Investigation of Angular Momentum Associated with Hypervelocity Space Debris Impacts in the Low Earth Orbit

Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30, pp. Pr_73-Pr_78, 2016 Investigation of Angular Momentum Associated with Hypervelocity Space Debris Impacts in the Low Earth Orbit By Masahiro NISHIDA, 1) Koichi HAYASHI, 2) Hiroshi ODA, 3) Hirohisa KUROSAKI, 4) Toshifumi YANAGISAWA, 4) and Masumi HIGASHIDE 4) 1) Nagoya Institute of Technology, Nagoya, Japan 2) National Institute of Technology, Toba College, Toba, Japan 3) Japan Aerospace Exploration Agency,Tsukuba, Japan 4) Japan Aerospace Exploration Agency, Chofu, Japan (Received July 31st, 2015) Active debris removal (ADR) of large objects, such as rocket bodies, is considered to be one of the best solutions to address the accumulation of space debris. Therefore, a good understanding of the rotational states of rocket bodies is essential for designers of ADR systems. Optical observations of old rocket bodies have shown that some of them are rotating. To assess the possibility that collisions between small pieces of space debris and these objects causes the rotation of them, we conducted hypervelocity impact tests to measure the efficiency of momentum transfer from projectiles to an aluminum target. The aluminum target was vertically hung from the ceiling. After a 1 mm projectile, representing a small piece of space debris, struck the aluminum target, a pendulum motion was initiated. The efficiency of the momentum transfer was calculated using the maximum angle of the pendulum swing. In this study, the efficiencies of the impact speeds ranging from 3 to 7 km/sec were investigated using the two-stage light-gas gun at the Institute of Space and Astronautical Science at Japan Aerospace Exploration Agency. Although much faster speeds are required to determine if the collisions of small space debris cause the rotations of rocket bodies, the results that were obtained could show that the efficiency of momentum transfer increases with impact velocity. Key Words: Hypervelocity Impact, Momentum, Ejecta, Aluminum Alloy Target, Projectile 1. Introduction In the past 50 years of space-based activities, thousands of spacecraft have been launched into Earth s orbit. Space debris, which include defunct satellites, rocket bodies, missionrelated objects, and fragments, are non-functional objects. The quantity of space debris is increasing annually and it is no longer possible ignore the risk of collisions. When large, uncontrolled objects, such as rocket bodies and non-functional satellites, collide with smaller pieces of debris, the overall quantity of debris further increases. To maintain a certain degree of control over the occurrence of collisions in this environment, active debris removal (ADR) is required. 1) For the ADR of large target objects, understanding their respective attitudes and rotation states is important, so that a device can be attached to these objects (e.g., a tether, engine) to provide an additional thrust to lower their orbits. Although eddy currents were believed to stop the rotations in a few months, optical observations showed that some old rocket bodies were rotating at a few degrees per second, which is too fast to effectively attach the aforementioned devices. 2,3) Currently, no explanations exist for what causes the rotations. One reason may be attributed to the collision of small space debris. Headon collisions between objects in the Low Earth Orbit (LEO) occur at about 14 km/s. When a small piece of space debris strikes a large object, a crater is formed on the latter and fragments are ejected from their respective surfaces. Therefore, the momentum transferred to the larger object may cause it to rotate. There are several studies on the momentum transfer of projectiles in the case of hypervelocity impacts. Nysmith and Denardo examined the momentum transfer when projectiles struck thin aluminum targets. 4) Yanagisawa et al. studied momentum transfer in oblique impacts with nylon projectiles and thick mortar and basalt targets. 5-8) Shirono et al. studied linear and angular momentum transfer efficiencies for oblique impacts on spherical mortar targets. 9) Walker has been studying the momentum enhancement that occurs when aluminum projectiles strike granite targets. 10,11) With respect to asteroid impacts, some studies also have been conducted on the momentum transfer of brittle material targets. Hoerth et al. are examining the momentum transfer of various types of porous stones. 12) Stickle et al. are also examining the momentum transfer of various brittle targets including strong rocks, weakly cemented rocks, highly porous rocks, and sand. 13) Kage et al. are examining the momentum transfer of bricks and plasters. 14) However, few studies have focused specifically on the momentum transfer between ductile material projectiles and targets, especially in the context of hypervelocity impacts of space debris in the LEO. In this study, we investigate the momentum transfer in hypervelocity-impact experiments, which involve the use of an aluminum alloy target and an aluminum sphere projectile. The aluminum alloy target was hung from a beam. After the Copyright 2016 by the Japan Society for Aeronautical and Space Sciences and ISTS. All rights reserved. Pr_73

Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30 (2016) projectiles struck the stationary targets, pendulum motions were initiated. These motions of the targets were recorded using images obtained from a high-speed video camera. We examined the effects of impact velocity on momentum transfer, in particular, the efficiency of momentum transfer. If the efficiency is high enough to rotate large objects in space, this information would be considered in system construction for future active debris removal missions. Using a space debris environment model, we can understand what quantity of space debris of a specific size exists in the orbit where target rocket bodies are present. Combining this information with the efficiency of momentum transfer identified in this study, we can approximate what portion of rocket bodies in the orbit are rotating, and with what rotational ratio. This should be the most important factor to be considered when realizing an ADR system. Fig. 1. Jetting, cone of ejecta, and cratering on the target due to the hypervelocity impact of a projectile. 2. Model and Momentum Transfer Assumptions When an aluminum, spherical projectile strikes a thick aluminum target at hypervelocity, a substantial amount of material is ejected from the crater (Fig. 1). Since jetting and cone of ejecta are the main processes of ejection in the case of ductile materials, the total momentum transferred to the target right after the impact, p total, equals the sum of the projectile momentum before impact, p in = m proj v proj, the jetting momentum, p jet, and the momentum of ejecta cone, p ejecta, where I 0,, M target, g and L are the inertia moment of target after impact, the angular velocity of target right after impact, the mass of target after impact, the gravitational acceleration, and the distance between the rotating center of the target and the center of gravity. The angular velocity of target right after impact,, was calculated using Eq.(4) and each swing angle,. The total momentum transferred to the target, p total, was calculated by the angular momentum of target right after impact, the product of I 0 and, decided by the distance between the rotating center and the impact point of the projectile on the target. The efficiency of momentum transfer was estimated from Eq. (3) with the measured p total and the known p in. The aforementioned calculation considers p total under ideal conditions. In reality, the following effects should be considered: (i) friction on the bearings, (ii) air resistance around the target, and (iii) momentum transferred by the light gas (hydrogen) hitting the target. As the swing angle of the target gradually decreased with time, friction on the bearings is important and we corrected for the effects of friction following the method described in Table 1 of chapter 4. Since the pressure of the test chamber was 1.5 to 6 Pa, we assumed that air resistance was negligible. To examine the effects of the light gas (hydrogen) hitting the target, we carried out several light-gas gun experiments using a sabot without the projectile; it was observed that the target did not move at all. This means that the effect of the light gas was less than one pixel on the images (approximately 0.1º) which is the measuring limit, even at the impact velocities of 6.95 and 7.01 km/s. The results obtained by Yanagisawa and Hasegawa 8) also showed that the light gas did not affect the motion of the target. When the specimens were set far from the acceleration tube, light gas did not affect the motion of target. Since is a function of m proj and v proj,, the measurement error can be estimated by the individual parameters. The measurement errors of mass (electronic balance), velocity (oscilloscope and measurement interval) and swing angle (time interval and resolution of high speed video camera) were 1.5%, 0.3% and 1%. The measurement error of was 1.5%. p total = p in + p jet + p ejecta, (1) where m proj and v proj are the mass and impact velocity of the projectile before impact, respectively. Introducing the efficiency of momentum transfer: pjet pejecta jet ejecta p p, (2) in in Eq. (1) is re-written as ptotal 1. (3) pin We calculated p total using the maximum swing angle obtained using images from a high-speed video camera used in the hypervelocity-impact experiments as follows. By applying the principle of conservation of mechanical energy, the rotation energy of target right after the impact: 1 2 I0 M target g L 1 cos 2 (4) Fig. 2. Target and experimental setup. Pr_74

