Dynamical model of binary asteroid systems through patched three-body problems

The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.     

Utilization of an H-reversal trajectory of a solar sail for asteroid deflection

Near Earth Asteroids have a possibility of impacting the Earth and always represent a threat. This paper proposes a way of changing the orbit of the asteroid to avoid an impact. A solar sail evolving in an H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of the solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact the target asteroid along an H-reversal trajectory. The impact...     

Deflection of Hazardous Near-Earth Objects by High Concentrated Sunlight and Adequate Design of Optical Collector

Some detailed astronomical and applied aspects deflection of hazardous near-Earth objects (NEO) by direct high concentrated sunlight, causing intensive local ablation of their surfaces, are considered. The major requirements to solar concentrating optics within a single collector (a large mirror) approach, along with the asteroid properties being most substantial in achieving the predetermined effect for the period less than a year (mid-thrust action), are discussed. Such a hastened strategy may become topical in the case of late detection of potential danger, and also, if required, in providing the possibility for some additional action. It is also more acceptable in the public perception and keeping the peace for mankind rather than a long-run expectation of the incorrigible deflection resulting shortly ahead of the predicted hazard. The conventional concave reflectors have been graved to be practically inapplicable within the high concentrating geometry. This is primarily because of the dramatic spread of their focal spots at needful inclinations of optical axis from the direction toward the Sun, as well as of problematic use of the secondary optics. An alternative design of a mirrored ring-array collector is presented (as a tested and approved point-focus version of innovative reflective lenses for sunlight concentration within this approach), and comparative analysis was made. The assessment argues in favor of such a type of high-aperture optics having more capabilities than conventional devices. Mainly, this is because of the underside position (as respects the entrance aperture) of its focal area that allows avoidance of target shadowing the reflecting surfaces and minimizes their coating by the ejected debris. By using the modern asteroids database, some key estimations have been obtained. The surface irradiance around 4–5 MW/m² (average across the focal spot concentration level ~5 × 10³) for the ring-array collector size ~0.5 of asteroid diameter might suffice to deflect a 0.5-km-diameter NEO during several months. For the larger diameter NEOs, to 1.3–2.2 km, the required collector sizes are about the asteroid diameters, and they are even greater for more massive objects.     

Possible potentially threatening co‐orbiting material of asteroid 2000EE104 identified through interplanetary magnetic field disturbances

Near‐Earth objects (NEOs) with diameters of <300 m are difficult to detect from the Earth with radar or optical telescopes unless and until they approach closely. If they are on collisional courses with the Earth, there is little that can be done to mitigate the considerable damage. Although destructive collisions in space are rare for 1 km diameter bodies and above, once hit by a sizeable impactor, such a NEO can develop a relatively dense cloud of co‐orbiting material in which destructive collisions are relatively frequent. The gas and nanoscale dust released in the destructive collisions can be detected remotely by downstream spacecraft equipped with magnetometers. In this paper, we use such magnetic disturbances to identify regions of near‐Earth space in which high densities of small objects are present. We find that asteroid (138175) 2000EE104 currently may have a cloud of potentially threatening co‐orbiting material. Due to the scattered co‐orbitals, there can be a finite impact probability whenever the Earth approaches the orbit of asteroid 2000EE104, regardless of the position of the asteroid itself.     

Optimum trajectories for spacecraft mission to asteroid Apophis with a return to the Earth

A topical task for astronautics is to prepare a mission to the asteroid Apophis that is approaching the Earth. Determination of energetically favorable trajectories for a spacecraft involved in this mission with a return to the Earth has been considered. Two possible variants of engines for this mission are analyzed. The first variant employs electric engines with low jet thrust, while the second variant employs a spacecraft accelerated and controlled by only high-thrust engines. It is shown that both variants can be used in the mission to Apophis, but the use of electric engines with low thrust allows the project characteristics to be significantly improved.     

木星探测轨道分析与设计

研究了与木星探测相关的轨道设计问题.重点关注木星探测轨道与火星、金星等类地行星探测轨道的不同及由此带来的轨道设计难点.首先分析了绕木星探测任务轨道的选择.建立近似模型讨论了向木星飞行需要借助多颗行星的多次引力辅助,对地木转移的多种行星引力辅助序列,使用粒子群算法搜索了2020年至2025年之间的燃料最省飞行方案并对比得到了向木星飞行较好的引力辅助方式为金星-地球-地球引力辅助.结合多任务探测,研究了航天器在飞向木星途中穿越主小行星带飞越探测小行星的轨道设计.最后,给出2023年发射完整的结合引力辅助与小行星多次飞越的木星探测轨道设计算例.     

