Orbital Debris Modeling and Applications at Kyushu University

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Toshiya HANADA1,2,5, Yuya ARIYOSHI2, Masahiko UETSUHARA2, Makoto TAGAWA2, Hongru CHEN2, Yuki TSUTSUMI2, Akira DOI2, Satomi KAWAMOTO3, Toshifumi YANAGISAWA3, Kozue HASHIMOTO4, Aritsune KAWABE4, and Yukihito KITAZAWA4

1 International Center for Space Weather Science and Education, Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan 2 Department of Aeronautics and Astronautics, Kyushu University 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 3 Aerospace Research and Development Directorate, Japan Aerospace Exploration Agency 7-44-1 Jindaiji Higashi-machi, Chofu-shi, Tokyo 182-8522, Japan 4 IHI Corporation TOYOSU IHI BUILDING, 1-1, Toyosu 3-chome, Koto-ku, Tokyo 135-8710, Japan 5 092-802-3047 / Fax: 092-802-3001 / E-mail: [email protected]

ABSTRACT

This paper briefly introduces efforts made at Kyushu University in the area of orbital debris modeling and applications. The orbital debris modeling, which describes debris generation and orbit propagation, enables us to build orbital debris evolutionary models as essential tools to predict the future orbital debris population, and as applications to discuss what and how to do for orbital debris mitigation and remediation. The orbital debris modeling also enables us to devise an effective search strategy applicable for breakup fragments in the geostationary region using ground-based optical sensors, and to evaluate the effectiveness of space-based measurements of objects not tracked from the ground, both to contribute to space situational awareness. Ultimately, this paper includes atmospheric density modeling necessary for orbital decay and re-entry analyses, and space tether modeling to assess risks of using electrodynamic tethers for removing hazardous objects from the low Earth orbit region.

1. INTRODUCTION

Orbital debris modeling techniques describe debris generation and orbit propagation. Thus, orbital debris modeling at Kyushu University was initiated with satellite impact testing in order to understand debris generation. First, as an initial study, simulated spacecraft walls were selected as targets while solid stainless steel spheres were used as projectiles [1]. The impact speeds were up to approximately 300 m/s, and the outcomes were all non-catastrophic (only a small amount of fragments were generated from impact craters or holes on the target walls). Secondly, CANSAT, a micro-satellite popularized in universities teaching space engineering, was prepared to investigate the outcome of a catastrophic impact [2]. Main structure had five round layers with a diameter of 14 cm, made of carbon fiber reinforced plastic and assembled with plastic spacers, and was 16 cm in height. The CANSAT was hit with an aluminum alloy solid sphere at a speed of 1.35 km/s to be completely fragmented. Thirdly, 15-cm cubic micro-satellites were prepared to investigate the outcome of hypervelocity and low-velocity impacts [3]. Fourthly, 20-cm cubic micro-satellites were prepared to investigate the effects of impact directions [4]. Finally, 20-cm cubic micro-satellites covered with multi-layer insulation (MLI) and equipped with a solar panel were prepared to investigate MLI and solar panel pieces [5]. It should be noted that the impact testing using cubic micro-satellites were all

ⓒ Japanese Rocket Society 229 JSTS Vol. 26, No. 2 conducted under contract with the NASA Orbital Debris Program Office. After completion of the initial study of satellite impact testing, Kyushu University started to develop an orbital debris evolutionary model for the geostationary region, named GEODEEM [6-8]. An orbital debris evolutionary model requires an orbit propagator, thus Kyushu University also started to develop it. First, we developed two different numerical orbit integrators those can reproduce archived orbital history of selected objects in the geostationary region. One integrates the rate of change in the orbital elements in the Gaussian form of the variation of parameter equations, whereas another is based on Cowell’s formulation. The orbit propagators developed can characterize, track and predict the behavior of individual and groups of space objects in the geostationary region, so that we can conduct search survey of breakup fragments in the geostationary region as will be described later. Finally, we developed an analytical orbit integrator to be incorporated into the GEODEEM, which provides the secular and long-term variations of orbital elements. After development of the GEODEEM, Kyushu University also developed an orbital debris evolutionary model for the low-Earth orbit region, named LEODEEM, jointly with Japan Aerospace Exploration Agency (JAXA) [9,10]. The LEODEEM tracks individually all objects with perigee altitudes below 2000 km. Therefore, an orbit propagator incorporated into the LEODEEM should include the atmospheric drag. First, we added the atmospheric drag to the numerical orbit integrators, so that the numerical integrators can reproduce the archived orbital history of selected objects in the low Earth orbit region, geostationary transfer orbits, and Molniya type orbits. Then, we also added the atmospheric drag to the analytical orbit integrator based on [11]. Beside, debris generation mode in the low Earth orbit region is believed to be collision, unlike in the geostationary region. Therefore, the LEODEEM incorporates a one-by-one approach in order to calculate the probability of collision. After development of the LEODEEM, the GEODEEM has been upgraded based on the same modeling techniques adopted in the LEODEEM [12]. Finally, both models have been merged into a new orbital debris evolutionary model to track all Earth-orbiting objects, to be named NEODEEM. Currently, we use the NEODEEM to conduct future projections as will be described later. As mentioned earlier, the orbital debris modeling techniques describe debris generation and orbit propagation. Therefore, the orbital debris modeling enables us to build orbital debris evolutionary models as essential tools to predict the future orbital debris population, and as applications to discuss what and how to do for orbital debris mitigation and remediation. Details of the satellite impact testing and orbital debris evolutionary models were presented in a previous volume, [13]. This paper briefly introduces other applications of the orbital debris modeling techniques, including how to select hazardous objects to be removed from the low Earth orbit region, how to conduct debris measurements not only from the ground but also in space, how to improve orbital decay and re-entry predictions, and how to assess risks of using electrodynamic tethers to remove hazardous objects from the low Earth orbit region.

