森 治

Abstract Volatile and organic-rich C-type asteroids may have been one of the main sources of Earth’s water. Our best insight into their chemistry is currently provided by carbonaceous chondritic meteorites, but the meteorite record is biased: only the strongest types survive atmospheric entry and are then modified by interaction with the terrestrial environment. Here we present the results of a detailed bulk and microanalytical study of pristine Ryugu particles, brought to Earth by the Hayabusa2 spacecraft. Ryugu particles display a close compositional match with the chemically unfractionated, but aqueously altered, CI (Ivuna-type) chondrites, which are widely used as a proxy for the bulk Solar System composition. The sample shows an intricate spatial relationship between aliphatic-rich organics and phyllosilicates and indicates maximum temperatures of ~30 °C during aqueous alteration. We find that heavy hydrogen and nitrogen abundances are consistent with an outer Solar System origin. Ryugu particles are the most uncontaminated and unfractionated extraterrestrial materials studied so far, and provide the best available match to the bulk Solar System composition.

In this article, a self-reconfiguring OrigamiSat concept is presented. The reconfiguration of the proposed OrigamiSat is triggered by combining the effect of 4D material (i.e. origami’s edges) and changes in the local surface optical properties (i.e., origami’s facets) to harness the solar radiation pressure acceleration. The proposed OrigamiSat uses the principle of solar sailing to enhance the effect of the Sun radiation to generate momentum on the Aluminised Kapton (Al-Kapton) origami surface by transitioning from mirror-like to diffusely reflecting optical properties of each individual facet. Numerical simulations have demonstrated that local changes in the optical properties can trigger reconfiguration. A minimum of 1-m edge size facet is required for a thick-origami to generate enough forces from the Sun radiation. The thick-origami pattern is 3D-printed directly on a thin Al-Kapton film (the solar sail substrate which is highly reflective). An elastic filament (thermoplastic polyurethane TPU) showed best performance when printing directly on the Al-Kapton and the Acrylonitrile Butadiene Styrene with carbon fiber reinforcement (ABS/cc) is added to augment the origami mechanical properties. The 4D material (shape memory polymer) is integrated only at specific edges to achieve self-deployment by applying heat. Two different folding mechanisms were studied: 1) the cartilage-like, where the hinge is made combining the TPU and the 4D material which make the mounts or valleys fully stretchable, and 2) the mechanical hinge, where simple hinges are made solely of ABS/cc. Numerical simulations have demonstrated that the cartilage-like hinge is the most suitable design for light-weight reconfigurable OrigamiSat when using the solar radiation pressure acceleration. We have used build-in electric board to heat up the 4D material and trigger the folding. We envisage embedding the heat wire within the 4D hinge in the future.

The Hayabusa2 spacecraft investigated the C-type (carbonaceous) asteroid (162173) Ryugu. The mission performed two landing operations to collect samples of surface and subsurface material, the latter exposed by an artificial impact. We present images of the second touchdown site, finding that ejecta from the impact crater was present at the sample location. Surface pebbles at both landing sites show morphological variations ranging from rugged to smooth, similar to Ryugu’s boulders, and shapes from quasi-spherical to flattened. The samples were returned to Earth on 6 December 2020. We describe the morphology of >5 grams of returned pebbles and sand. Their diverse color, shape, and structure are consistent with the observed materials of Ryugu; we conclude that they are a representative sample of the asteroid.

Deployable payloads have been used to expand mission opportunities and enable autonomous navigation and guidance under uncertain terrain conditions. A spacecraft may deploy an artificial marker toward the surface of the target body. An estimation of the deployment trajectory of markers can provide important information for guidance and navigation. We propose a method estimating the deployment trajectory using only images and evaluate its accuracy and reliability. In addition, to determine the spacecraft's relative attitude with respect to the asteroid surface, we introduce an attitude estimation method using the spacecraft's own shadow. The results shown in this paper confirm that the estimated trajectory is sufficiently accurate and thus the proposed method is a viable option for future missions for determining the trajectory of deployable payloads using only images of a deployment.