Feasibility study for near-earth-object tracking by a piggybacked micro-satellite with penetrators

As of August 2007, over 5000 near-earth-objects (NEO) have been discovered. Some already represent a potential danger to the Earth while others might become hazards in the future. The Planetary Society organised in 2007 the “Apophis Mission Design Competition” in response to this potential threat with the objective to identify promising concepts to track NEOs; the asteroid 99942 Apophis was taken as the study case. This paper describes the “Houyi” proposal which was evaluated by the competition jury as an innovative approach to this problem. Instead of launching a large satellite for NEO tracking, this novel concept proposes a miniaturized satellite that is piggybacked onto a larger (scientific) mission. Such mission design would drastically reduce the costs for NEO surveillance. The presented scenario uses the ESA’s SOLO mission as a design baseline for the piggyback option. This paper summarizes the architecture of this CubeSat towards Apophis and extends the previous study by focusing on the feasibility of a piggybacked mission in terms of propulsion requirements.     

On the deflection of asteroids with mirrors

This paper presents an analysis of an asteroid deflection method based on multiple solar concentrators. A model of the deflection through the sublimation of the surface material of an asteroid is presented, with simulation results showing the achievable impact parameter with, and without, accounting for the effects of mirror contamination due to the ejected debris plume. A second model with simulation results is presented analyzing an enhancement of the Yarkovsky effect, which provides a significant deflection even when the surface temperature is not high enough to sublimate. Finally the dynamical model of solar concentrators in the proximity of an irregular celestial body are discussed, together with a Lyapunov-based controller to maintain the spacecraft concentrators at a required distance from the asteroid.     

A concept for providing warning of earth impacts by small asteroids

The atmospheric detonation of a 17 m-asteroid above Chelyabinsk, Russia on 2013 February 15 shows that even small asteroids can cause extensive damage. Earth-based telescopes have found smaller harmless objects, such as 2008 TC3, a 4 m-asteroid that was discovered 20h before it exploded over northeastern Sudan (Jenniskens, 2009). 2008 TC3 remains the only asteroid discovered before it hit Earth because it approached Earth from the night side, where it was observed by large telescopes searching for near-Earth objects (NEO’s). The larger object that exploded over Chelyabinsk approached Earth from the day side, from too close to the Sun to be detected from Earth. A sizeable telescope in an orbit about the Sun-Earth L1 (SE-L1) libration point could find objects like the “Chelyabinsk” asteroid approaching approximately from the line of sight to the Sun about a day before Earth closest approach. Such a system would have the astrometric accuracy needed to determine the time and impact zone for a NEO on a collision course. This would give at least several hours, and usually 2–4 days, to take protective measures, rather than the approximately two-minute interval between the flash and shock wave arrival that occurred in Chelyabinsk. A perhaps even more important reason for providing warning of these events, even smaller harmless ones that explode high in the atmosphere with the force of an atomic bomb, is to prevent mistaking such an event for a nuclear attack that could trigger a devastating nuclear war. A concept using a space telescope similar to that needed for an SE-L1 monitoring satellite, is already conceived by the B612 Foundation, whose planned Sentinel Space Telescope could find nearly all 140 m and larger NEO’s, including those in orbits mostly inside the Earth’s orbit that are hard to find with Earth-based telescopes, from a Venus-like orbit (Lu, 2013). Few modifications would be needed to the Sentinel Space Telescope to operate in a SE-L1 orbit, 0.01 AU from Earth towards the Sun, to find most asteroids larger than about 5 meters that approach the Earth from the solar direction. The spacecraft would scan 165 square degrees of the sky around the Earth every hour, finding asteroids when they are brightest (small phase angle) as they approach Earth. We will undertake Monte Carlo studies to see what fraction of asteroids 5 m and larger approaching from the Sun might be found by such a mission, and how much warning time might typically be expected. Also, we will check the overall coverage for all Earth-approaching NEO’s, including ground-based observations and observations by the recently-launched NEOSSat, which may best fill any gaps in coverage between that provided by an SE-L1 telescope and ground-based surveys. Many of the objects as large as 50 m, like the one that created Meteor Crater in Arizona, will not be found by current NEO surveys, while they would usually be seen by this possible mission even if they approached from the direction of the Sun. We should give better warning for future “Bolts out of the blue.”     

Modeling orbital gamma‐ray spectroscopy experiments at carbonaceous asteroids

To evaluate the feasibility of measuring differences in bulk composition among carbonaceous meteorite parent bodies from an asteroid or comet orbiter, we present the results of a performance simulation of an orbital gamma‐ray spectroscopy (GRS) experiment in a Dawn‐like orbit around spherical model asteroids with a range of carbonaceous compositions. The orbital altitude was held equal to the asteroid radius for 4.5 months. Both the asteroid gamma‐ray spectrum and the spacecraft background flux were calculated using the MCNPX Monte‐Carlo code. GRS is sensitive to depths below the optical surface (to ≈20–50 cm depth depending on material density). This technique can therefore measure underlying compositions beneath a sulfur‐depleted (e.g., Nittler et al. 2001 ) or desiccated surface layer. We find that 3σ uncertainties of under 1 wt% are achievable for H, C, O, Si, S, Fe, and Cl for five carbonaceous meteorite compositions using the heritage Mars Odyssey GRS design in a spacecraft‐deck‐mounted configuration at the Odyssey end‐of‐mission energy resolution, FWHM = 5.7 keV at 1332 keV. The calculated compositional uncertainties are smaller than the compositional differences between carbonaceous chondrite subclasses.     

Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids

Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.     

Physical characteristics of Hayabusa target Asteroid 25143 Itokawa

In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.     

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.     

The near-Earth objects and their potential threat to our planet

The near-Earth object (NEO) population includes both asteroids (NEAs) and comet nuclei (NECs) whose orbits have perihelion distances q<1.3 AU and which can approach or cross that of the Earth. A NEA is defined as a “potentially hazardous asteroid” (PHA) for Earth when its minimum orbit intersection distance (MOID) comes inside 0.05 AU and it has an absolute magnitude H<22 mag (i.e. mean diameter > 140 m). These are big enough to cause, in the case of impact with Earth, destructive effects on a regional scale. Smaller objects can still produce major damage on a local scale, while the largest NEOs could endanger the survival of living species. Therefore, several national and international observational efforts have been started (i) to detect undiscovered NEOs and especially PHAs, (ii) to determine and continuously monitor their orbital properties and hence their impact probability, and (iii) to investigate their physical nature. Further ongoing activities concern the analysis of possible techniques to mitigate the risk of a NEO impact, when an object is confirmed to be on an Earth colliding trajectory. Depending on the timeframe available before the collision, as well as on the object’s physical properties, various methods to deflect a NEO have been proposed and are currently under study from groups of experts on behalf of international organizations and space agencies. This paper will review our current understanding of the NEO population, the scientific aspects and the ongoing space- and ground-based activities to foresee close encounters and to mitigate the effects of possible impacts.     

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.     

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.     

Capturing near earth objects

Recently,Near Earth Objects(NEOs) have been attracting great attention,and thousands of NEOs have been found to date.This paper examines the NEOs' orbital dynamics using the framework of an accurate solar system model and a Sun-Earth-NEO three-body system when the NEOs are close to Earth to search for NEOs with low-energy orbits.It is possible for such an NEO to be temporarily captured by Earth;its orbit would thereby be changed and it would become an Earth-orbiting object after a small increase in its velocity.From the point of view of the Sun-Earth-NEO restricted three-body system,it is possible for an NEO whose Jacobian constant is slightly lower than C1 but higher than C3 to be temporarily captured by Earth.When such an NEO approaches Earth,it is possible to change its orbital energy to nearly the zero velocity surface of the three-body system at point L1 and make the NEO become a small satellite of the Earth.Some such NEOs were found;the best example only required a 410 m s-1 increase in velocity.     

Peculiarities of the motion of asteroid 99942 Apophis

The Apophis asteroid attracted the attention of scientists immediately after its discovery in 2004, because the initially determined orbit of this asteroid assumes a possible collision with Earth in April 2029. The size of Apophis is about several hundred meters, and its collision with Earth might result in a large regional or even global catastrophe. At present, the trajectory of Apophis has been calculated more accurately, and a collision in 2029 has ruled out; the asteroid will pass Earth at a distance of about 37 000 km from its center. However, close approaches or collisions are possible after 2029, including the most probable in 2036. The risk of collision in 2036 is well known and actively examined by the scientists. In this study, we consider the peculiarities of the asteroid motion associated with its approach in 2029 and with a possible close approach in 2036. The trajectories scatter during the approaches and the loss of accuracy is associated with these scatterings. As a result, the trajectory of Apophis may become nondeterministic after 2036; that is, it cannot now be determined unambiguously. Although such events are very unlikely, it is interesting to examine a variety of alternative variants of Apophis’ close approaches and collisions with Earth immediately after 2036. The effects of small variations in the asteroid velocity at different moments in time after its impact with a certain mass are discussed.     

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.     

Capturing near earth objects

Recendy,Near Earth Objects (NEOs) have been attracting great attention,and thousands of NEOs have been found to date.This paper examines the NEOs'orbital dynamics using the framework of an accurate solar system model and a SunEarth-NEO three-body system when the NEOs are close to Earth to search for NEOs with low-energy orbits.It is possible for such an NEO to be temporarily captured by Earth; its orbit would thereby be changed and it would become an Earth-orbiting object after a small increase in its velocity.From the point of view of the Sun-Earth-NEO restricted three-body system,it is possible for an NEO whose Jacobian constant is slightly lower than C1 but higher than C3 to be temporarily captured by Earth.When such an NEO approaches Earth,it is possible to change its orbital energy to nearly the zero velocity surface of the three-body system at point L1 and make the NEO become a small satellite of the Earth.Some such NEOs were found; the best example only required a 410 m s-1 increase in velocity.