Shapes,structures,and evolution of small bodies

Small bodies are among the best tracers of our Solar System’s history.A large number of space missions to small bodies(past and future)offer a unique opportunity to use these bodies as a natural laboratory to study the different processes,mechanical structures,and responses that drive the origin and evolution of small bodies,which are connected to the origin,evolution,and current architecture of the Solar System.Images of small bodies sent by spacecraft have revealed unexpectedly rich and complex geological worlds.In addition to very diverse compositions,small bodies in the Solar System have highly diverse shapes and structures,which reflect both different evolutionary paths and material properties.Furthermore,each individual body has diverse geological features on its surface,which include craters of various sizes and depths,boulders of different sizes and morphologies,lineaments,fractures,pits,signatures of landslides,terraces,and ridges.Such a geological richness could not be detected via ground-based observations,and we are still at the beginning of understanding their significance on the low-gravity surfaces on which they manifest.The combination of space mission data and numerical modeling allows us to enrich our understanding of the origin,evolution,and physical properties of these fascinating bodies.For instance,starting from the shape models,bulk densities,and spin rates determined from space mission data,we can investigate the formation mechanisms that lead to the observed properties of small bodies.We can also infer the interior and mechanical properties(e.g.,friction and cohesion)that allow a small body to be structurally stable,as well as its further potential evolution under processes such as a spin rate increase or an impact.Then,considering the various processes that these bodies experience during their evolution,we can investigate how these processes modify their properties and,in turn,how those properties influence the outcome of these processes.This paper reviews our current knowledge of small-body shapes and structures and discusses the various processes that are responsible for their formation and evolution,which can modify the characteristics of the bodies.We separately consider each population of small bodies,although in some cases,such as active asteroids and comets,the distinction between two populations solely in terms of physical properties is not clear.We then summarize the main findings regarding the physical properties of small bodies that have been the target of rendezvous or sample return missions.

The present status and prospects in the research of orbital dynamics and control near small celestial bodies

Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the modeling of dynamics environment and the orbital dynamics mechanism. This paper introduced state-ofthe-art researches, major challenges, and future trends in this field. Three topics are mainly discussed： the gravitational field modeling of irregular-shaped small celestial bodies, natural orbital dynamics and control, and controlled orbital dynamics. Finally, constructive suggestions are made for China’s future space exploration missions.

Autonomous orbit determination for the probe around small body

The algorithm of autonomous orbit determination for the probe around small body is studied. In the algorithm, first, the observed images of the body are compared with its pre-computed model of the body to obtain the location of the limb features of the body in the inertial coordinate. Second, the information of the images and features in utilized to obtain the position of the probe using the Levenberg-Marquardt algorithm. The position is then input to an extended Kalman filter which determines the real time orbit of the probe. Finally, considering the effective of the irregular small body shape perturbation and the small body model parameter error on the orbit determination precise, the procedure of autonomous orbit determination is validated using digital simulation.

Spacecraft motion analysis about rapid rotating small body

The orbital dynamics equation of a spacecraft around an irregular sphere small body is established based on the small body’s gravitational potential approximated with a tri-axial ellipsoid. According to the Jacobi integral constant, the spacecraft zero-velocity curves in the vicinity of the small body is described and feasible motion region is analyzed. The limited condition and the periapsis radius corresponding to different eccentricity against impact surface are presented. The stability of direct and retrograde equator orbits is analyzed based on the perturbation solutions of mean orbit elements.

Condensed Matter Analogy of Impact Crater Formation

Impact craters exist on various solid objects in the planetary system. A simplified analogy of the process of their formation is here analyzed by standard solid state physics and the so called dynamic quantized fracture mechanics. An expression which links the crater volume to the parameters of the impactor and the target is obtained within the two approaches. For low impactor energy, this expression is of the same mathematical form as the one resulting from recent experiments. It is shown that the formation of an impact crater is possible even without heating of the target, if the critical stress in the target satisfies certain conditions. The critical value of the stress needed for the occurence of a fracture is calculated for three craters： two terrestrial and one lunar craters. The approach presented here uses only measurable material parameters, and therefore is more realistic than the treatement of the same problem using the cohesive energy of materials.

