (MPC) database. The root mean square error of post-fit residuals is about 0.2 arc second (comparable with that of the Jet Propulsion Laboratory (JPL)/Horizons), and the post-fit residuals of optical observations in 2004 are decreased. At the end, we implement error analysis on the asteroid (469219) Kamoòalewa's orbit in detail, and also predict its orbit error at the time interval between 2020 and 2025.     

小行星(469219) Kamo`oalewa轨道的确定与误差分析

作为一颗与地球共轨道的小行星,(469219)Kamo'oalewa是一个具有很高研究价值的近地小天体,也是中国首次小行星探测计划的目标天体之一.针对其轨道特性,建立了兼顾太阳、地球和月球非球形引力作用的小行星动力学模型.并在该模型的基础上,利用国际小行星中心(Minor Planet Center,MPC)提供的2004|2018年间的光学观测数据对该小行星的轨道进行确定.拟合后观测残差的均方根误差约为0:2″(与美国喷气推进实验室的Horizons在线历表系统相当),其中2004年期间数据的观测残差有所改进.最后,对小行星(469219)Kamo'oalewa的轨道误差进行了详细分析,并预报了2020-2025年期间该小行星的轨道误差.     

地球动力学扁率及其与岁差章动的关系

由岁差常数求得的日月岁差是天文学的重要参数之一,它和地球动力学扁率相联系。地球动力学扁率在章动理论的计算中也是一个重要的物理量。介绍了由不同的观测方法和模型给出的地球动力扁率值,并讨论了它也岁差的关系和对章动计算的影响。在刚体地球章动振幅的计算中,地球动力学扁率值起着尺度因子的作用,要改善刚体地球章动振幅的计算,需要修改目前的黄经总岁差值。非刚体地球章动的转换函数中所采用的简正模和常数都直接或间接地依赖地球动力学扁率值。在IAU1980章动理论中,计算刚体地球章动振幅所使用的地球动力学扁率值计算转换函数中简正模频率和常数所使用的地球动力学扁率值并不一致。随着观测和计算精度的提高,地球动力学扁率值的不一致将影响章动振幅的计算。在建立刚体地球章地动理论中,如何解释地球动力学扁率值的差异,如何选取地球动力学扁率值,还有待进一步的研究。     

The population of natural Earth satellites

We have for the first time calculated the population characteristics of the Earth’s irregular natural satellites (NESs) that are temporarily captured from the near-Earth-object (NEO) population. The steady-state NES size–frequency and residence-time distributions were determined under the dynamical influence of all the massive bodies in the Solar System (but mainly the Sun, Earth, and Moon) for NEOs of negligible mass. To this end, we compute the NES capture probability from the NEO population as a function of the latter’s heliocentric orbital elements and combine those results with the current best estimates for the NEO size–frequency and orbital distribution. At any given time there should be at least one NES of 1-m diameter orbiting the Earth. The average temporarily-captured orbiter (TCO; an object that makes at least one revolution around the Earth in a co-rotating coordinate system) completes (2.88 ± 0.82) rev around the Earth during a capture event that lasts (286 ± 18) d. We find a small preference for capture events starting in either January or July. Our results are consistent with the single known natural TCO, 2006 RH₁₂₀, a few-meter diameter object that was captured for about a year starting in June 2006. We estimate that about 0.1% of all meteors impacting the Earth were TCOs.     

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.     

弹性地球各种几何轴和物理轴的定义

基于经典的弹性地球自转动力学理论,建立了极移和章动的联合动力学方程。由此给出了弹性地球各种几何轴和物理轴(Tisserand轴、自转轴、瞬时形状轴、角动量轴、CEP和CIP轴)的极移、岁差章动的动力学方程,明确了各种轴的定义及其之间的理论关系。理论研究表明,联合动力学方程要比经典动力学方程综合性强易于理解,可同时求解极移和章动,特别是在文[1]理论中出现的倾斜模(TOM),在此只是作为了一个特解而存在。     

Formation of the binary near‐Earth object 1996 FG3: Can binary NEOs be the source of short‐CRE meteorites?

Abstract— 1996 FG₃ is a binary near‐Earth object (NEO) that was likely formed during a tidal disruption event. Our results indicate that the formation of this binary object was unlikely to have occurred when the progenitor had a encounter velocity with the Earth significantly smaller than its current value (10.7 km/s); The formation of the binary object on an orbit similar to the present one is possible, and the survival of the satellite constrains this to have happened less than 1.6 Ma ago. However, the binary object could also have been formed when the progenitor's encounter velocity with Earth was >12 km/s, and in this case we cannot constrain its formation age. Our results indicate that tidal disruptions occurring among NEOs with low velocity encounters with Earth are unlikely to produce long‐lasting NEO binaries. Thus, tidal disruption may not be able to completely re‐supply the observed population. This would imply that a significant fraction of the observed NEO binaries evolved out of the main asteroid belt. Overall, our results suggest to us that the CM2 meteorites having cosmic ray exposure (CRE) ages of ?200,000 yr were likely liberated by the tidal disruption of a primitive NEO with a relative velocity with the Earth significantly smaller than that of 1996 FG₃. We propose a list of such objects, although as far as we know, none of the candidates is a binary for the reasons described above.     

