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.     

The role of meteoritics in spaceflight missions and vice versa

Abstract— Research on extraterrestrial materials plays a critical role in formulating the science rationale and design for spacecraft missions, and, conversely, spaceflight holds great promise for solving perplexing problems in meteoritics. The connections between meteoritics and sample-return missions are obvious: Meteorite research can define sampling strategies, the capabilities of sampling devices, acceptable levels of chemical contamination and physical alteration of samples, and the conditions under which samples are stored prior to and during recovery. For their part, sample-return missions can provide geologic context for meteorites, increased sampling diversity (including materials not sampled as meteorites, such as unconsolidated regolith, ices, and atmosphere), calibration for crater-counting chronology, and ground truth for remote sensing measurements of meteorite parent bodies. Meteoritics also relates to spacecraft flyby, rendezvous, and lander missions that do not necessarily return samples. Specific illustrations of this mutual relationship, based on a selection of recent or planned spacecraft missions include: Identifying source asteroid classes for ordinary and carbonaceous chondrites and reconstructing their thermal and collisional histories (Galileo, NEAR, Clementine II, and Muses-C); determining the extent to which cometary dust and interstellar grains are found as interplanetary dust particles and assessing volatile abundances, isotopic compositions, and molecular species in cometary nuclei (Stardust and Rosetta); understanding the compositions of ancient Martian crust and the mantle sources for SNC meteorites, as well as inventorying the planet's volatile reservoirs and interactions (Mars Pathfinder, Mars Global Surveyor, and Mars Volatiles and Climate Surveyor); assessing whether lunar meteorites provide a more representative chemical sampling of the highlands crust and of mare volcanism than do Apollo samples (Galileo, Clementine, and Lunar Prospector). Spaceflight is the first priority of the space agencies that fund most research on extraterrestrial materials, and the continued level of support for such research may be linked, in part, to its use in exploration by spacecraft.     

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.     

Discovery of an asteroid and quasi‐satellite in an Earth‐like horseshoe orbit

Abstract— The newly discovered asteroid 2002 AA₂₉ moves in a very Earth‐like orbit that relative to Earth has a unique horseshoe shape and allows transitions to a quasi‐satellite state. This is the first body known to be in a simple heliocentric horseshoe orbit, moving along its parent planet's orbit. It is similarly also the first true co‐orbital object of Earth, since other asteroids in 1:1 resonance with Earth have orbits very dissimilar from that of our planet. When a quasi‐satellite, it remains within 0.2 AU of the Earth for several decades. 2002 AA₂₉ is the first asteroid known to exhibit this behavior. 2002 AA₂₉ introduces an important new class of objects offering potential targets for space missions and clues to asteroid orbit transfer evolution.     

Be/X-ray binaries

The interest in X/γ-ray Astronomy has grown enormously in the last decades thanks to the ability to send X-ray space missions above the Earth’s atmosphere. There are more than half a million X-ray sources detected and over a hundred missions (past and currently operational) devoted to the study of cosmic X/γ rays. With the improved sensibilities of the currently active missions new detections occur almost on a daily basis. Among these, neutron-star X-ray binaries form an important group because they are among the brightest extra-solar objects in the sky and are characterized by dramatic variability in brightness on timescales ranging from milliseconds to months and years. Their main source of power is the gravitational energy released by matter accreted from a companion star and falling onto the neutron star in a relatively close binary system.     

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.     

On the Family of the Binary Asteroid 423 Diotima

We identified the family of the binary asteroid 423 Diotima consisting of 411 members in the phase space of orbital elements—semimajor axes a (or mean motions n), eccentricities e, and inclinations i—by using an electronic version of the ephemerides of minor planets EMP-2003 containing osculating orbital elements for 34992 asteroids of the main belt. The 9/4 resonance with Jupiter clearly separates the family of 423 Diotima from the family of Eos, which, according to EMP for 2003, contains 1204 asteroids.     