2. HOW TO SELECT HAZARDOUS OBJECTS TO BE REMOVED FROM SPACE

As demonstrated in [14], the current debris population in the low Earth orbit region would continue to increase even with an ideal best-case scenario (no new launches). This demonstration indicates that the density of objects in the low Earth orbit region is high enough that collisions between objects could cause a cascade. Each collision generates debris, which increase the likelihood of further collisions. Therefore, orbital debris removal is believed to be essential for sustainable human space activities. However, a huge cost may be needed to realize an orbital debris removal. One of solutions for this issue is to maximize the effectiveness of the remediation per one orbital debris removal. Main source of future debris population is collisions between objects, so that we should prevent accidental collisions generating more and more debris. Therefore, this section proposes selection indexes of colliding objects to be removed from the low Earth orbit region in view

303 of minimizing the probability of accidental collisions.

A. Proposing Indexes and Target Objects to Be Removed Kyushu University proposes two indexes for selecting target objects to be removed from the low Earth orbit region in priority [15]. The first index, labeled as KU1, is defined as the time for the cumulative probability of accidental collisions to reach a given threat level. The first index (KU1) considers the urgent necessity to remove colliding objects. The second index, labeled as KU2, is defined as the expected number of fragments to be generated by accidental collisions during the time evaluated by the first index (KU1). The second index (KU2) considers the potential contributions to the future debris population. Target objects selected by each index are investigated prior to evaluate the effectiveness of the remediation. The initial population in the low Earth orbit region is as of 1 May 2009 and includes all 10 cm and larger objects with perigee altitudes below 2000 km. NEODEEM, which is an orbital debris evolutionary model developed at Kyushu University under contract with Japan Aerospace Exploration Agency, is used to calculate the two indexes of each object in the initial population for selecting. The threat level for KU1 (i.e. the cumulative probability of accidental collisions) is set to be 0.001 for this study. Figure 1 compares top 100 objects selected by each index as a function of inclination and altitude. Distributions of top 100 objects are very similar in both indexes and 73 objects are mutually selected by both indexes. Target objects to be removed can be grouped into three orbital regions; 1) altitudes between 800 km and 1000 km and an inclination of 65 degrees, 2) an altitude of around 800 km and an inclination of 70 degrees, and 3) altitudes between 600 km and 800 km and an inclination of 100 degrees. In addition to objects in the three orbital regions, KU1 selects spacecraft with an altitude of around 800 km and an inclination of 85 degrees. On the other hand, KU2 selects rocket bodies with an altitude around 900 km and an inclination of around 82 degrees.

B. Effectiveness of the Remediation The effectiveness of the remediation is compared between the two indexes defined in the previous subsection. The same initial population as in the previous subsection is used as the baseline in order to evaluate the effectiveness of the remediation based on each index. Two more initial populations are prepared for this comparison study. One excludes top 100 objects selected by the first index (KU1), whereas the other excludes top 100 objects selected by the second index (KU2). Therefore, three different populations in total are projected using the NEODEEM appeared in the previous subsection. In order to evaluate the instability of each initial population, future launches and explosions are not allowed in this comparison study. We assume that the mean of 60 Monte

Fig. 1. Altitude and inclination of top 100 targets to be removed: (left) KU1, (right) KU2.

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Carlo runs represents the resulting environment and that the standard deviation is the error of each environment. Figures 2, 3, and 4 compare population growth within 200 years, population snapshots on 1 January 2209, and the cumulative number of accidental collisions within 200 years, respectively. As demonstrated in Fig. 2, both indexes (KU1 and KU2) can prevent accidental collisions effectively. It

Fig. 2. Comparison in the accidental collisions within 200 years: (left) catastrophic, (right) non-catastrophic.

