Solar radiation pressure on (99942) Apophis

Near-Earth asteroid (99942) Apophis currently resides among the top positions on the list of objects with small, yet non-zero impact probability with the Earth. For that reason an unusual observational and theoretical effort has been dedicated to precisely characterize its future orbit. Here we discuss orbital perturbation of Apophis due to incident and reflected solar radiation pressure (SRP). We both revisit recent analytical estimate of the SRP effects for this body and also formulate a numerical approach allowing us to compute the SRP orbital perturbation under general assumptions. Contrary to some previous results, we show that SRP has a much smaller effect on the Apophis trajectory than does the thermal re-radiation force which produces the Yarkovsky effect. When the Yarkovsky effect becomes constrained enough in the future, our approach may be used to improve the orbit determination for this asteroid.     

Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun–Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of $\Delta v$ Δ v . Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs.     

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.     

Trajectory Analysis and Design for A Jupiter Exploration Mission

The trajectory design for a Jupiter exploration mission is investigated in this paper. The differences between the Jupiter exploration trajectory and the Mars or Venus exploration trajectory are mainly concerned about. Firstly, the selection of the Jupiter-centered orbit is analyzed based on the Galileo Jupiter mission. As for the Earth-Jupiter transfer orbit, the fuel consumption of the direct transfer is too large. So the energy-saving technologies such as the planetary gravity assist should be used for the trajectory to the Jupiter. The different sequences of planetary gravity assists are examined by applying the Particle Swarm Optimization (PSO). According to the searched result, the Venus-Earth-Earth sequence (VEEGA) is the most effective one for the Jupiter mission. During the Jupiter mission, the spacecraft will pass though the main asteroid belt between the orbits of Mars and Jupiter, and may encounter multiple asteroids. Therefore the Jupiter mission is able to combine with the main-belt asteroid flyby mission. The design method of the intermediate asteroid flyby trajectory is also considered. At last, an entire trajectory for the Jupiter mission launched in 2023 is presented.     

Attitude stability of a spacecraft on a stationary orbit around an asteroid subjected to gravity gradient torque

Attitude stability of spacecraft subjected to the gravity gradient torque in a central gravity field has been one of the most fundamental problems in space engineering since the beginning of the space age. Over the last two decades, the interest in asteroid missions for scientific exploration and near-Earth object hazard mitigation is increasing. In this paper, the problem of attitude stability is generalized to a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied via the linearized equations of motion, in which the harmonic coefficients $C_{20}$ and $C_{22}$ of the gravity field of the asteroid are considered. The necessary conditions of stability of this conservative system are investigated in detail with respect to three important parameters of the asteroid, which include the harmonic coefficients $C_{20}$ and $C_{22}$ , as well as the ratio of the mean radius to the radius of the stationary orbit. We find that, due to the significantly non-spherical shape and the rapid rotation of the asteroid, the attitude stability domain is modified significantly in comparison with the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field. Especially, when the spacecraft is located on the intermediate-moment principal axis of the asteroid, the stability domain can be totally different from the classical stability domain. Our results are useful for the design of attitude control system in the future asteroid missions.     

Capillary action in a crack on the surface of asteroids with an application to 433 Eros

Some asteroids contain water ice, and a space mission landing on an asteroid may take liquid to the surface of the asteroid. Gas pressure is very weak on the surface of asteroids. Here we consider the capillary action in a crack on the surface of irregular asteroids. The crack is modeled as a capillary which has a fixed radius. An asteroid's irregular gravitational potential influences the height of the liquid in the capillary. The height of the liquid in the capillary on the surface of such asteroids is derived from the asteroid's irregular gravitational potential. Capillary mechanisms are expected to produce an inhomogeneaous distribution of emergent liquid on the surface. This result is applied to asteroid 433 Eros, which has an irregular, elongated, and concave shape. Two cases are considered: (1) we calculate the height of the liquid in the capillary when the direction of the capillary is perpendicular to the local surface of the asteroid; (2) we calculate the height of the liquid in the capillary when the direction of the capillary is parallel to the vector from the center of mass to the surface position. The projected height in the capillary on the local surface of the asteroid seems to depend on the assumed direction of the capillary.     

