ISTS 2004-r-10 Motion and Shape Determination of LEO Debris Using Optical Telescope

Transcription

1 ISTS 004-r-10 Motion and Shape Determination of LEO Debris Using Optical Telescope Toshifumi Yanagisawa, Atsushi Nakajima and Takeo Kimura Japan Aerospace Exploration Agency , Jindaiji-Higashi-machi, Chofu-shi, Tokyo 18-85, JAPAN ( tyanagi@chofu.jaxa.jp) Abstract We succeeded in determining a tri-axial ellipsoid model of one LEO debris, its rotational axis direction in the celestial sphere, a compositional parameter and its rotation period using only light curve data that was taken by an optical telescope. The brightness of the LEO debris was monitored for 6 days. The method of least squares is applied to determine these values. The derived axial ratios of the LEO debris is 100:18:15, the coordinates of the rotational axis direction in celestial sphere are R.A. = 314 degrees and Dec = 8 degrees and its rotation period is 43 seconds. These results show optical telescopes are sufficient to determine the shape and the motion of LEO debris. 1. Introductions Space debris may be a serious problem in the near future. In the low earth orbit (LEO) region, numbers of space debris exist. Many explosions of the fuel in rockets that create more space debris were observed. We should take steps to meet the situation for the development of human activity in the space as soon as possible. Japan Aerospace Exploration Agency is studying about three fields in space debris problem, observations, protections and mitigations. In the mitigation field, the system that captures space debris or damaged satellites and removes it from the orbit is considered [1-3]. In order to evaluate the system, the motion and the shape of existing space debris must be investigated. Radar observation is possible to investigate them effectively. However, such a radar observation facility takes a number of costs to be constructed Copyright 004 by the Japan Society for Aeronautical and Space Sciences and ISTS. All rights reserved. and maintained. Optical observations are also possible to do same things at less expense. Optical telescopes are not possible to observe direct shapes and motions of objects at a few thousand km altitude as radar observations are, but these values are assumed from the light curve data. In the observation field, we are developing an optical observation system that observes LEO satellites and debris using a 35cm telescope and a fast-readout CCD camera [4]. Fig. 1 shows our observation system. The telescope is mounted on a 3-axial mount that is able to track any type of orbits. The facility is able to measure the brightness of LEO objects 10 times in a second. Fig. shows the light curve data of cosmos08 rocket body that were taken by our observation facility. X and Y-axis show the observation time and the brightness of the target in analog-to-digital unit (ADU), respectively. From the figure, the object repeats the increase and the decrease of its brightness. This means that the object is rotating and has an elongated shape. Numbers of observations or multi-site observations reveal more detailed information. The tri-axial ellipsoidal model or more Fig. 1: The optical observation system.

2 Fig. : The light curve data of cosmos08r/b. Sophisticated shape models are possible and the rotational axis direction in the celestial sphere is determined. Further more, another rotation component except the principal axial rotation such as a precession may be detectable. We observed this LEO debris 6 days and derived its shape, the rotational axis direction and the rotation period. In this paper, we describe the observation details, how we analyze the observed data, the results and their interpretations. The observed data is analyzed almost automatically. Therefore, we are able to detect data of a number of targets if the weather condition is good. We are going to get such light curve data periodically, investigate the characteristic of the motion and the shape of LEO debris and contribute the construction of the future debris retrieval system. automatically is created for this study. We can monitor the brightness of the target, precisely. The details of the system are described at Nakajima et al [4]. After observation of a few targets, we found out one LEO debris that shows a periodical brightness change as shown in Fig.. That is cosmos 08 rocket body (International number is B) owned by USSR. Its apogee, perigee and inclination are 855km, 834km and 70 degrees, respectively. Then, we observed this target intensively to get its shape and motion related values previously described, two times on January 6 and 8, and one time on February 16, 17, 19 and Analysis of the observed data We assumed that 1) the shape of the target was a tri-axial ellipsoid, ) it is rotating around the shortest axis and 3) the rotation axis is fixed in the celestial sphere for the simplicity. Fig. 3 and Debris Observer. Observation details First, we searched for the target that shows a periodical brightness change. The orbital elements of bright LEO satellites and debris are provided at various web sites (for example, ). We used the orbital determination software, STK (satellite toll kit, ) manufactured by AGI to calculate the AER (azimuth, elevation and range) values and find out proper targets that are visible from our site. Our observation system shown in Fig1 can track a specified target almost automatically using its orbital element. It takes 10 images of the target per second. Software that finds out the target in images and measures its brightness Brightness 90 Fig. 3: Various geometries of debris and an observer Time Fig. 4: Corresponding light curve of the various geometries in Fig