Linking meteorites to their asteroid parent bodies: The capabilities of dust analyzer instruments during asteroid flybys

Linking meteorites to their asteroid parent bodies remains an outstanding issue. Space-based dust characterization using impact ionization mass spectrometry is a proven technique for the compositional analysis of individual cosmic dust grains. Here we investigate the feasibility of determining asteroid compositions via cation mass spectrometric analyses of their dust ejecta clouds during low (7–9 km s⁻¹) velocity spacecraft flybys. At these speeds, the dust grain mass spectra are dominated by easily ionized elements and molecular species. Using known bulk mineral volume abundances, we show that it is feasible to discriminate the common meteorite classes of carbonaceous chondrites, ordinary chondrites, and howardite–eucrite–diogenite achondrites, as well as their subtypes, relying solely on the detection of elements with ionization efficiencies of ≤700 or ≤800 kJ mol⁻¹, applicable to low (~7 km s⁻¹) and intermediate (~9 km s⁻¹) flyby speed scenarios, respectively. Including the detection of water ion groups enables greater discrimination between certain meteorite types, and flyby speeds ≥10 km s⁻¹ enhance the diagnostic capabilities of this technique still further. Although additional terrestrial calibration is required, this technique may allow more unequivocal asteroid-meteorite connections to be determined by spacecraft flybys, emphasizing the utility of dust instruments on future asteroid missions.     

On asteroid distribution

The existing explanations for the asteroid distribution in the main belt (between the orbits of Mars and Jupiter) are based on numerical integration of resonance orbits in models with more than two degrees of freedom. We suggest an approach based on the investigation of the families of periodic solutions of the planar circular restricted three-body problem, i.e., a model with two degrees of freedom. This work shows that (a) the distribution of asteroids near the (p + 1)/p resonances and position of the outer boundary of the main asteroid belt can be explained within the planar circular restricted three-body problem and (b) this problem does not explain the asteroid distribution near other resonances.     

Absolute photometry of small main-belt asteroids in 2007–2009

We present the results of absolute photometry – the absolute brightness H_V, the effective diameter, (B)VR color indices, composite light curves, period of rotation and amplitude of variations – of several small asteroids in the inner main-belt: 1344 Caubeta, 1401 Lavonne, 2947 Kippenhahn, 3913 Chemin, 3956 Caspar, 4375 Kiyomori, 4555 1987 QL, 5484 Inoda, 5985 1942 RJ, 6949 Zissell and main-belt asteroid 6867 Kuwano. The photometric observations of these objects were made in the period 2007–2009 as part of a project of photometric studies of small main-belt asteroids that involves a collaboration of a number of asteroid photometrists around the world.     

Sample Return Missions from Minor Bodies: Achievements, Future Plan and Observational Support

We are entering in a new era of space exploration signed by sample return missions. Since the Apollo and Luna Program, the study of extraterrestrial samples in laboratory is gathering an increased interest of the scientific community so that nowadays exploration program of the Solar System is characterized by swelling sample return missions. Beside lunar samples, the NASA Stardust mission was the first successful space mission that on 15 January 2006 brought to Earth solid extraterrestrial samples collected from comet 81P/Wild 2 coma. Grains were collected during cometary fly-by into aerogel and once on Earth have been extracted for laboratory analyses. In the coming two decades many space missions on going or under study will harvest samples from minor bodies. Measurements required for detailed analysis that cannot be performed from a robotic spacecraft, will be carried out on Earth laboratories with the highest analytical accuracy attainable so far. An intriguing objective for the next sample return missions is to understand the nature of organic compounds. Organic compounds found in Stardust grains even if processed to large extend during aerogel capturing are here reported. Major objectives of Marco Polo mission are reported. Various ground-based observational programs within the framework of general characterizations of families and classes, cometary–asteroid transition objects and NEOs with cometary albedo are discussed and linked to sample return mission.     