Abstract C-type asteroids¹ are considered to be primitive small Solar System bodies enriched in water and organics, providing clues to the origin and evolution of the Solar System and the building blocks of life. C-type asteroid 162173 Ryugu has been characterized by remote sensing^2–7 and on-asteroid measurements^8,9 with Hayabusa2 (ref. ¹⁰). However, the ground truth provided by laboratory analysis of returned samples is invaluable to determine the fine properties of asteroids and other planetary bodies. We report preliminary results of analyses on returned samples from Ryugu of the particle size distribution, density and porosity, spectral properties and textural properties, and the results of a search for Ca–Al-rich inclusions (CAIs) and chondrules. The bulk sample mainly consists of rugged and smooth particles of millimetre to submillimetre size, confirming that the physical and chemical properties were not altered during the return from the asteroid. The power index of its size distribution is shallower than that of the surface boulder observed on Ryugu¹¹, indicating differences in the returned Ryugu samples. The average of the estimated bulk densities of Ryugu sample particles is 1,282 ± 231 kg m⁻³, which is lower than that of meteorites¹², suggesting a high microporosity down to the millimetre scale, extending centimetre-scale estimates from thermal measurements^5,9. The extremely dark optical to near-infrared reflectance and spectral profile with weak absorptions at 2.7 and 3.4 μm imply a carbonaceous composition with indigenous aqueous alteration, matching the global average of Ryugu^3,4 and confirming that the sample is representative of the asteroid. Together with the absence of submillimetre CAIs and chondrules, these features indicate that Ryugu is most similar to CI chondrites but has lower albedo, higher porosity and more fragile characteristics.

A novel approach for shape control of membrane structures is presented to realize their use in three-dimensional and variable configurations. The shape control is accomplished by exciting a spinning membrane. The membrane forms a shape consisting of several vibration modes, depending on the input frequency, and the wave surface stands still when its frequency is synchronized with the spin rate; that is, the wave propagation and the spin cancel each other, resulting in a static wave surface in the inertial frame. This idea enables control of continuous membrane structures with large deformation using fewer actuators than conventional methods. This paper describes the general theory of the static wave-based shape control. The mathematical model of membrane vibration, the classification of control input, and the control system for exciting a static wave are summarized. The proposed method is demonstrated through a ground experiment. A 1 m large polyimide film is rotated and vibrated in a vacuum chamber, and the output shape is measured using a real-time depth sensor. It is shown that the observed shapes agree with numerical simulation results. An additional simulation that models the Japanese solar sail Interplanetary Kite-craft Accelerated by Radiation Of the Sun (IKAROS) demonstrates that the proposed method also works with a practically large-scalemembraneinthespaceenvironment.

Planetesimals—the initial stage of the planetary formation process—are considered to be initially very porous aggregates of dusts1,2, and subsequent thermal and compaction processes reduce their porosity3. The Hayabusa2 spacecraft found that boulders on the surface of asteroid (162173) Ryugu have an average porosity of 30–50% (refs. 4–6), higher than meteorites but lower than cometary nuclei7, which are considered to be remnants of the original planetesimals8. Here, using high-resolution thermal and optical imaging of Ryugu’s surface, we discovered, on the floor of fresh small craters (<20 m in diameter), boulders with reflectance (~0.015) lower than the Ryugu average6 and porosity >70%, which is as high as in cometary bodies. The artificial crater formed by Hayabusa2’s impact experiment9 is similar to these craters in size but does not have such high-porosity boulders. Thus, we argue that the observed high porosity is intrinsic and not created by subsequent impact comminution and/or cracking. We propose that these boulders are the least processed material on Ryugu and represent remnants of porous planetesimals that did not undergo a high degree of heating and compaction3. Our multi-instrumental analysis suggests that fragments of the highly porous boulders are mixed within the surface regolith globally, implying that they might be captured within collected samples by touch-down operations10,11.

This paper reports on the manufacturing and evaluation of a solar power sail membrane prototype for the OKEANOS project. The in-house prototype was built by the Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency. Mechanical and electrical evaluation tests were conducted. The membrane, thin-film solar cells, reflectivity control devices were good condition after the manufacturing and handling. The improvements in the manufacturing process and design were found. The manufacturing process and design were fundamentally established. After the prototype, improvement plans for the manufacturing process and design were tried. We have a prospect of manufacturing the flight model sail and continue to the development.