3 show various geometries of debris and an observer, and their corresponding light curves. A tri-axial ellipsoidal model whose axis ratio is 6:3: is considered. Straight lines on debris show rotational axes. If an angle between the rotational axis and observer s line of sight is 0 degree, the observer detects constant brightness because the debris s cross section does not change. On the other hand, in case of 90 degrees, the amplitude of the brightness becomes a maximum. Equation (1) shows the amplitude (max brightness / min brightness) caused by geometries of debris and an observer. a b cos θ + c sin θ A =, a b c b a cos θ + c sin θ Here, a:b:c is the axial ratio of the ellipsoid and θ is an angle between the rotational axis and observer s line of sight. The amplitude is also affect by the phase angle that is between direction to the sun from debris and that to the site. As the phase angle becomes large, the real amplitude increases as Equation (). A real = ( 1+ Mα )A Here, M and α is a constant parameter and the phase angle, respectively. Equation () is empirically derived by Zappala et al.[5] who work on researches of asteroids. The constant parameter M differs with debris compositions. If a unit vector of the rotational axis direction and an observer s line of sight in the celestial sphere are described as (l, m, n) and (x, y, z), respectively and a is assumed to be 1, the real amplitude is described as Equation (3). c + ( b A real = (1 + Mα ) c (1 c )( lx + my + nz) c )( lx my nz) Unlike asteroid observations, debris is observable many times for various geometries and phase angles even in one pass. Fig. 5 and 6 show observed passes of cosmos 08 rocket body on January 6 and their corresponding light curves. The phase angle changes from 1.4 to degrees and the amplitude does from.1 to 3.1. The phase angle (1) () (3) Fig. 5: Two passes of cosmos 08 rocket body on January 6. Right side pass is observed at from 19:03:51 to 19:09:7(UT). Left side pass is at from 0:45:47 to 0:5:08(UT). (a) (b) Fig. 6: (a) and (b) show the light curves of the right and left side pass of Fig. 5, respectively. of right side pass in Fig. 5 is larger than the left. The corresponding light curve described in Fig. 6 (a) shows larger amplitude than Fig. 6 (b) that is assumed from Equation (). Unknown parameters

4 90 Dec R.A. Fig. 7: The error distribution of rotation axis direction in the celestial sphere. X and Y-axis describe Right Ascension and Declination of the celestial coordinates, respectively. The yellow circle on the graph shows the minimum point of the error that indicates (R.A.,Dec)=(314,8 ). are M, b, c, l, m and n (c b 1 and l + m + n = 1). x, y, and z are calculated from observed directions. The method of least squares is applied to derive these parameters using amplitudes, phase angles and observed directions of 30 data sets during 6 days observations. c The results and their interpretations Fig. 7 shows the error distribution of the rotational axis direction in the celestial sphere. X and Y-axis describe Right Ascension and Declination of the celestial coordinates, respectively. Errors of the blue region are high. The dark red region where the errors are low is plausible for the direction of rotational axis. The yellow circle on the graph shows the minimum point of the error. The coordinates of the circle is (R.A.,Dec)=(314,8 ). There is also low value regions of error around R.A=135. This is reasonable because opposite direction of the rotational axis also indicates minimum value of the error. Fig. 8 describes the error distribution of b and c values (value of a is assumed to be 1.). The plausible values of b and c are in the dark red region where errors are low. At minimum point indicated by a yellow circle on the graph the values b and c are 0.18 and 0.15, respectively. Therefore, the axial ratio of the ellipsoidal model is about 100:18:15. The parameter M described in Equation () was 0.03 deg -1 at those minimum error points. Zappala et al. found that the parameter is 0.03, and Fig. 8: The error distribution of b and c values (value of a is assumed to be 1.). At minimum point indicated by a yellow circle on the graph the values b and c are 0.18 and 0.15, respectively. deg -1 for the S-, C-, and M-type asteroid, respectively[5]. So, our derived value 0.03 is not strange value. We don t know what material shows the value 0.03 yet but we extracted a parameter that implies the composition of cosmos 08 rocket body. Rotation period of cosmos 08 rocket body was about 43 seconds. Our light curve observations using an optical telescope revealed the rough shape, the rotational axis direction, a parameter concerning the composition and the rotation period of cosmos 08 rocket body. At the altitude of cosmos 08 rocket body (about 1000km), it is impossible for ordinary telescopes to confirm shapes and motions of targets, directory. The system using adaptive optics may b