Possible records of space weathering on Vesta: Case study in a brecciated eucrite Northwest Africa 1109

Records of space weathering are important for understanding the formation and evolution of surface regolith on airless celestial bodies. Current understanding of space weathering processes on asteroids including asteroid‐4 Vesta, the source of the howardite–eucrite–diogenite (HED) meteorites, lags behind what is known for the Moon. In this study, we studied agglutinates, a vesicular glass‐coating lithic clast, and a fine‐grained sulfide replacement texture in the polymict breccia Northwest Africa (NWA) 1109 with electron microscopy. In agglutinates, nanophase grains of FeNi and FeS were observed, whereas npFe⁰ was absent. We suggested that the agglutinates in NWA 1109 formed from fine‐grained surface materials of Vesta during meteorite/micrometeorite bombardment. The fine‐grained sulfide replacement texture (troilite + hedenbergite + silica) should be a result of reaction between S‐rich vapors and pyroxferroite. The unique Fe/Mn values of relict pyroxferroite indicate a different source from normal HED pyroxenes, arguing that the reaction took place on or near the surface of Vesta. The fine‐grained sulfide replacement texture could be a product of nontypical space weathering on airless celestial bodies. We should pay attention to this texture in future returned samples by asteroid exploration missions.     

Stability of Surface Motion on a Rotating Ellipsoid

The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid.     

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.     

Simulated asteroid materials based on carbonaceous chondrite mineralogies

A set of high‐fidelity simulated asteroid materials, or simulants, was developed based on the mineralogy of carbonaceous chondrite meteorites. Three varieties of simulant were developed based on CI1 chondrites (typified by Orgueil), CM2 chondrites (typified by Murchison), and CR2/3 chondrites (multiple samples). The simulants were designed to replicate the mineralogy and physical properties of the corresponding meteorites and anticipated asteroid surface materials as closely as is reasonably possible for bulk amounts. The simulants can be made in different physical forms ranging from larger cobbles to fine‐grained regolith. We analyzed simulant prototypes using scanning electron microscopy, X‐ray fluorescence, reflectance spectroscopy at ambient conditions and in vacuum, thermal emission spectroscopy in a simulated asteroid environment chamber, and combined thermogravimetry and evolved gas analysis. Most measured properties compare favorably to the reference meteorites and therefore to predicted volatile‐rich asteroid surface materials, including boulders, cobbles, and fine‐grained soils. However, there were also discrepancies, and mistakes were made in the original mineral formulations that will be updated in the future. The asteroid simulants are available to the community from the nonprofit Exolith Lab at UCF, and the mineral recipes are freely published for other groups to reproduce and modify as they see fit.     

Space weathering and the interpretation of asteroid reflectance spectra

Lunar-style space weathering is well understood, but cannot be extended to asteroids in general. The two best studied Asteroids (433 Eros and 243 Ida) exhibit quite different space weathering styles, and neither exhibits lunar-style space weathering. It must be concluded that at this time the diversity and mechanisms of asteroid space weathering are poorly understood. This introduces a significant unconstrained variable into the problem of analyzing asteroid spectral data. The sensitivity of asteroid surface material characterizations to space weathering effects - whatever their nature - is strongly dependent upon the choice of remote sensing methodology. The effects of space weathering on some methodologies such as curve matching are potentially devastating and at the present time essentially unmitigated. On other methodologies such as parametric analysis (e.g., analyses based on band centers and band area ratios) the effects are minimal. By choosing the appropriate methodology(ies) applied to high quality spectral data, robust characterizations of asteroid surface mineralogy can be obtained almost irrespective of space weathering. This permits sophisticated assessments of the geologic history of the asteroid parent bodies and of their relationships to the meteorites. Investigations of the diversity of space weathering processes on asteroid surfaces should be a fruitful area for future efforts.     

Extended two-body problem for rotating rigid bodies

Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, comprised of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. In particular, connections between the periodic orbits of such two different moons are achieved. The strategy is applicable for any type of direct transfers that satisfy the analytical constraints. Case studies are presented for the Jovian and Uranian systems. The transition of the transfers into higher-fidelity ephemeris models confirms the validity of the MMAT method as a fast tool to provide possible transfer options between two consecutive moons.