Fig. 3. Comparison in the population growth within 200 years.

Fig. 4. Comparison in the population on January 1, 2209.

325 can be concluded, therefore, that the population growth can be effectively suppressed by the remediation based on either of the two indexes (see also Fig. 3). However, KU2 looks better than KU1 in Figs. 2 and 3. This is because, as compared in Fig. 4, that KU2 can suppress the population growth at an altitude range between 900 km and 1000 km in comparison to KU1. Removing 100 objects at the beginning of the projections seems to be unrealistic. The “no future launches” assumption is also unrealistic. Reasonable launch traffics and realistic removal strategies should be incorporated in future works.

3. DEBRIS MEASUREMENTS

U.S. Iridium 33 (commercial communication satellite) and Russian Cosmos 2251 (defunct communications rely station) ran into each other above northern Siberia on 10 February 2009. This was the first-ever accidental collision between two intact objects. After this accidental collision, space situation awareness becomes one of the keys for sustainable space development and utilization for humankind. In order to contribute to space situational awareness, Kyushu University targets three debris size and orbital regimes: 1) objects greater than 10 cm in the geostationary region, 2) objects greater than 1 cm in the low Earth orbit region, and 3) objects smaller than 1 cm in the low Earth orbit region. This section briefly introduces researches regarding each regime.

A. Search Survey of Breakup Fragments in the Geostationary Region Kyushu University proposes to apply the orbital debris modeling techniques to devise an effective search strategy applicable for breakup fragments in the geostationary region [16-18]. The orbital debris modeling techniques describe debris generation and orbit propagation to effectively conduct predictive analyses of space objects that include characterizing, tracking and predicting the behavior of individual and groups of space objects. Figure 5 illustrates our approach and workflow for the search survey. First, we generate fragments from a breakup event in the geostationary region, cited in literatures (e.g. [19-22]), using the NASA standard breakup model 2001 revision (see also [23]). Then, we propagate their orbit until planned observation date to predict population of the generated fragments. The resulting population specifies effectively when, where and how we should conduct optical measurements using ground-based telescopes. Secondly, therefore, we conduct “planning and observation” based on the resulting population. We select a couple of candidate points in geocentric equatorial inertial coordinates. Then, we keep looking at each point for a relatively long duration. In order to effectively detect debris in the geostationary region, however, images should be taken with non-sidereal mode. Therefore, one set of images will be taken for several minutes with non-sidereal mode, and then the pointing will be changed in order to keep looking at the specified single point in

Fig. 5. Approach and workflow.

633 JSTS Vol. 26, No. 2 geocentric equatorial inertial coordinates. Thirdly, based upon the resulting population, we predict motion of fragments passing through the specified single point in geocentric equatorial inertial coordinates during the observation. Motion prediction characterizes the behavior of groups of fragments from a single breakup event. Therefore, the motion prediction can clearly distinguish fragments generated by a target breakup event from other detected objects. The motion prediction also specifies effectively and precisely how we should process successive images to detect moving objects. Fourthly, therefore, we apply the motion prediction to a track-before-detection technique, which stacks successive images shifted according to the assumed motion of the target object, in order to detect faint fragments from the target breakup event. Finally, we assume how the target breakup event has released fragments based on correlated and uncorrelated targets (CTs/UCTs) detected by the image processing, and then properly describe the target breakup event to improve the debris generation. This improvement provides a better definition of the current situation in the geostationary region. Actual observation was conducted at the JAXA Nyukasa Observatory on 4 March 2011. Figure 6 demonstrates observation planning to search lost fragments from the US Titan IIIC Transtage exploded on 21 February 1992. We mask the invisible region from the JAXA Nyukasa Observatory on the predicted population, and then overlay the Earth shadow at the nominal geostationary altitude. In the visible region, the point where most fragments will be detected is at 195.5 degrees in geocentric right ascension and –6.5 degrees in geocentric declination. The duration of actual observation was set from 13:00 UT to 20:20 UT, so that the JAXA Nyukasa Observatory was able to keep looking at the point during the observation. Beside, we confirmed that there was no bright star in the field of view during the observation. The actual observation took 49 sets of 32 successive images to result in the total number of 1568 images. Figure 7 demonstrates the two-dimensional motion of the US Titan IIIC Transtage fragments in a series of successive images taken during the observation. Figure 7 also compares “most likely” motion and measurements. This “most likely” motion includes approximately 70 % of the US Titan IIIC Transtage fragments. Objects appearing inside the “most likely” motion are most likely from the US Titan IIIC Transtage. Indeed, a correlated target appearing inside the “most likely” motion is 1968-081H, a US Titan Transtage fragment. Besides, backward propagations have confirmed that the three uncorrelated targets appearing inside the “most likely” motion are associated with the US Titan IIIC Transtage. Therefore, the “most likely” approach works well to clearly distinguish the US Titan IIIC Transtage fragments from other objects. It should be noted that the fragment and three uncorrelated targets are relatively bright and over the limiting magnitude of a single CCD image (magnitude of 15.5). Staking method can detect faint objects by stacking successive images that have been shifted according to the assumed motion of the target object [24]. The staking method enables us to detect dimmer objects below the limiting magnitude of a single CCD image. Figure 7 also specifies two

Fig. 6. Predicted population and observation planning.

