Generating two-line elements (TLE) of artificial space objects from optical observations: Preliminary results Abdul Rachman and Tiar Dani Citation: AIP Conference Proceedings 1677, 050013 (2015); doi: 10.1063/1.4930674 View online: http://dx.doi.org/10.1063/1.4930674 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1677?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Instrumentation development for space debris optical observation system in Indonesia: Preliminary results AIP Conf. Proc. 1677, 050016 (2015); 10.1063/1.4930677 Liquid film thickness measurement by two-line TDLAS AIP Conf. Proc. 1592, 232 (2014); 10.1063/1.4872109 Is HD 147787 a double‐lined binary with two pulsating components? Preliminary results from a spectroscopic multi‐site campaign AIP Conf. Proc. 1170, 483 (2009); 10.1063/1.3246549 Two‐line, hands‐free telephone system J. Acoust. Soc. Am. 95, 1702 (1994); 10.1121/1.408532 A ‘‘two‐line’’ derivation of the relativistic longitudinal Doppler formula Am. J. Phys. 58, 187 (1990); 10.1119/1.16182
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Generating Two-Line Elements (TLE) of Artificial Space Objects from Optical Observations: Preliminary Results Abdul Rachmana) and Tiar Dani Space Science Center of Indonesian National Institute of Aeronautics and Space (LAPAN), Jl. Djundjunan 133, Bandung 40173, Indonesia a)
[email protected]
Abstract. Two-line elements (TLE) of an artificial space object can be generated from optical observations with modest instruments. In this preliminary study, ObsReduce was utilized for astrometric analysis to produce positional observations in IOD (Interactive Orbit Determination) format and ELFIND to generate the expected TLE. It turned out that analysis of a single image captured with a point-and-shoot camera in 16 seconds exposure time in a cloudy sky was sufficient to produce a TLE of the International Space Station (ISS) with comparable results in semi-major axis, eccentricity, inclination, RAA Node, and true longitude.
INTRODUCTION Identities of artificial space objects and other information including their motion can be found in their two-line elements (TLE) data. The primary source of TLE is the Space-Track website maintained by United States Space Command (USSPACECOM). Unfortunately, not all of artificial space objects’ TLE data are available. This is related with the insufficiency of the currently operating space surveillance system to detect and catalog all of the objects and the inevitability of classified objects. Monitoring of artificial space objects especially nearly reentered ones is one of the main programs of LAPAN. The program utilizes data from Space-Track as the primary source and, sometimes, from amateur observation network for classified data. To increase data availability, a research using optical instruments is currently conducted in LAPAN [1]. Data obtained using telescope and digital camera [2] are analyzed astrometrically and photometrically [3] to generate the TLE of the observed objects and to further understand their orbital and physical characteristics. Optical observation using digital camera (with or without telescope) is only one type of optical observation. It belongs to the same group with photographic plate or film as opposed to visual observation in which the observer’s eye is involved in determining the direction of the satellite at a certain time [4]. With its capability to provide relatively high accuracy in wide field of view at low cost, optical observation using digital camera is a very reasonable choice today. This paper will describe how we generate TLE from optical observations using astrometry. After validating the results, we discuss how to improve the accuracy. We hope that this study (which is likely to be the first of its kind in Indonesia) will motivate further researches related to optical observations of artificial space objects.
DATA AND METHOD We used an image containing a streak of International Space Station (ISS) when it passed under the Orion constellation in the morning of Oct 10, 2013 as seen in Fig. 1. This figure is cropped from the original image taken with a focal length of 24mm (in 35mm film) equivalents to focal of view of about 84°. The image was taken by The 5th International Conference on Mathematics and Natural Sciences AIP Conf. Proc. 1677, 050013-1–050013-4; doi: 10.1063/1.4930674 © 2015 AIP Publishing LLC 978-0-7354-1324-5/$30.00
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Abdul Rachman from a location in Bandung (06°53'18'' S, 107°35'26" E, 770 m ASL) with a Samsung WB250F camera and a tripod. The camera was set up using ISO 800, f/4.2, and 16 seconds exposure time beginning at 04:14:46 WIB. We also used TLE data of ISS with epoch of Oct 9, 2013 at 20:47:41 UT obtained from Space-Track [5]. Two softwares namely ObsReduce 1.3 (available from www.satobs.org) and ELFIND 5 (available from http://satelliteorbitdetermination.com) were utilized.