© 2020 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. In this paper, the deployed shape of spinning square solar sails was investigated through dynamic nonlinear finite element analysis of the full model of the solar power sail of the world’s first solar sail: Interplanetary Kite-craft Accelerated by Radiation of the Sun (IKAROS). The on-orbit photographs of IKAROS revealed that the sail membrane was deformed toward the sun and the membrane maintained its deployed shape during very low-spinrate operations. To clarify the mechanism of the deformation and high stiffness, the authors of the present study previously performed deployed shape analyses of one-quarter of one square sail by employing Abaqus and reported that the phenomenon was probably caused by curvatures of thin-film devices attached to the membrane. In this study, a finite element model of the entire square sail of IKAROS was created. Furthermore, deployed shape analysis under several combinations of curvatures and spin rates was conducted by employing the dynamic solver “Abaqus/ Explicit.” The results indicated that the sail deformations were induced by the curvatures of thin-film devices and that umbrella and saddle shapes appeared owing to the curvatures. The results also indicated that the electric harnesses between the sail and spacecraft supported the sail shape when the spin rate was low.

© 2020 IAA Automated spacecraft docking is a technology that has long been pursued. Deep space explorers and small spacecraft can carry fewer resources for docking, such as navigation sensors or latching structures, than can their larger near-Earth counterparts. The concept of the probe–cone docking mechanism is an effective solution to this problem. In this approach, a probe attached to the chaser satellite is guided automatically to the connection part of the target satellite by a conical structure. It is important to have a shock attenuation mechanism at the docking interface to prevent the chaser from being bounced away from the target. In the present paper, an automated docking mechanism that uses a flexible and deployable boom as the probe is proposed, and results of an analysis of the multi-body system dynamics are presented. Although analytical investigations into docking dynamics have been reported, the dynamics depend on many interdependent design parameters, the interaction of which is yet to be investigated. The present work involved a numerical analysis of the effect of each design parameter on the satellite behavior. An energy-based index that can predict the success or failure of docking was also developed in this study. In addition, a design scheme for the parameters is presented based on the results of the analysis in which the optimal combination of the design parameters is determined by searching the solution space.

© 2020, The Author(s), under exclusive licence to Springer Nature Limited. The asteroid (162173) Ryugu and other rubble-pile asteroids are likely re-accumulated fragments of much larger parent bodies that were disrupted by impacts. However, the collisional and orbital pathways from the original parent bodies to subkilometre rubble-pile asteroids are not yet well understood1–3. Here we use Hayabusa2 observations to show that some of the bright boulders on the dark, carbonaceous (C-type) asteroid Ryugu4 are remnants of an impactor with a different composition as well as an anomalous portion of its parent body. The bright boulders on Ryugu can be classified into two spectral groups: most are featureless and similar to Ryugu’s average spectrum4,5, while others show distinct compositional signatures consistent with ordinary chondrites—a class of meteorites that originate from anhydrous silicate-rich asteroids6. The observed anhydrous silicate-like material is likely the result of collisional mixing between Ryugu’s parent body and one or multiple anhydrous silicate-rich asteroid(s) before and during Ryugu’s formation. In addition, the bright boulders with featureless spectra and less ultraviolet upturn are consistent with thermal metamorphism of carbonaceous meteorites7,8. They might sample different thermal-metamorphosed regions, which the returned sample will allow us to verify. Hence, the bright boulders on Ryugu provide new insights into the collisional evolution and accumulation of subkilometre rubble-pile asteroids.

© 2020, Tsinghua University Press. 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 efficiently throughout the period.

Copyright © (2017) by International Astronautical Federation. All rights reserved. The use of deployable membrane structures is expected for future large-area space structures, such as solar sails or large antennas, because they are lightweight and can be stored compactly at the launch. However, the technology to deploy sail membranes using centrifugal force had hardly been demonstrated ever. JAXA has studied the technology of spin deployment for long time. As one of the achievements, we have succeeded to deploy the 200 m2 class sail using centrifugal force in the IKAROS mission, which is the first solar sail demonstration in the world. The deployment of the sail was one of the most important missions of IKAROS. We could have shown the effectiveness of the developed deployment technology. JAXA is currently planning the spin deployment of a 2000 m2 class large sail as next generation spacecraft by sophisticating the technology and knowledge of IKAROS. This paper introduces the unexpected phenomena happened on orbit demonstration of IKAROS, as well as the problems of the deployment mechanism. Then, the improvement of the mechanism and its reflection status to the next mission are reported.