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Fig. 7. “Most likely” motion and measurements.

different assumptions made for the stacking method. One motion range includes 1968-081H, a US Titan IIIC Transtage fragment, and an uncorrelated target appearing inside the “most likely” motion, whereas another motion range includes two uncorrelated targets appearing inside the “most likely” motion. A set of 32 successive images is processed by the stacking method, so that the theoretical gain is approximately 2.5 in magnitude. As demonstrated, the stacking method with the motion prediction successfully detected one new uncorrelated target at the latter motion range (magnitude of 18). However, computational time necessary for the stacking method to process a set of 32 successive images is approximately 4.5 hours using up-to-date single CPU core. Therefore, it is still nearly impossible for the stacking method to complete image processing of 49 sets, taken during the observation, before follow-up observation to determine the orbit precisely. Enhancement of the stacking method based on a Field Programmable Gate Array technology, also under development at JAXA, and/or based on a robust-concept algorithm, under development at IHI Corporation, may reduce computational time necessary to process.

B. System Performance Evaluation of Space-based Optical Sensor Kyushu University has conducted a feasibility study of space-based optical measurements, targeting objects larger than 1 cm in size [25,26]. The minimum size of objects cataloged by the US Space Command is 10 cm, so that hypothetical fragments between 1 cm and 10 cm in size are generated based on major historical breakups in [27-31]. The number of hypothetical fragments is 38,007, whereas the number of cataloged objects of which two-line element sets are available is 9,543. Consequently, 47,550 objects in total are prepared for this feasibility study. First, we evaluate an altitude at which a space-based optical sensor should be inserted. This evaluation is conducted in terms of the effective number of objects at each altitude bin and the number of objects crossing each altitude bin. Figure 8 clearly indicates that there are two altitudes at which both parameters take a higher value: 1) 450 km, and 2) 850 km. Therefore, those two altitudes can be considered as promising candidates. Secondly, we evaluate an orbital plane on which a space-based sensor should be put. Since optical sensors perceive reflection of sunlight from objects, sun-synchronous orbits, on which sunlight

835 JSTS Vol. 26, No. 2 falls always from the same direction, would be better. Another good point of sun-synchronous orbits is that once we select an altitude its inclination can be determined uniquely to establish the corresponding sun-synchronous orbit. Thus, orbital element to be evaluated is only right ascension of the ascending node. In order to incorporate three different conditions on sunlight direction, three different ascending nodes are selected: 1) 0:00, 2) 3:00, and 3) 6:00, all in local sidereal time. Sunlight is always parallel to the orbital plane in the case of 0:00, while in the case of 6:00, sunlight is always perpendicular to the orbital plane. Thirdly, we make a selection of orbit for a space-based optical sensor to be inserted. There are six orbits to be compared as a result of the first and second evaluations (i.e. two altitudes by three orbital planes). Each orbit is evaluated in terms of the number of passage events, which satisfy the followings: 1) within 500 km from the sensor, 2) visual magnitude of 14 or brighter, and 3) traveling velocity of 0.4 degree/sec or slow within the visual field. Sampling frequency is assumed to be 4 Hz in this evaluation. Figure 9 provides the passage event distribution as a function of visual magnitude to select a sun-synchronous orbit with an altitude of 850 km and local sidereal time of the ascending node of 0:00. Finally, we evaluate a direction in which a space-based sensor should be pointed. The field of

Fig. 8. Effective number of objects at each altitude bin and number of objects crossing each altitude bin, both are normalized by the maximum.

Fig. 9. Passage event distribution in terms of visual magnitude.

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Fig. 10. Passage event distribution in terms of azimuth and elevation.

view of a space-based sensor is assumed to be 13 degrees by 13 degrees for this evaluation. The passage event distribution is evaluated in terms of azimuth and elevation. Azimuth is measured from the orbital velocity vector on the local horizontal plane, whereas elevation is measured from the local horizontal plane. Figure 10 provides the passage event distribution as a function of azimuth and elevation. It is quite difficult to distinguish between the Earth albedo and reflection of sunlight from objects, so that Fig. 10 also specifies the edge of the Earth by dashed line in red. Outside the edge of the Earth, the orientation in which most objects will be detected is at –171 degrees in azimuth and 1 degrees in elevation. The feasibility study introduced here is conducted based on a simplified criterion, not related to the specification of any space-based sensors currently available, or to be realized promptly, or under development. Therefore, we need to modify a criterion to incorporate the specification of candidate space-based sensors in order to devise a more realistic and promising mission plan. Since the final goal of space-based measurements is to determine targets’ orbit to individually track them, we also need to improve initial orbit determination that works under very short arc and time observation condition.