Small water bodies in China:Spatial distribution and influencing factors

Inland water bodies,including ponds,lakes,reservoirs,and rivers,provide extensive ecosystem services for human beings.Among these,small water bodies(SWBs),such as ponds and small reservoirs,are more common landscape features and important biogeochemical reactors.SWBs can significantly influence biogeochemical processes and hydrologic cycles.However,due to their small size,SWBs(<10 ha)have been largely ignored in natural resource surveys,leading to a limited understanding of their spatial distribution in China.Insufficient geospatial datasets of SWBs limit the accurate assessments of resource utilization and fluxes of biogenic elements in both aquatic and terrestrial ecosystems.To address this,in this study,we applied a convolutional neural network and a visual interpretation approach to extract SWBs from high-resolution satellite images from Google Earth.The spatial distribution of SWBs in China was mapped,and drivers of the spatial pattern of SWBs were also identified.As a result,a total of 5.18 million water bodies with a surface area larger than 0.1 ha,including ponds,lakes,and reservoirs,were identified.These water bodies(>0.1 ha)cover approximately 179300 km^(2),which is approximately 1.8%of the land area in China.In addition,the combined shoreline length of the water bodies was approximately 2157400 km.Of these water bodies,96.85%were SWBs,accounting for 17.85%of the total water area and 76.4% of the total shoreline length.Precipitation,terrain,and human activity cumulatively explained 45% of the variance in SWB distribution,with precipitation being the strongest climatic explanatory factor.Our results provide important data for determining the roles of SWBs in biogeochemical cycles,habitat protection,and hydrological cycles.

Main Mineralization Mechanism of Magmatic Sulphide Deposits in China

Before intruding, primary magmas have undergone liquation and partial crystallization atdepth; as a result the magmas are partitioned into barren magma, ore-bearing magma, ore-richmagma and ore magma, which then ascend and are injected into the present locations once ormultiple times, thus forming ore deposits. The above-mentioned mineralizing process is knownas deep-seated magmatic liquation-injection mineralization. The volume of the barren magma isgenerally much larger than those of the ore-bearing magma, ore-rich magma and ore magma. Inthe ascending process, most of the barren magma intrudes into different locations or outpoursonto the ground surface, forming intrusions or lava flows. The rest barren magma, ore-bearingmagma, ore-rich magma and ore magma may either multiple times inject into the same space inwhich rocks and ores are formed or separately inject into different spaces in which rocks and oresare formed. The intrusions containing such deep-seated magmatic liquation-injection depositshave a much smaller volume, greater ore potential and higher ore grade than that of in-situmagmatic liquation deposits. Consequently this mineralizing process results in the formation oflarge deposits in small intrusions.

Measuring the mechanical properties of small body regolith layers using a granular penetrometer

Small bodies in the solar system are known to be covered by a layer of loose unconsolidated soil composed of grains ranging from dusty sands to rugged boulders.Various geophysical processes have modified these regolith layers since their origin.Therefore,the landforms on regolith-blanketed surfaces hold vital clues for reconstructing the geological processes occurring on small bodies.However,the mechanical strength of small body regolith remains unclear,which is an important parameter for understanding its dynamic evolution.Furthermore,regolith mechanical properties are key factors for the design and operation of space missions that interact with small body surfaces.The granular penetrometer,which is an instrument that facilitates in situ mechanical characterization of surface/subsurface materials,has attracted significant attention.However,we still do not fully understand the penetration dynamics related to granular regolith,partially because of the experimental difficulties in measuring grain-scale responses under microgravity,particularly on the longer timescales of small body dynamics.In this study,we analyzed the slow intrusion ofa locomotor into granular matter through large-scale numerical simulations based on a soft sphere discrete element model.We demonstrated that the resistance force of cohesionlessregolith increases abruptly with penetration depth after contact and then transitions to a linear regime.The scale factor of the steady-state component is roughly proportionalto the internal friction of the granular materials,which allows us to deduce the shearstrength of planetary soils by measuring their force depth relationships.When cohesion is included,due to the brittle behavior of cohesive materials,the resistance profile is characterized by a stationary state at a large penetration depth.The saturation resistance,which represents the failure threshold of granular materials,increases with the cohesion strength of the regolith.This positive correlation provides a reliable tool for measuring the tensile strength of granular regolith in small body touchdown missions.