Scientific Value of the Laser Ranging of Asteroid Icarus

The space mission of the laser ranging of asteroid Icarus is that a laser reflector and a timer are placed on the No.1566 asteroid and the laser interference ranging is conducted between the asteroid and the ground-based station for making the precise measurements of the PPN parameters γ and β, solar quadrupolar moment J₂, time rate of change ?/G of the gravitational constant and barycentric gravitational constant of the solar system objects. With the development of laser techniques, the timing accuracy of 10 ps (or 3 mm expressed by the amount of ranging) can be realized. In 2015 the asteroid Icarus will be close to the earth, which provides a better launch window for the Icarus lander. In the present article the 2003 interplanetary ephemeris frame of the PMOE is adopted to simulate the laser ranging between the ground-based station and the asteroid for 800 days from 2015 September 25 on and obtain the indeterminacies of 18 parameters, among which those of γ, β, J₂ and ?/G are respectively 7.8 × 10⁻⁸, 9.0 × 10⁻⁷, 9.8 × 10⁻¹¹ and 7.0 × 10−15yr⁻¹, with each being 1 to 3 orders higher than the available experimental accuracy. The simulated result shows that this space mission is of scientific significance to the test of the theory of relativity, determination of the fundamental parameters of solar system and test of the space-time fundamental laws.     

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.     

Frozen orbits for satellites close to an Earth-like planet

We say that a planet is Earth-like if the coefficient of the second order zonal harmonic dominates all other coefficients in the gravity field. This paper concerns the zonal problem for satellites around an Earth-like planet, all other perturbations excluded. The potential contains all zonal coefficientsJ ₂ throughJ ₉. The model problem is averaged over the mean anomaly by a Lie transformation to the second order; we produce the resulting Hamiltonian as a Fourier series in the argument of perigee whose coefficients are algebraic functions of the eccentricity — not truncated power series. We then proceed to a global exploration of the equilibria in the averaged problem. These singularities which aerospace engineers know by the name of frozen orbits are located by solving the equilibria equations in two ways, (1) analytically in the neighborhood of either the zero eccentricity or the critical inclination, and (2) numerically by a Newton-Raphson iteration applied to an approximate position read from the color map of the phase flow. The analytical solutions we supply in full to assist space engineers in designing survey missions. We pay special attention to the manner in which additional zonal coefficients affect the evolution of bifurcations we had traced earlier in the main problem (J ₂ only). In particular, we examine the manner in which the odd zonalJ ₃ breaks the discrete symmetry inherent to the even zonal problem. In the even case, we find that Vinti's problem (J ₄+J ₂ ² =0) presents a degeneracy in the form of non-isolated equilibria; we surmise that the degeneracy is a reflection of the fact that Vinti's problem is separable. By numerical continuation we have discovered three families of frozen orbits in the full zonal problem under consideration; (1) a family of stable equilibria starting from the equatorial plane and tending to the critical inclination; (2) an unstable family arising from the bifurcation at the critical inclination; (3) a stable family also arising from that bifurcation and terminating with a polar orbit. Except in the neighborhood of the critical inclination, orbits in the stable families have very small eccentricities, and are thus well suited for survey missions.     

TOWARDS AN INTEGRATED SCIENTIFIC AND SOCIAL CASE FOR HUMAN SPACE EXPLORATION

I will argue that an ambitious programme of human space exploration, involving a return to the Moon, and eventually human missions to Mars, will add greatly to human knowledge. Gathering such knowledge is the primary aim of science, but science’s compartmentalisation into isolated academic disciplines tends to obscure the overall strength of the scientific case. Any consideration of the scientific arguments for human space exploration must therefore take a holistic view, and integrate the potential benefits over the entire spectrum of human knowledge. Moreover, science is only one thread in a much larger overall case for human space exploration. Other threads include economic, industrial, educational, geopolitical and cultural benefits. Any responsibly formulated public space policy must weigh all of these factors before deciding whether or not an investment in human space activities is scientifically and socially desirable.     