5 Figure 9: The light curve inversion model of asteroid 6489 Golevka (left) and its radar based model at the same geometry (right). enable to do that. Even such a system, geostationary target is not visible. Radar observations are required for such a work. However, such a radar observation facility takes a number of costs to be constructed and maintained. In Japan, there is one radar observation site for LEO debris, Kamisaibara Spaceguard Center, but it is designed for track many LEO debris simultaneously not for direct imaging [6]. Optical observation systems for this work are much cheaper. Multi site observations must get same result of this study using only one pass because a target is observed at various phase angles and geometries from many sites, simultaneously. In Fig. 6(a), spiky increases of brightness except the global change are visible periodically. That maybe caused some additional structure. This implies a simple tri-axial ellipsoid model is inadequate for cosmos 08 rocket body. Kaasalainen et al. developed more sophisticated techniques, the light curve inversion model, to estimate shapes and motions of asteroids using only light curve data [7]. Fig. 9 describes their light curve inversion model of asteroid 6489 Golevka (left) and its radar based model at the same geometry (right). Their light curve inversion model considerably reproduces original shapes rather than the tri-axial ellipsoid model. The model is also able to detect non-primal axis rotation like a precession. From only light curve data, we can do nearly same thing as radar observations can. We would like to develop our technique to theirs and derive more detail shapes and motions of LEO debris in the future. These techniques must contribute to the future debris retrieval system that captures space debris or damaged satellites and removes it from the orbit. 5. Conclusions We succeeded in determining a rough shape of one LEO debris, cosmos 08 rocket body, its rotational axis direction in the celestial sphere, a compositional parameter and its rotation period using light curve data that was taken by an optical telescope. Target s axial ratio of a simple tri-axial ellipsoidal model is 100:18:15. The celestial coordinates of the rotational axis direction are R.A.=314 degrees and Dec=8 degrees. The parameter concerning to its composition is 0.03 deg -1. The rotation period is about 43 seconds. All these values surprisingly come from only brightness changes of cosmos 08 rocket body. Figure 10 summarizes the derived values from this study. We showed optical observations and a modeling based on its observational data are sufficient to determine the shape and the motion of LEO debris.

6 And these techniques must contribute to the future debris retrieval system. References [1] S. Kibe, S. Kawamoto, Y.Okawa, F. Terui, S. Nishida, G. Gilardi, R&D of the Active Removal System for Post-Mission Space Systems IAC-03-IAA , 003 [] S. Kawamoto, S. Nishida, S Kibe, Research on a Space Debris Removal System NAL Research Progress , pp.84-87, 003 [3] Y. Ishige, S. Kawamoto, S. Kibe, Study on Electrodynamic Tether System for Space Debris Removal Operation, IAF-0-A.7.04, 00 [4] A. Nakajima, T. Yanagisawa, T. Kimura, T. Isobe, T. Tsuji, M. Yamamoto, T. Hoshino, M. Suzuki, H. Futami, Space Debris Observation by Ground-Based Optical Telescope, Proc. nd Int. Symp. Space Technology and Science, pp , 000 [5] V. Zappala, A. Cellino, A. M. Barucci, M. Fulhchignoni, D. F. Lupishko, Astron. Astrophys, vol.31, pp , 1990 [6] Y. Taromaru, K. Nonaka, T. Tajima, M. Sawabe, T. Yokota, S. Isobe, Overview of NASDA Orbital Analysis System and Bisei/Kamisaibara Space Guard Centers, Proc.3 rd Int. Symp. Space Technology and Science, pp , 003 [7] M. Kaasalainen, S. Mottola, M. Fulchignoni, Asteroid Models from Disk-integrated Data, Asteroid, The University of Arizona Press, pp