C. IDEA: In-situ Debris Environmental Awareness Kyushu University has initiated the project for in-situ debris environmental awareness (IDEA), aiming to establish an in-situ and real-time measurements network to monitor micron-size debris in the low Earth orbit region [32-34]. Today, information on micron-size debris has not been continuously available yet in any orbital regimes. The IDEA project intends to deploy a group of small satellites into a congested altitude of which micron-size debris are to be monitored. They are supposed to be launched sequentially as secondary payloads with a primary satellite to a same altitude, in which case it is possible to work out the debris environment for the primary satellite at the same time. In total, 5 satellites are planned to deploy into the same altitude and/or different altitudes where the assessment of the micron-size debris is highly required. Population estimation is one of essential measures for the environmental assessment of orbital debris in any size regimes. The number of orbits, on which ground-based sensors can directly track objects to individually identify, is the essential parameter to evaluate the population of relatively large objects. On the other hand, the population of smaller objects, not tracked from the ground, is

1037 JSTS Vol. 26, No. 2 evaluated as flux, which represents a statistical number of objects passing through unit area per unit time. Flux-based population models for micron-size regime are built in the well-known orbital debris environmental models: the MASTER series being developed by ESA, and the ORDEM series being developed by NASA [35,36]. Retrieved surface inspections can estimate fluxes on which those surfaces were. The observed fluxes in such several orbits, intermittently collected from early 1980s to early 2000s, have provided considerable empirical evidences to support the validity of the flux-based population models in the low Earth orbit region and its modeling approaches [35,36]. Those population models, though, still have large uncertainties in orbital altitudes away from the observed orbits and also current situations are unclear due to the limitation of sample retrieval capabilities of spacecraft and/or their portion [35]. The capability limitation and the current unclear situations are calling for a novel observation technique to enhance them. A dust sensor adopted for the project will be a promising solution for the aforementioned demand. The dust sensor is simple to produce and easy to use but novel to require less calibration tests. The dust sensor is non-conductive thin film on which resistive lines are formed at fine pitch. The dust sensor has been proposed jointly by Institute for Q-shu Pioneers of Space, Incorporation and IHI Corporation, and is currently under development at Japan Aerospace Exploration Agency [37]. Impact can be detected when one or more resistive lines are severed, so that the dust sensor can directly determine the size of debris impacted on. Beside, time and location at impact can also be recorded as information to be forwarded to the ground station in near real time. First, we investigate incoming direction of micron-size debris with respect to a satellite in a sun-synchronous orbit. Figure 11 provides the flux distribution as a function of azimuth (left) and elevation (right) in a sun-synchronous orbit with an altitude of approximately 800 km. The flux predicted by ESA’s MASTER 2005 is intensively distributed at ram, whereas the flux predicted by NASA’s ORDEM 2000 is dispersed at ram, ram – 45 degrees, and ram + 45 degrees. Regarding the flux distribution as a function of elevation, most debris come in horizontally, at an elevation between – 5 degrees and + 5 degrees. Consequently, as illustrated in Fig. 12, Fig. 11 may result in two different orientations relative to the ram of a cubic satellite for a further analysis: 1) one surface oriented to the ram, and 2) two surfaces oriented at 45 degrees to the ram. It may be noted that a detector on the zenith-facing side is suitable for good detection of micrometeoroids. We also intend to introduce micrometeoroids flux measurements in the near future. Secondly, we assess the flux variation on the cubic satellite illustrated in Fig. 12 in order to

Fig. 11. Flux distribution in terms of: (left) azimuth, and (right) elevation.

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1 2 1 T (In-track) T (In-track)

Cubic 2 Cubic

Satellite Satellite

W (Cross- W (Cross- N(Radial) track) N(Radial) track) Fig. 12. Orientation relative to the ram: (left) one surface orientated to the ram, and (right) two surfaces oriented at 45 degrees to the ram.

Fig. 13. Flux on each surface defined in Fig. 12: (left) one surface orientated to the ram, and (right) two surfaces oriented at 45 degrees to the ram.

determine which of the two orientations provides a better assessment of the current situation of micron-size debris. For each orientation, the flux on each panel of the cubic satellite is integrated out based on Fig. 11 to depict Fig. 13. It is important for the project to have a high degree of confidence in the assessment of the current situation of the micron-size debris. Since a higher flux results in a higher degree of confidence we should choose which of the two orientations shows a higher flux. It is concluded from Fig 13, therefore, that two surfaces oriented at 45 degrees to the ram expect a higher flux in comparison to one surface oriented to the ram. This conclusion selects two surfaces oriented at 45 degrees relative to the ram of the cubic satellite for the dust sensor to be mounted on. As mentioned earlier, the dust sensor adopted for the project can also record time and location at impact as information. Thus, the project realizes a high temporal-spatial resolution capability to cognize environmental change as the result of a breakup. Currently, therefore, we investigate how and where a group of small satellites equipped with the dust sensor can be aware of the dynamic environmental change to identify a breakup causing it.