M. NISHIDA et al.: Investigation of Angular Momentum Associated with Hypervelocity Space Debris Impacts in the Low Earth Orbit Note that when there is no ejecta and jetting, = 0. In general, is greater than unity for hypervelocity impacts and increases with the impact velocity. Although such increasing tendencies were found in previous studies, the dependency of the efficiency on the impact velocity is still unknown, in particular, in the context of a high-velocity regime. 3. Experimental Setup To measure the total momentum p total, we used a pendulumtype experimental setup (Fig. 2). The pendulum target is an aluminum plate (A5052-H112) with a width of 28 mm, depth of 8 mm, and a length of 105 mm. The aluminum plate was connected with glue to a steel shaft that is 75 mm long. The aluminum target was vertically hung from a ceiling using both ends as bearing supports. The aluminum target started swinging after impact. The pendulum motions of the targets and the maximum swinging angle were measured using a high-speed video camera (nac MEMRECAM HX-3). The motions of projectiles and ejecta were also observed using an ultra-high-speed video camera (nac ULTRA cam). The moment of inertia was calculated by considering the size and mass of the aluminum plate and the steel shaft. We used aluminum alloy (2017-T4) projectiles with a diameter of 1.0 mm. The projectiles were accelerated using a two-stage light-gas gun. The simulation was conducted at the Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA). The impact velocities ranged from 3 to 7 km/s. Even at 7 km/s, the crater depth was approximately 3 mm, which was less than half of the target thickness. Hence, the target was considered to be sufficiently thick for these impact experiments. the ejecta collected from the test chamber after the impact experiment was conducted. Ejecta greater than several mm in size could be collected, even though the diameter of projectiles was 1.0 mm. Figures 6 and 8 show the photographs of aluminum targets at impact velocities of 5.25 km/s and 4.14 km/s, respectively. Compared to the results at 6.19 km/s, the maximum angle of pendulum swing decreased. Figures 7 and 9 show the image of cone of ejecta taken by a high-speed video camera. Regardless of the impact velocity, the cone angle of ejecta was approximately 60 for both cases. The maximum angle of pendulum swing for each impact test was measured from images of the pendulum motion using image analysis software (ImageJ). However, the bearing has friction, so the maximum swing angle of the target decreases. Table 1 shows the transition of the maximum swing angle and (a) Just before impact 4. Results and Discussion Figure 3 shows the behavior of aluminum targets before and after the impact. The aluminum target started to move in a pendulum motion after the impact and reached the maximum swing angle as shown in Fig. 3(b). The ejecta were observed just after the impact. Figure 4 shows that many ejecta were scattered in the reverse direction of the incoming aluminum projectile and that the cone of ejecta was clearly formed in the direction in which the ejecta were scattered. Figure 5 shows (b) Maximum swing angle at 131.8 ms after Fig. 3(a) Fig. 3. Pendulum motion of aluminum targets (6.19 km/s). Cycle Maximum swing angle of target, degree Table 1. Transition of maximum swing angle and potential energy. Potential energy, 10-3 J Angular displacement, degree Diminution of potential energy, 10-3 J Energy loss per angular displacement one degree, 10-6 J/degree 1 23.48 2.866 - - - 1.5 22.61 2.660 46.09 0.206 4.463 2 21.98 2.516 44.59 0.144 3.238 2.5 21.5 2.408 43.48 0.107 2.470 3 20.72 2.239 42.22 0.170 4.019 3.5 20.22 2.133 40.94 0.106 2.580 4 19.47 1.979 39.69 0.154 3.875 4.5 18.98 1.882 38.45 0.097 2.535 5 18.27 1.745 37.25 0.136 3.677 5.5 17.60 1.620 35.87 0.125 3.474 Pr_75

Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30 (2016) Fig. 4. Photograph of ejecta taken by an ultra-high-speed video camera, 5.71 μs after impact; impact velocity 6.19 km/s. (a) Just before impact Fig. 5. Fragments and particles collected from the test chamber. (b) Maximum swing angle at 130.6 ms after obtaining Fig. 7(a) Fig. 8. Pendulum motion of aluminum targets (4.14 km/s). (a) Just before impact Fig. 9. Photograph of ejecta taken by an ultra-high-speed video camera, 5 μs after impact; impact velocity 4.14 km/s. Table 2. Measured maximum angle of pendulum swing and efficiency of momentum transfer. (b) Maximum swing angle at 147.4 ms after obtaining Fig. 6(a) Fig. 6. Pendulum motion of aluminum targets (5.25 km/s). Impact velocity, km/s Measured maximum swing angle of target, degrees Estimated maximum swing angle of target, degrees Efficiency of momentum transfer, 3.18 10.4 10.7 0.25 4.14 12.9 13.2 0.22 5.06 14.5 14.7 0.34 5.25 26.6 26.9 0.54 5.29 17.9 18.2 0.36 6.19 23.6 23.9 0.54 7.17 23.7 24.0 0.64 Fig. 7. Photograph of ejecta taken by an ultra-high-speed video camera, 3.75 μs after impact; impact velocity 5.25 km/s. Pr_76

M. NISHIDA et al.: Investigation of Angular Momentum Associated with Hypervelocity Space Debris Impacts in the Low Earth Orbit Fig. 10. Effects of impact velocity on the efficiency of momentum transfer. Impact velocity, km/s Table 3. Target mass before and after impact. Target mass before impact, g Target mass after impact, g Mass loss, mg 3.18 71.1182 71.1180 0.2 4.14 70.6320 70.6325 0.5 5.06 71.0822 71.0809 1.3 5.25 70.6784 70.6755 2.9 5.29 70.4731 70.4718 1.3 6.19 71.7641 71.7615 2.6 7.17 70.6389 70.6330 5.9 the impact velocities in km/sec. A value of 600 rotates typical rocket bodies (with diameters approximately 2.6 m wide and 5 m long) at about 1 degree per second when a 1- mm-sized aluminum sphere comes into contact at an impact velocity of 14 km/s. This is the maximum collision velocity in the LEO. Although η was less than 1.0 at an impact velocity of 7 km/s, the value clearly increases with increasing impact velocity. We cannot distinguish whether increases linearly or exponentially considering the available data only. If it increases exponentially, it may reach 600 at 14 km/s. To explore this possibility, we need to conduct further experiments with impact velocities greater than 8 km/s. Even does not reach 600, clarifying the exact value of from 8 km/s to 14 km/s leads the important understanding about what is happening in the space environment. Some part of the rotations of the rocket bodies may attribute to the collision of small space debris. Table 4. Crater depth and diameter after impact experiments. Impact velocity, km/s Crater depth, mm Crater diameter, mm Crater depth/diameter 3.18 1.49 2.57 0.58 4.14 1.83 3.43 0.53 5.06 1.89 3.28 0.57 5.25 2.14 3.76 0.57 5.29 2.08 3.61 0.57 6.19 2.28 3.96 0.58 7.17 2.68 4.20 0.64 Fig. 11. Effects of weight loss on the efficiency of momentum transfer. potential energy of the target. An averaged energy loss in the far right column of Table 1 was calculated with the consideration of these parameters. Approximately 3.37 10 6 J of energy per angular displacement of one degree was consumed by friction during the pendulum motion. The estimated maximum swing angle values in Table 2 were modified by this value. The efficiency of momentum transfer,, was calculated from Eq. (3) with the impact velocity, the maximum angle of pendulum swing (listed in Table 2), and the size and mass of aluminum targets. Figure 10 shows the values along with Table 3 shows the target mass measured before and after the impact. While the loss of mass was not clearly related to the impact velocity, there was a clear correlation with the efficiency of momentum transfer,, as shown in Fig. 11. When the impact velocity was 7.17 km/s, the mass loss associated with the target was very large. When the impact velocity was 4.14 km/s, the target mass after impact was greater than that before impact. It is highly possible that a part of projectile was embedded in the bottom of the crater. Finally, Table 4 shows the crater size on the target surface after impact tests were conducted. Since the crater size was very small, the crater did not affect the moment of inertia of the aluminum alloy target. The ratio of crater depth to crater diameter is calculated in Table 4. Other than the results for impact velocities of 4.14 km/s and 7.17 km/s, this ratio was in the range of 0.57 0.58. The crater depth/diameter ratio at an impact velocity of 4.14 km/s was small, which corresponds to the formation of a shallow crater. It is highly possible that a part of projectile was embedded in the bottom of crater. When the impact velocity was 7.17 km/s, the increase of crater depth was larger than that of the crater diameter; as a result, the crater depth/diameter ratio was large. It seems that the mass loss associated with the target was very high along with a large amount of total ejecta. The crater bottom was markedly uneven. The crater feature at an impact velocity of 7.17 km/s was drastically different from the results associated with lower Pr_77