Orbital and mission planning constraints for the deflection of NEOs impacting on Earth

This paper is the third in a series. Paper 1 presented the results of numerical modeling of deflections of NEOs in route of collision with the Earth. The model was applied to a variety of dynamical cases including both asteroidal and cometary NEOs. Paper 2 introduced the concept of “distributed deflection,” i.e., the possibility to provide the ΔV necessary to deflect an object with a succession of maneuvers each of which would have been insufficient per se to obtain the desired result. In both papers no assumptions were made on the physical composition and structure of the NEO, nor on the details of the possible deflection maneuvers from the point of view of mission analysis. Moreover, ΔV-plots were computed assuming only along-track impulses (both in the positive and negative directions), because it is easy to demonstrate that in general this is energetically the most favorable configuration. Also in the present paper no assumptions were made on the physical composition and structure of the NEO, even if order of magnitude considerations are made on the physical feasibility of a deflection, in terms of the internal strength of the NEO. We present here the results of an investigation on the mission requirements necessary to deflect an object (or contribute to a succession of deflecting maneuvers) in terms of accessibility of the spacecraft terminal orbit from Earth with the current launchers.     

Kinetic energy of a non-spherical elastic earth mantle with andoyer variables

Continuing the study of the rotation of a deformable Earth begun by Getino and Ferrandiz (1990, 1991a, 1991b, 1993, 1994) for an Earth model with an elastic spherical mantle, in this paper on one hand we deal with the effect of the ellipticity, and on the other hand, we include the toroidal solution of the displacement vector. Taking an axis symmetrical, slightly ellipsoidal Earth, the modification due to the ellipticity is introduced into the solution of the displacement vector for both spheroidal and toroidal modes, and, after defining the adequate variables, we give the canonical formulation of the corresponding increase in the kinetic energy.     

Spacecraft Orbit Determination with The B-spline Approximation Method

It is known that the dynamical orbit determination is the most common way to get the precise orbits of spacecraft. However, it is hard to build up the precise dynamical model of spacecraft sometimes. In order to solve this problem, the technique of the orbit determination with the B-spline approximation method based on the theory of function approximation is presented in this article. In order to verify the effectiveness of this method, simulative orbit determinations in the cases of LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and HEO (Highly Eccentric Orbit) satellites are performed, and it is shown that this method has a reliable accuracy and stable solution. The approach can be performed in both the conventional celestial coordinate system and the conventional terrestrial coordinate system. The spacecraft's position and velocity can be calculated directly with the B-spline approximation method, it needs not to integrate the dynamical equations, nor to calculate the state transfer matrix, thus the burden of calculations in the orbit determination is reduced substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can serve as a conventional algorithm in the spacecraft orbit determination.     

Source regions and timescales for the delivery of water to the Earth

Abstract— In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas‐free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter‐Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus‐Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.     

The Dynamical Evolution of the Atens

In this investigation the orbits of 21 Atens (semimajor axes smaller than the Earth) are studied with the aid of numerical integrations over the time interval of one million years. The dynamical model was a 6-body Solar System, where the perturbations of Uranus and Neptune were ignored, and where Mercury's mass was added to the Sun's mass. Thus mean motion resonances, secular resonances and the Kozai resonance were fully taken into account. The evolution of the semimajor axes shows the typical step function like pattern which we know also from comets although some Atens have a very fuzzy development of the orbital elements, and some of them stay in a mean motion resonance for very long time. The evolution from Atens to Apollos (with semimajor axes larger than the Earth) and vice versa is also a phenomenon which we could observe. The main goal was the study of encounters of the Atens with the Earth and Venus. We found out that Venus encounters occur somewhat more often than Earth encounters (approximately one within the distance Earth - Moon every 40000 years with Venus, one every 50000 years with the Earth). This revised version was published online in July 2006 with corrections to the Cover Date.     

A planetary system with an escaping Mars

The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ _E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ _E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low Energy Transfer to the Moon

In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less Vthan a standard Hohmann transfer. In this paper, we apply the dynamical systems techniques developed in our earlier work to reproduce systematically a Hiten-like mission. We approximate the Sun–Earth–Moon-spacecraft 4-body system as two 3-body systems. Using the invariant manifold structures of the Lagrange points of the 3-body systems, we are able to construct low energy transfer trajectories from the Earth which execute ballistic capture at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations.     

Remarks on dynamical ellipticity at the Earth's

In this paper, two factors — the redistribution of the density and the variation in the angular velocity of the Earth rotation, that affect the adopted value of the flattening for equidensity surface within the Earth, are discussed. The computational results show that the contribution of the redistribution of the density in the Earth interior (especially in the core) on the change of the flattening at the core-mantle boundary (CMB) is marginal, and that the calculated value of the flattening at the CMB can be in good agreement with the VLBI observed value so long as the fact that the angular velocity of the Earth rotation has undergone the tidal evolution is taken into account. As a result, this paper presents a set of recommended values of the dynamical parameters of the Earth (see Table III) for computing Earth's forced nutation series.     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.