     

Reliability of estimates for the sizes of spots on asteroid surfaces made by the spectral-frequency method

A new spectral-frequency method (SFM) for the study of solid body surfaces is briefly described. This method allows estimation of the sizes of various spots. Estimates for the sizes of spots on asteroid surfaces made by the SFM and other methods are compared and discussed. The sizes of spots on the surface of asteroid 1620 Geographos determined by the SFM are well consistent with those of the craters obtained from radar data. The sizes of hydrosilicate spots on the surface of asteroid 21 Lutetia found by the SFM agree with those of the craters determined by the Rosetta spacecraft. The size of a blue spot on the surface of asteroid 4 Vesta found by the SFM is consistent with the size of the well-known crater on the south pole of the asteroid. It is inferred that the SFM is a promising method for the estimation of the sizes of spots on asteroid surfaces.     

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.     

Evidence-based robust design of deflection actions for near Earth objects

This paper presents a novel approach to the robust design of deflection actions for near Earth objects (NEO). In particular, the case of deflection by means of solar-pumped laser ablation is studied here in detail. The basic idea behind laser ablation is that of inducing a sublimation of the NEO surface, which produces a low thrust thereby slowly deviating the asteroid from its initial Earth threatening trajectory. This work investigates the integrated design of the space-based laser system and the deflection action generated by laser ablation under uncertainty. The integrated design is formulated as a multi-objective optimisation problem in which the deviation is maximised and the total system mass is minimised. Both the model for the estimation of the thrust produced by surface laser ablation and the spacecraft system model are assumed to be affected by epistemic uncertainties (partial or complete lack of knowledge). Evidence Theory is used to quantify these uncertainties and introduce them in the optimisation process. The propagation of the trajectory of the NEO under the laser-ablation action is performed with a novel approach based on an approximated analytical solution of Gauss’ variational equations. An example of design of the deflection of asteroid Apophis with a swarm of spacecraft is presented.     

The NEAR‐Shoemaker x‐ray/gamma‐ray spectrometer experiment: Overview and lessons learned

Abstract— The near‐Earth asteroid rendezvous (NEAR)‐Shoemaker remote‐sensing x‐ray/gamma‐ray spectrometer (XGRS) completed more than a year of operation in orbit and on the surface of 433 Eros. Elemental compositions for a number of regions on the surface of Eros have been derived from analyses of the characteristic x‐ray and gamma‐ray emission spectra. The NEAR XGRS detection system was included as part of the interplanetary network (IPN) for the detection and localization of gamma‐ray bursts (GRBs). Preliminary results for both the elemental composition of the surface of Eros and the detection of GRBs have been obtained. In addition to the science results, the design and operation of the NEAR XGRS is considered. Significant information important for the design of future remote sensing XGRS systems has been obtained and evaluated. We focus on four factors that became particularly critical during NEAR: (1) overall spacecraft design, (2) selection of materials, (3) increase of the signal‐to‐noise ratio and (4) knowledge of the incident solar x‐ray spectrum.     

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.     

A Research on the Imaging Strategy and Imaging Simulation of Toutatis in the Chang’e-2 Flyby Mission

For the Chang’e-2 extended mission of asteroid exploration, the illumination conditions for imaging the asteroid Toutatis are calculated in this paper according to the orbital parameters of both the Chang’e-2 detector and the asteroid, as well as the incident angles of sunlight. On this basis, it is suggested to take photographs after flyby, and the orientation of the camera's optical axis in the coordinate system deflned by Earth's mean equator and equinox at J2000.0 is proposed to be (118.02°, 22.03°). Based on the shape model of Toutatis determined by the foreign radar data, the orientation of the asteroid in the inertial space is calculated at the rendezvous time. Using the Oren-Nayar diffuse-reflection model and the relative positions among the sun, the asteroid, and the detector, together with the cameras orientation, the imaging simulations are performed on the starry sky background respectively at the distances of 300 km, 500 km, and 1000 km from the asteroid after flyby. The results of simulations are verified further by the optical images of Toutatis obtained in the mission.     

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.