The solar power sail is an original Japanese concept in which electric power is generated by thin-film solar cells attached on the solar sail membrane. Japan Aerospace Exploration Agency (JAXA) successfully demonstrated the world’s first solar power sail technology through IKAROS (Interplanetary Kite-craft Accelerated by Radiation of the Sun) mission in 2010. IKAROS demonstrated photon propulsion and power generation using thin-film solar cells during its interplanetary cruise. Scaled up, solar power sails can generate enough power to drive high specific impulse ion thrusters in the outer planetary region. With this concept, we propose a landing or sample return mission to directly explore a Jupiter Trojan asteroid using solar power sail-craft OKEANOS (Oversize Kite-craft for Exploration and AstroNautics in the Outer Solar System). After rendezvousing with a Trojan asteroid, a lander separates from OKEANOS to collect samples, and perform in-situ analyses in three proposed mission sequences, including sending samples back to Earth. This paper proposes a system design for OKEANOS and includes analyses of the latest mission.

Solar radiation pressure (SRP) impinging on spacecraft is usually regarded as a disturbance for attitude motion, but it can be harnessed to solve the very problem it creates. Active SRP control is possible with solar radiation powered thin-film devices such as reflectivity control devices or liquid crystal devices with reflective microstructure. Thermal radiation pressure (TRP) can likewise be used to solve flight attitude problems caused by SRP, TRP, or other factors. TRP on solar cells can be controlled by switching regulators under the control of them, resulting in temperature change. These SRP/TRP controls are free from mechanisms, such as reaction wheels, and thus they do not produce internal disturbances. In addition, the magnitude of SRP/TRP torques is generally much smaller than internal disturbance torques produced by reaction wheels, which creates a potential for precision far beyond that achieved with mechanical controls. This paper summarizes how SRP/TRP can be used by means of numerical simulations of typical control methods. The usefulness of this mechanism-free attitude control is verified for future use on both Earth orbiting satellites and interplanetary spacecraft including solar sails.

<p>Solar sail technique was demonstrated in the IKAROS mission. However, the membrane of IKAROS has deformed to a shape that was not flat. The whole membrane changes greatly like an umbrella shape or a saddle shape depending on the warping direction of the thin-film devices on the membrane, such as thin-film solar cells, reflectivity control devices and dust counters. Objection of this study is to clarify mechanism of influence on solar radiation pressure (SRP) torque due to warp of thin-film device and its solution method. Therefore, the shape of the overall membrane is clarified by using a simple finite element model and the SRP torque with respect to the shape is calculated, and the mechanism of the overall shape change in warpage and its influence is clarified. As a result, the influence on SRP is related to membrane stiffness and warped direction and it is found that the suitable conditions to minimize SRP torque are as follows: a) the sail is warped in the radial direction, b) the base film of the sail has low stiffness, c) the outermost part of the sail has high stiffness, and d) the length of bridges between petals is short.</p>

© 2020 American Association for the Advancement of Science. All rights reserved. The near-Earth asteroid (162173) Ryugu is thought to be a primitive carbonaceous object that contains hydrated minerals and organic molecules. We report sample collection from Ryugu’s surface by the Hayabusa2 spacecraft on 21 February 2019. Touchdown images and global observations of surface colors are used to investigate the stratigraphy of the surface around the sample location and across Ryugu. Latitudinal color variations suggest the reddening of exposed surface material by solar heating and/or space weathering. Immediately after touchdown, Hayabusa2’s thrusters disturbed dark, fine grains that originate from the redder materials. The stratigraphic relationship between identified craters and the redder material indicates that surface reddening occurred over a short period of time. We suggest that Ryugu previously experienced an orbital excursion near the Sun.

The Hayabusa2 spacecraft investigated the small asteroid Ryugu, which has a rubble-pile structure. We describe an impact experiment on Ryugu using Hayabusa2’s Small Carry-on Impactor. The impact produced an artificial crater with a diameter &gt;10 meters, which has a semicircular shape, an elevated rim, and a central pit. Images of the impact and resulting ejecta were recorded by the Deployable CAMera 3 for &gt;8 minutes, showing the growth of an ejecta curtain (the outer edge of the ejecta) and deposition of ejecta onto the surface. The ejecta curtain was asymmetric and heterogeneous and it never fully detached from the surface. The crater formed in the gravity-dominated regime; in other words, crater growth was limited by gravity not surface strength. We discuss implications for Ryugu’s surface age.