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4. ATMOSPHERIC DENSITY MODELING

The atmospheric drag affects near Earth satellite’s motion to a considerable level. The drag acceleration is

1 2 adrag (Cd A/ m)v 2 where A/m is the area-to-mass ratio, Cd is the drag coefficient, is the atmospheric density, and v is the velocity of satellite relative to the co-rotating atmosphere. As problems like orbital lifetime, collision probability, reentry prediction and so forth are of great concern, modeling the atmospheric drag on space objects has been intensively studied. The A/m, Cd, neutral winds, and which factor the drag effect, however, are usually poorly estimated. The A/m can be possibly well calculated by satellite’s operator based on attitude determination, Cd can be further understood from experiment, neutral winds and density are studied via more and more orbit observation in order to construct atmosphere pattern around Earth. Based on the available acceleration data measured by the satellites CHAMP and Grace, we also attempt to improve the density modeling to reduce the position uncertainty. The widely used density models like MSIS and Jacchia are thought not to sufficiently consider the space weather effect with generally 15% - 30% error under severe space weather condition. The geomagnetic index 3-hourly ap/kp index is thought to be lack of resolution. The index Dst which also manifests the magnitude of storm and is updated every 1 hour has been suggested to approach density variation [38]. As the complicated coupling between solar, magnetosphere, ionosphere, and thermosphere brings the difficulty in modeling, we try to adopt the neural network, considering its nonlinear property would express physics process driving the density dynamics. It has been mentioned that the geomagnetic activity are especially under estimated on density variation [38]. Here, our network is trained with the storm-time density as output and the corresponding geomagnetic index (Dst), solar activity index (F10.7 and 81-day average F10.7), time (day of year for seasonal effect) and satellite position (latitude, height and daytime hemisphere or nighttime hemisphere) as inputs. The model is built to make up MSIS model, i.e. when the geomagnetic condition becomes critical, which is assumed to be with ap > 80, density calculation shifts to neural network model. The new model is referred as integrated model later in the discussion. The orbital drag accelerations were well measured by the two satellites CHAMP and Grace, which are provided by Information System and Data Center (ISDC), together with the corresponding satellite positions. We use the density data calculated by The University of Colorado CHAMP-GRACE Team [39]. The space weather data necessary for this study is acquired from [40]. The structure of neural network is set to receive a sequence of Dst data to express the energy accumulated in thermosphere. In addition, the model is actually made up of two neural networks for south and north hemisphere respectively, since the density in two hemispheres response inversely to season. The Japanese X-ray astronomical observation satellite ASCA, which was launched on 20 February 1993 to an orbit at an altitude between 525 km and 615 km with an inclination of 31 degrees, suffered from a severe atmospheric drag and torque induced by a super geomagnetic storm happened on 15-16 July 2000 (ap = 400, Dst = 301). It failed to recover its attitude to receive sufficient solar power supply before its power run off. Its attitude continued spinning afterwards, and orbit continued decaying at a higher rate than expected because its drag coefficient also grew due to the spinning attitude. It is of value to reconstruct the atmospheric disturbance on ASCA as the information for understanding potential space risk and future satellite design. For that reason, we select ASCA as a subject to compare the density predicted by our integrated model and NRLMSISE-00 model. Assuming ASCA’s A/m and its Cd are well known, which are thought to be associated with