Trans. JSASS Aerospace Tech. Japan Vol. 14, No. ists30 (2016) impact velocities. The hypervelocity impacts that were at a speed greater than 8 km/s have the potential to result in significant mass loss and a high efficiency of momentum transfer. We need to conduct further experiments with velocities over 8 km/s to gain further insights, and we plan to carry out some hypervelocity-impact experiments at an impact velocity of 10 km/s at the University of Dayton Research Institute. 5. Conclusion We measured the momentum associated with an aluminum target when it came into contact with a projectile traveling at hypervelocities ranging from 5 to 7 km/s. The efficiency of momentum transfer,, which represents extra momentum caused by the phenomena of hypervelocity impacts, was estimated using the maximum angle of the pendulum swing. We confirmed that increased with increasing impact velocities up to a value of approximately 0.6 at 7 km/s. When is 600, typical rocket bodies rotated at about 1 degree per second when 1-mm-sized aluminum spheres collided with them at impact velocities of 14 km/s. This is considered as a typical collision velocity in the LEO. Although the value confirmed in this study was less than 1.0 at 7 km/s, this value clearly increased with increasing impact velocity. However, we cannot distinguish whether increases linearly or exponentially with the data from this study only. Further experiments with greater impact velocities must be conducted to explore the behaviors of around impact velocities of 14 km/s. Combining the value at 14 km/s with the space debris environment model, we can determine what portion of rocket bodies in the LEO are rotating, and with what rotational ratio. This information is considered to be the most important factor for the development of realistic ADR systems and greatly contributes to finding an effective solution to resolve the problem of space debris in the future. Acknowledgments The authors are greatly indebted to nac Image Technology, Mr. Hiroyasu Sasaki, Mr. Kensuke Kobori, and Mr. Kota Sekioka, for their help in taking images using high-speed cameras. This study was supported by ISAS, JAXA as a collaborative program with the Space Plasma Laboratory (the Hypervelocity Impact Facility). References 1) Liou, J. C.: An Update on LEO Environment Remediation with Active Debris Removal, Orbital Debris Quarterly News, 15 (2011), pp. 4-6. 2) Kurosaki, H., Yanagisawa, T. and Nakajima, A.: Observation of Light Curves of Space Objects, Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, (2009), Ed.: S. Ryan, p.e80. 3) Yanagisawa, T. and Kurosaki, H.: Shape and Motion Estimate of LEO Debris Using Light Curves, Advances in Space Research, 50 (2012), pp. 136 145. 4) Nysmith, C. R. and Denardo, B. P.: Experimental Investigation of the Momentum Transfer Associated with Impact into Thin Aluminium Targets, NASA-TN-D-5492, 1969. 5) Yanagisawa, M., Eluszkiewicz, J. and Ahrens, T.J.: Angular Momentum Transfer in Low Velocity Oblique Impacts: Implications for Asteroids, Icarus, 94 (1991), pp. 272-282. 6) Yanagisawa, M., Hasegawa, S. and Shirogane, N.: Momentum and Angular Momentum Transfer in Oblique Impacts: Implications for Asteroid Rotations, Icarus, 123 (1996), pp. 192-206. 7) Yanagisawa, M. and Hasegawa, S.: Angular Momentum Transfer in Oblique Impacts: Implications for 1989ML, Earth Planets Space, 51 (1999), pp. 1163-1171. 8) Yanagisawa, M. and Hasegawa, S.: Momentum Transfer in Oblique Impacts: Implications for Asteroid Rotations, Icarus, 146 (2000), pp. 270-288. 9) Shirono, S., Tada, M., Nakamura, A. M., Kadono, T., Rivkin, A. and Fujiwara, A.: Efficiency of Linear and Angular Momentum Transfer in Oblique Impact, Planetary and Space Science, 41 (1993), pp. 687-692. 10) Walker, J. D., Chocron, S., Durda, D. D., Grosch, D.J., Derek N. M., Richardson, C. and Asphaug, E.: Momentum Enhancement from Aluminum Striking Granite and the Scale Size Effect, International Journal of Impact Engineering, 56 (2013), pp. 12 18. 11) Walker, J. D. and Chocron, S.: Damage Modeling, Scaling and Momentum Enhancement for Asteroid and Comet Nucleus Deflection, Procedia Engineering, 103 (2015), pp. 636-641. 12) Hoerth, T., Schafer, F., Hupfer, J., Millon, O. and Wickert, M.: Momentum Transfer in Hypervelocity Impact Experiments on Rock Targets, Procedia Engineering, 103 (2015) pp. 197-204. 13) Stickle, A., Atchison, J., Barnouin, O., Cheng, A., Crawford, D., Ernst, C., Fletcher, Z. and Rivkin, A.: Modeling Momentum Transfer from Kinetic Impacts: Implications for Redirecting Asteroids, Procedia Engineering, 103 (2015), pp. 577-584. 14) Kage, S., Uenishi, S., Tanka, M., Koura, T. and Akahoshi, Y.: Development of Equipment to Estimate Momentum Shift in NEO Orbit Change by a Spacecraft Impact, Procedia Engineering, 103 (2015), pp. 273-278. Pr_78