© 2020, The Author(s), under exclusive licence to Springer Nature Limited. Carbonaceous (C-type) asteroids1 are relics of the early Solar System that have preserved primitive materials since their formation approximately 4.6 billion years ago. They are probably analogues of carbonaceous chondrites2,3 and are essential for understanding planetary formation processes. However, their physical properties remain poorly known because carbonaceous chondrite meteoroids tend not to survive entry to Earth’s atmosphere. Here we report on global one-rotation thermographic images of the C-type asteroid 162173 Ryugu, taken by the thermal infrared imager (TIR)4 onboard the spacecraft Hayabusa25, indicating that the asteroid’s boulders and their surroundings have similar temperatures, with a derived thermal inertia of about 300 J m−2 s−0.5 K−1 (300 tiu). Contrary to predictions that the surface consists of regolith and dense boulders, this low thermal inertia suggests that the boulders are more porous than typical carbonaceous chondrites6 and that their surroundings are covered with porous fragments more than 10 centimetres in diameter. Close-up thermal images confirm the presence of such porous fragments and the flat diurnal temperature profiles suggest a strong surface roughness effect7,8. We also observed in the close-up thermal images boulders that are colder during the day, with thermal inertia exceeding 600 tiu, corresponding to dense boulders similar to typical carbonaceous chondrites6. These results constrain the formation history of Ryugu: the asteroid must be a rubble pile formed from impact fragments of a parent body with microporosity9 of approximately 30 to 50 per cent that experienced a low degree of consolidation. The dense boulders might have originated from the consolidated innermost region or they may have an exogenic origin. This high-porosity asteroid may link cosmic fluffy dust to dense celestial bodies10.

<p>At bipropellant chemical propulsion systems, iron in oxidizer is one of the topics to be noted and controlled. Actually, to avoid the influence of the iron ingredient, several long term mission spacecraft such as interplanetary probes flush the oxidizer piping periodically. The major influence of steel contaminated oxidizer is known to be flow decay. Still, operation data of the HAYABUSA2 spacecraft indicates possibility of other drawbacks. This paper discusses its impact to the reactivity of the hypergolic propellant, especially for the propellant combination of N₂H₄/MON3, which is the case of HAYABUSA2. A series of open cup firing tests show that the reactivity deteriorates when the oxidizer is contaminated with iron.</p>

<p>A thin-film device mounted on development type membrane structure is limited to arrangement and deployment on the plane. In this paper, we propose a three-dimensional film structure (3D film) that can stereoscopically place and deploy thin-film devices. This method can be widely applied to non-spin type or spin type developable structures having a mast structure. In this paper, in order to apply to non-spin / spin type developed structures, we evaluate extension shapes of 3D film by crease and condition of existence / nonexistence of centrifugal force, and placement and arrangement of thin-film devices.</p>

© 2019, Tsinghua University Press. A solar power sail demonstrator “IKAROS” demonstrated solar sailing technology in 2010. The membrane of the spinning solar sail IKAROS is estimated to be deformed toward the Sun. The deformation was kept even under low spin-rate. Previous studies suggest that curvature of thin-film solar cells on the membrane increases the out-of-plane stiffness by finite element analysis. Shape, out-of-plane stiffness, and natural frequency of membranes have to be predicted for solar sails with thin-film devices, such as thin-film solar cells, dust counters, and reflectivity control devices in order to reduce the margins of sail size and propellant mass against disturbance solar pressure torque acting on the membrane. In this paper, the effect of a curved thin-film device on the natural frequency of a rectangle membrane under uniaxial tension was investigated. Three types of membranes were evaluated: a membrane with a curved thin-film device, a membrane with a flat thin-film device, and a plane membrane. Geometric nonlinear finite element analysis and eigenvalue analysis were conducted to investigate the natural frequencies under varying tension. The simulations were verified by vibration experiments. It was found that under low tension, the natural frequency of the membrane with the curved thin-film device is significantly higher than that of the others and that under high tension, the natural frequency of the membrane with the thin-film device is slightly lower than that of the plane membrane. In addition, parametric analysis on the curvature of the thin-film device shows that natural frequency at low tension is sensitive to the curvature. The eigenvalue analysis of a whole solar sail with the curved thin-film devices also suggests that the curvature remarkably affects the vibration modes. In conclusion, curved thin-film devices have a significant impact on the out-of-plane stiffness of a membrane under low tension.