1340 satellite’s altitude, shape and attitude motion that can be possibly known by the satellite operator. Thus, satellite’s ballistic coefficient (BC), which equals to Cd A/m, we use is adjusted by minimizing the difference of the orbit decay between an early two-line element set (TLE) to a later TLE and that orbit decay by numerically propagating between the two epochs with the corresponding orbit inputs derived from the early TLE. Although ASCA started to be influenced by the expansion of density at around 15:00 on 15 July, it was still able to maintain its orbit and attitude, but it became tottering after 22:00 due to a huge brake. During 22:30-23:20, its angular momentum sharply decreased by 4 Nms [41]. Thus, assuming the satellite started to spin afterwards, BC used in the propagation before 23:20 is adjusted using the TLEs before and near the beginning of the storm, and after 23:20, BC is adjusted using the TLEs after and near the end of the storm. As it can be seen from Fig. 14, during July 15, 22:00 - July 16, 09:00, the integrated model displays the intensive density enhancement, as implied above, whose peak value is 1.04 10-11 kg/m3 which is 1.5 times the density by NRLMSISE00 and 10 times the density by the theoretical used exponential density model, i.e. 1.14 10-12 kg/m3. The difference should be of interest for satellite design and orbit planning. As it is said in [42], the true density was 100 times greater than that for which its attitude control system had been designed to manage. After the anomaly is unexpectedly noticed, the operation group of ASCA tried to transit to safe mode, while it was confronting the largest atmospheric torque, eventually the transition failed to achieve. If the extreme density environment attributed to the great geomagnetic storm that would occur once to twice during 11-year solar cycle is well estimated with good forecast of geomagnetic index and density model, by designing the control system with higher resistivity or carefully operating the attitude control in advance of the density expansion, the satellite can withstand or recover from density attacks and enjoy a longer lifetime. On the other hand, the storm caused the satellite at the altitude 470 km where atmospheric is not supposed to be obvious to decay 850 m in only 2 days. NRLMSISE underestimates the decay with the error around 180 m. The integrated model almost makes up this

1.2E-11 Attitude 1.1E-11 started to Integrated Model ] 3 1E-11 deviate 9E-12 NRLMSISE-00 8E-12 7E-12 6E-12 5E-12 4E-12 3E-12 2E-12 1E-12 0 Atmospheric Atmospheric Density [kg/m 15 Jul 0:00 15 Jul 12:00 16 Jul 0:00 16 Jul 12:00 17 Jul 0:00 17 Jul 12:00 18 Jul 0:00 18 Jul 12:00 Time

Fig. 14. Predicted orbital density for ASCA on 15-18 July 2000.

6846.4 6846.2 TLE Integrated Model 6846 NRLMSISE-00 6845.8 6845.6 6845.4 6845.2 Semi-major Axis Semi-major Axis [km] 6845 15 Jul 0:00 15 Jul 12:00 16 Jul 0:00 16 Jul 12:00 17 Jul 0:00 17 Jul 12:00 18 Jul 0:00 18 Jul 12:00 Time Fig. 15. Historical and predicted orbit decay of ASCA on 15-18 July 2000.

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8E-11 ] 3 7E-11 Integrated Model 6E-11 NRLMSISE-00 5E-11 4E-11 3E-11 2E-11 1E-11 Atmospheric Density [kg/m 0 24 Aug 0:00 24 Aug 12:00 25 Aug 0:00 25 Aug 12:00 26 Aug 0:00 Time Fig. 16. Predicted orbital density for YOHKOU on 24-26 August 2005.

6665 Integrated Model 6664 NRLMSISE-00 TLE 6663

6662

6661

6660 Semi-major Axis [km] Axis Semi-major

6659 24 Aug 0:00 24 Aug 12:00 25 Aug 0:00 25 Aug 12:00 26 Aug 0:00 Time Fig. 17. Historical and predicted orbit decay of YOHKOU on 24-26 August 2005.

difference, as demonstrated in Fig. 15. We also employ this model in the orbit prediction of satellite YOHKOU in the major geomagnetic storm (ap = 300, Dst = 216) on 24-25 August 2005, when YOHKOU’s attitude had been below 290 km where satellite is thought to reentry, in order to exam the performance of the networks model in reentry prediction. The predicted density and propagated orbit employing integrated model and NRLMSISE00 are shown in Figs. 16 and 17. At this attitude, the general density is 10 times the density at ASCA’s orbit. Therefore, the difference between networks model and NRLMSISE00 becomes evident. This can be easily seen from the prominent orbit decay. YOHKOU decayed 5.2 km during this storm, NRLMSISE predicts 2 km less than that, and the integrated model reduces the error to 0.7 km. During the period of high solar activity, this improvement tends to be more important in predicting the reentering objects with rapidly changing orbit elements.

5. SPACE TETHERS

Space Tethers have a variety of applications such as electrical power generation, orbital elevation and interplanetary exploration. Space tethers also have promised as a de-orbiting system that removes orbital debris from the low Earth orbit region actively. This de-orbiting system uses a long conductive strand to perform an orbit transfer using Lorentz force exerted by the geomagnetic field on the conductive strand. The length of the conductive strand may be on the order of several kilometers to generate Lorentz force enough to descend effectively. Therefore, the de-orbiting system may have a risk that it collides with other space objects in orbit because of its long configuration. This section describes a risk of a tether system during a mission of orbital debris removal.