Motion reconstruction of the small carry-on impactor aboard Hayabusa2

Subsurface exploration is one of the most ambitious scientific objectives of the Hayabusa2 mission.A small device called small carry-on impactor(SCI)was developed to create an artificial crater on the surface of asteroid Ryugu.This enables us to sample subsurface materials,which will provide a window to the past.The physical properties of the resulting crater are also useful for understanding the internal structure of Ryugu.Accurate understanding of the crater and ejecta properties,including the depth of excavation of subsurface materials,requires accurate information on impact conditions.In particular,the impact angle is a critical factor because it greatly influences the size and shape of the crater.On April 5,2019,the Hayabusa2 spacecraft deployed the SCI at 500 m of altitude above the asteroid surface.The SCI gradually reduced its altitude,and it shot a 2 kg copper projectile into the asteroid 40 min after separation.Estimating the position of the released SCI is essential for determining the impact angle.This study describes the motion reconstruction of the SCI based on the actual operation data.The results indicate that the SCI was released with high accuracy.

Simultaneous estimation of spacecraft position and asteroid diameter during final approach of Hayabusa2 to Ryugu

This paper presents the optical navigation results of the asteroid explorer Hayabusa2 during the final rendezvous approach phase with the asteroid Ryugu.The orbit determination of Hayabusa2 during the cruising phase uses a triangulation-based method that estimates the probe and asteroid orbits using the directions from which they are observed.Conversely,the asteroid size is available as optical information just prior to arrival.The size information allows us to estimate the relative distance between the probe and the asteroid with high accuracy,that is strongly related to the success or failure of the rendezvous.In this study,the relative distance and asteroid size in real space are simultaneously estimated in real time by focusing on the rate of change of the asteroid size observed in sequential images.The real-time estimation results coincided with those of precise analyses performed after arrival.

Guidance, navigation, and control of Hayabusa2 touchdown operations

Hayabusa2 is a Japanese sample return mission from the asteroid Ryugu.The Hayabusa2 spacecraft was launched on 3 December 2014 and arrived at Ryugu on 27 June 2018.It stayed there until December 2019 for in situ observation and soil sample collection,and will return to the Earth in November or December 2020.During the stay,the spacecraft performed the first touchdown operation on 22 February 2019 and the second touchdown on 11 July 2019,which were both completed sucssfully.Because the surface of Ryugu is rough and covered with boulders,it was not easy to find target areas for touchdown.There were several technical challenges to overcome,including demanding guidance,navigation,and control accuracy,to realize the touchdown operation.In this paper,strategies and technical details of the guidance,navigation,and control systems are presented.The flight results prove that the performance of the systems was satisfactory and largely contributed to the success of the operation.

Hayabusa2’s station-keeping operation in the proximity of the asteroid Ryugu

The Japanese interplanetary probe Hayabusa2 was launched on December 3,2014 and the probe arrived at the vicinity of asteroid 162173 Ryugu on June 27,2018.During its 1.4 years of asteroid proximity phase,the probe successfully accomplished numbers of record-breaking achievements including two touchdowns and one artificial cratering experiment,which are highly expected to have secured surface and subsurface samples from the asteroid inside its sample container for the first time in history.The Hayabusa2 spacecraft was designed not to orbit but to hover above the asteroid along the sub Earth line.This orbital and geometrical configuration allows the spacecraft to utilize its high-gain antennas for telecommunication with the ground station on Earth while pointing its scientific observation and navigation sensors at the asteroid.This paper focuses on the regular station-keeping operation of Hayabusa2,which is called“home position”(HP)-keeping operation.First,together with the spacecraft design,an operation scheme called HP navigation(HPNAV),which includes a daily trajectory control and scientific observations as regular activities,is introduced.Following the description on the guidance,navigation,and control design as well as the framework of optical and radiometric navigation,the results of the HP-keeping operation including trajectory estimation and delta-V planning during the entire asteroid proximity phase are summarized and evaluated as a first report.Consequently,this paper states that the HP.keeping operation in the framework of HPNAV had succeeded without critical incidents,and the number of trajectory control delta-V was planned fficiently throughout the period.

Design and flight results of GNC systems in Hayabusa2 descent operations

Hayabusa2 is a Japanese sample return mission from the near-Earth asteroid Ryugu.The Hayabusa2 spacecraft was launched on December 3,2014,and reached the asteroid on June 27,2018.It remained there until November 13,2019 for in situ observation and soil sample collection and will return to the Earth in November or December 2020.During its stay at the asteroid,Hayabusa2 performed descent operations 16 times.This paper presents an overview of a guidance,navigation,and control method used in such descent operations.The method consists of on-board and on-ground guidance systems to control the spacecraft and an image-based navigation technique that uses a shape model and ground control points of the asteroid.Flight results in the first touchdown operation are shown as an example,which demonstrate that the method showed a good performance overall and contributed to the success of the mission.