Asteroid taxonomic signatures from photometric phase curves

We explore the correlation between an asteroid’s taxonomy and photometric phase curve using the H, G₁₂ photometric phase function, with the shape of the phase function described by the single parameter G₁₂. We explore the usability of G₁₂ in taxonomic classification for individual objects, asteroid families, and dynamical groups. We conclude that the mean values of G₁₂ for the considered taxonomic complexes are statistically different, and also discuss the overall shape of the G₁₂ distribution for each taxonomic complex. Based on the values of G₁₂ for about half a million asteroids, we compute the probabilities of C, S, and X complex membership for each asteroid. For an individual asteroid, these probabilities are rather evenly distributed over all of the complexes, thus preventing meaningful classification. We then present and discuss the G₁₂ distributions for asteroid families, and predict the taxonomic complex preponderance for asteroid families given the distribution of G₁₂ in each family. For certain asteroid families, the probabilistic prediction of taxonomic complex preponderance can clearly be made. In particular, the C complex preponderant families are the easiest to detect, the Dora and Themis families being prime examples of such families. We continue by presenting the G₁₂-based distribution of taxonomic complexes throughout the main asteroid belt in the proper element phase space. The Nysa–Polana family shows two distinct regions in the proper element space with different G₁₂ values dominating in each region. We conclude that the G₁₂-based probabilistic distribution of taxonomic complexes through the main belt agrees with the general view of C complex asteroid proportion increasing towards the outer belt. We conclude that the G₁₂ photometric parameter cannot be used in determining taxonomic complex for individual asteroids, but it can be utilized in the statistical treatment of asteroid families and different regions of the main asteroid belt.     

Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem.     

The invention that opened the solar system to exploration

The invention of gravity-propelled interplanetary space travel (also known as “gravity-assist trajectories”) in the early 1960s broke the high-energy barrier of classical space travel based on reaction propulsion, and made possible the exploration of the entire solar system with instrumented spacecraft. In this concept, a free-fall spacecraft is launched from a launch planet P₁ to a nearby planet P₂ such that its gravitational field (superimposed on the gravitational field of the Sun) catapults the vehicle to another planet P₃, which in turn is used to repeat the process. Thus, through a series of planetary encounters, a gravity-propelled trajectory P₁-P₂-P₃-P₄-…-P_N is generated. This paper describes how the invention was conceived and how the difficult mathematical problem of computing the trajectories was solved in order to numerically investigate and use the invention in actual missions. The crucial roles played by the UCLA Computing Facility and the Departments of Mathematics and Physics are also described.     

Spectral properties and mineral compositions of acapulcoite–lodranite clan meteorites: Establishing S‐type asteroid–meteorite connections

Except for asteroid sample return missions, measurements of the spectral properties of both meteorites and asteroids offer the best possibility of linking meteorite groups with their parent asteroid(s). Visible plus near‐infrared spectra reveal distinguishing absorption features controlled mainly by the Fe²⁺ contents and modal abundances of olivine and pyroxene. Meteorite samples provide relationships between spectra and mineralogy. These relationships are useful for estimating the olivine and pyroxene mineralogy of stony (S‐type) asteroid surfaces. Using a suite of 10 samples of the acapulcoite–lodranite clan (ALC), we have developed new correlations between spectral parameters and mafic mineral compositions for partially melted asteroids. A well‐defined relationship exists between Band II center and ferrosilite (Fs) content of orthopyroxene. Furthermore, because Fs in orthopyroxene and fayalite (Fa) content in olivine are well correlated in these meteorites, the derived Fs content can be used to estimate Fa of the coexisting olivine. We derive new equations for determining the mafic silicate compositions of partially melted S‐type asteroid parent bodies. Stony meteorite spectra have previously been used to delineate meteorite analog spectral zones in Band I versus band area ratio (BAR) parameter space for the establishment of asteroid–meteorite connections with S‐type asteroids. However, the spectral parameters of the partially melted ALC overlap with those of ordinary (H) chondrites in this parameter space. We find that Band I versus Band II center parameter space reveals a clear distinction between the ALC and the H chondrites. This work allows the distinction of S‐type asteroids as nebular (ordinary chondrites) or geologically processed (primitive achondrites).     

Diameters and albedos of thirty-six asteroids

Radiometric diameters and albedos of 36 asteroids, most previously unmeasured by this technique, are reported. These objects were selected primarily to resolve taxonomic ambiguities resulting from the lack of albedo information. Of the sample of 36, most are of the common types C, S, and M, but also represented are types A, D, F, and P. One object, 214 Aschera, is of the rare E type (only the fourth of its kind known); 87 Sylvia is the largest known member of the P class; and albedo combined with Arizona eight-color data from Tholen (1983, Asteroid Taxonomy from Cluster Analysis of Photometry: Implications for Origin and Evolution of the Asteroid Belt. PhD dissertation, University of Arizona, Tucson) indicate that 336 Lacadiera is of type D, one of the few members of this class found in the main asteroid belt, and a prime candidate for future space missions.