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A. Risk Assessment Flow Figure 18 provides a risk assessment flow to estimate the collision probability that the tether system collides with other orbiting objects when the tether system conducts a mission of orbital debris removal, and the mission success rate until the orbital debris removal is over. First, we propagate orbits of the tether system and other space objects to calculate the distance between the tether system and each space object based on a conjunction analysis. Once the minimum distance between the tether system and an object is less than a threshold value, we estimate the collision probability of the tether system against the object. The mission success rate is also estimated the resulting collision probability. This risk assessment flow is repeated until the tether system descends down to an altitude of 300 km. It is assumed, for this risk assessment, that the length of the conductive strand is 10 km and its

Propagate the orbit of the tether system and other satellites in orbit

Calculate the distance d between the tether system and other satellites by using position respectively

NO threshold of an approach distance YES Calculate a collision probability and a success rate

Fig. 18. Risk Assessment flow.

collision cross-section Elliptical region on a point of part of a tether EDT spacecraft

other satellite

Fig. 19. Definition of collision cross-sectional area.

1643 JSTS Vol. 26, No. 2 diameter is 1.98 mm. It is also assumed that the conductive strand is rigid and constantly oriented towards the nadir or the zenith. The removal target is ADEOS 2 spacecraft that is a Japanese environmental observation satellite suspended its operation in 2003. ADEOS 2 is assumed to be on a circular orbit at an altitude of approximately 800 km with an inclination of 98.6 degrees, where so many objects are crowded. The collision probability is numerically calculated at the foot of a perpendicular from the object to the tether. Therefore, as illustrated in Fig. 19, the cross-sectional area of the tether inside the error ellipsoid is only taken into account in calculating the collision probability.

B. Risk of Tether System Figure 20 provides the number of close approach as a function of altitude and distance between the removal system and a space object until the removal system descends down to an altitude of 400 km. Close approach happens frequently at an altitude range between 720 km and 800 km where space objects are crowded. Meanwhile, the number of close approach is dramatically small below 720 km. It is important, therefore, to consider how to reduce the number of close approach when the removal system passes through the crowded altitude range. Figure 21 demonstrates how much the mission success rate is sensitive to the mission starting time. The mission starting time on 1 January 2020 is changed at 4-hours interval, so that Fig. 21 compares seven cases in total. Solid line in Fig. 21 represents the mean of seven cases, whereas

500

400

300

200

100 Number of approach Number close 0 0 5 800 760 10 720 640 680 15 560 600 20 520 Approach distance[km] 440 480 25 400 Altitude[km]

Fig. 20. Number of close approach as a function of altitude and minimum distance.

Fig. 21. Comparison in the mission success rate.

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Fig. 22. Comparison in the number of close approach within 3 km.

Fig. 23. Collision probability of each close approach for the mission starting time of 24:00.

broken lines represent the standard deviation. Most cases are within the 1-sigma (standard deviation), but only the starting time of 24:00 is far off the mean. There is no correlation between the mission success rate and the mission starting time. Figure 21 indicates that the removal system can avoid fatal collisions by changing the mission starting time by several hours. Figure 22 compares the number of close approach within 3 km between the seven mission starting times as in Fig. 21. For the starting time of 20:00 no close approach within 1 km happens to result in the highest mission success rate in Fig. 21. It can be observed from Figs. 21 and 22 that a negative correlation between the mission success rate and the number of close approach. The more close approach within 1 km happens, the less the mission success rate becomes. Figure 23 estimates the collision probability of each close approach for the starting time of 24:00 to confirm why the mission success rate of the starting time of 24:00 is worst. There exist so many close approaches in a short time at the beginning. It is found that the removal system experiences a periodical close approach to a same object.

6. CONCLUSION

This paper briefly introduced efforts made at Kyushu University in the area of the orbital debris

1845 JSTS Vol. 26, No. 2 modeling and applications. The orbital debris modeling, which describe debris generation and orbit propagation, enables us to build orbital debris evolutionary models as essential tools to predict the future orbital debris population, and as applications to discuss what and how to do for orbital debris mitigation and remediation. The orbital debris modeling also enables us to devise an effective search strategy applicable for breakup fragments in the geostationary region using ground-based optical sensors, and evaluate the effectiveness of space-based measurements of objects not tracked from the ground, both to contribute to space situational awareness. Ultimately, the orbital debris modeling covers the atmospheric density modeling necessary for orbital decay and re-entry analyses, and the space tether modeling to assess risks of using electrodynamic tethers for removing hazardous objects from the low Earth orbit region. Kyushu University will pursue researches on the orbital debris modeling and applications for sustainable space development and utilization for humankind.

ACKNOWLEDGEMENTS

The authors who contribute Subsection 3.A wish to acknowledge Mr. H. Kurosaki of the JAXA Space Debris Unit for his dedicated assistance in the observations at the JAXA Nyukasa Observatory. IHI Corporation wishes to acknowledge US Air Force Office of Scientific Research (AFOSR) Asian Office of Aerospace Research and Development (AOARD) to support the research described in Subsection 3.A under the grant No. FA2386-10-1-4136 (AOARD 104136).

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