© 2019, Tsinghua University Press. The present paper proposes a control method to excite spinning solar sail membranes for three-dimensional use. Using optical property switching, the input is given as the change in magnitude of the solar radiation pressure. The resonance point of this system varies with the vibration state due to its nonlinearity and the change in equilibrium state. To deal with this, a state feedback control law that automatically tracks the resonance point is developed in the present study. The proposed method enables decentralized control of the actuators on the sail, each of which determines the control input independently using only the information of vibration state. The proposed method is validated using numerical simulations. The results show that the nonlinear system behaves differently from the linear system, and the vibration grows using the decentralized control regardless of resonance point variation.

The near-Earth carbonaceous asteroid 162173 Ryugu is thought to have been produced from a parent body that contained water ice and organic molecules. The Hayabusa2 spacecraft has obtained global multi-color images of Ryugu. Geomorphological features present include a circum-equatorial ridge, east/west dichotomy, high boulder abundances across the entire surface, and impact craters. Age estimates from the craters indicate a resurfacing age of <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"><m:mrow><m:mo>≲</m:mo><m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mn>6</m:mn></m:msup></m:mrow></m:math></inline-formula> years for the top 1-meter layer. Ryugu is among the darkest known bodies in the Solar System. The high abundance and spectral properties of boulders are consistent with moderately dehydrated materials, analogous to thermally metamorphosed meteorites found on Earth. The general uniformity in color across Ryugu’s surface supports partial dehydration due to internal heating of the asteroid’s parent body.

The Hayabusa2 spacecraft arrived at the near-Earth carbonaceous asteroid 162173 Ryugu in 2018. We present Hayabusa2 observations of Ryugu’s shape, mass, and geomorphology. Ryugu has an oblate ‘spinning top’ shape with a prominent circular equatorial ridge. Its bulk density, 1.19 ± 0.02 g cm^–3, indicates a high porosity (&gt;50%) interior. Large surface boulders suggest a rubble-pile structure. Surface slope analysis shows Ryugu’s shape may have been produced if it once spun at twice the current rate. Coupled with the observed global material homogeneity, this suggests that Ryugu was reshaped by centrifugally induced deformation during a period of rapid rotation. From these remote-sensing investigations, we identify a suitable sample collection site on the equatorial ridge.

© 2018 Elsevier Inc. Seismic shaking of small bodies has an important role in revealing information about internal structure and contributing to our understanding of microgravity geology. Since many small asteroids are likely to be rubble piles, it is important to understand their dynamics, which is largely different from that of monolithic asteroids. We introduce a new normal mode analysis method as an approach to seismic study based on a discrete element method (DEM), where a rubble pile is modeled as a group of elastic spheres bound together with gravitational force, with elastic repulsion forces following Hertzian contact theory and Mindlin's theory. Normal mode analysis is formulated by differentiating the interaction between particles around an equilibrium state. Our results show that normal modes and eigenfrequencies are independent of the size of the particles if their physical properties and geometry are identical. Furthermore, we apply a scaling law, which shows that the shape of normal modes does not change even if the size of a rubble pile is enlarged or contracted, but the eigenfrequency varies in inverse proportion with the scale to the power of two-thirds. We also compare normal modes between a rubble pile and a monolith and show that the shapes of normal modes are similar to each other, but the eigenfrequency is smaller in the rubble pile. Finally, we describe dynamic simulations to compare results from nonlinear DEM and results from linearization of the normal mode. It is found that normal mode analysis gives a good approximation for the frequency distribution when the kinetic energy is sufficiently small, and that the presence of tangential force between particles suppresses vibration motion.

<p>The membrane of a spinning solar sail IKAROS is considered to be deformed toward the Sun. The deformation was kept even under low spin rate. Previous studies suggest that curvature of thin-film solar cells on the membrane increases the out-of-plane stiffness. For a solar power sail OKEANOS, the shape, out-of-plane stiffness, and natural frequency have to be predicted. In this paper, the effect of a curved thin-film device on the natural frequency of a rectangle membrane under uniaxial tension is investigated. Three types of membranes are evaluated: a membrane with a curved thin-film device, a membrane with a flat thin-film device, a plane membrane. Geometric nonlinear finite element analysis and eigenvalue analysis are conducted to investigate the natural frequencies under varying tension. The simulations are verified by vibration experiments. It is found that under low tension, the natural frequency of the membrane with the curved thin-film device is significantly higher than that of the others and that under high tension, the natural frequency of the membrane with the thin-film device is slightly lower than that of the plane membrane. The results show that curved thin-film devices have a significant impact on the out-of-plane stiffness of a membrane under low tension.</p>