FIGURE 1. A streak of ISS as it passed above Bandung under the Orion constellation in Oct 10, 2013 at around 04:15 WIB. The object moved from lower left to upper right was bright enough to remain visible among the surrounding clouds. The length of the streak is about 17°.
Figure 2 illustrates the flow chart of the method in this study. First, the image was analyzed using ObsReduce to obtain the coordinate of the object accurately in IOD (Interactive Orbit Determination) format [6]. A typical IOD line contains identity of the object and station, sky condition at the station, time of the observation, object's position in equatorial or horizontal coordinate, and information about optical characteristics such as visual magnitude and flash period. Each observation is represented by one line of code in IOD. Next, the IOD data was processed using ELFIND to compute a set of orbital elements matching the observations. ELFIND approximates an unknown orbit from two or three observations and presents the computed orbit parameters as a TLE. Finally, we validated the results by comparing visually the streak produced by our TLE, the streak produced by reference TLE from SpaceTrack, and the observed streak. For this purpose, we also compared each orbital element of our TLE and reference TLE. analyzing the image with ObsReduce
genera6ng TLE with ELFIND
valida6ng the results
FIGURE 2. Flow chart of the method used in this study.
In ObsReduce, we used two end points of the observed streak as object's positions with three reference stars (forming a triangle) for each point (Table 1). The required physical lengths on the image between one pair of stars and between each star and the object are obtained from the pixel coordinates of the object and the stars. TABLE 1. Positions of ISS and reference stars used in astrometric analysis. Obs 1 2
Object's position At start of exposure At end of exposure
Time (WIB) 04:14:46 04:15:02
Reference star 1 Bellatrix Alnitak
Reference star 2 SAO 113001 SAO 132321
Reference star 3 SAO 112958 SAO 132732
RESULTS From ObsReduce we obtained two lines of code in IOD format (Table 2). TABLE 2. Two lines of IOD data produced in this study. Obs 1 2
IOD 25544 98 067A 25544 98 067A
0001 T 20131009211446000 18 25 0523852+074606 37 S 0001 T 20131009211502000 18 25 0601574-045238 37 S
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From ELFIND we obtained our TLE of ISS, which is 1 25544U 0000000 13282.88543982 0.00000073 00000-0 50000-4 0 2 25544 51.2796 259.9139 0010281 320.7157 227.9064 15.50786162
05 08
The streak produced by our TLE was able to match the observed streak better than the reference TLE as can be seen in Fig. 3. In fact, visual inspection indicated that both our TLE and reference TLE give somewhat similar orbits to a first approximation (Fig. 4). Comparing each of the six classical orbital elements of both TLEs told us that four of them namely semi-major axis, inclination, eccentricity, and RAA node are relatively the same (Table 3). In addition, even though the true anomalies and argument of perigees differ by more than 6°, the true longitudes (the summation of RAA node, argument of perigee, and true anomaly) differ less than 0.08°. An attention should be given to eccentricity value in this table. Even though the ratio of the two values is nearly 4, the value of both eccentricities are very small (less than 0.01). Therefore, the two values can be considered similar.
(a)
(b)
FIGURE 3. Comparison between the observed streak with referenced stars marked for each point of observations located at the end points of the streak (a) and the streak produced by TLE generated in this study and reference TLE (b).
(a)
(b)
FIGURE 4. Comparison between orbits produced by TLE generated in this study and reference TLE in 3D (a) and 2D (b). TABLE 3. Classical orbital elements (COE) extracted directly from TLE generated in this study and reference TLE at the beginning of the exposure time on Oct 10, 2013 at 04:14:46 WIB. COE Semi-major axis Inclination Eccentricity RAA node Argument of perigee True anomaly
TLE generated in this study 6798.8534 km 51.2989° 0.0000268 259.9216° 120.2239° 67.3721°
Reference TLE 6802.5695 km 51.6694° 0.0009235 259.9795° 126.4520° 61.1577°
Difference 3.7161 km 0.3705° 0.0009 0.0579° 6.2281° 6.2144°
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DISCUSSION The relatively accurate result of this study can be obtained due to unique characteristic of ISS. First, its high brightness which, according to Heavens-Above, can reach less than -3 allowed us to easily locate the two end points of its streak despite the surrounding clouds. Currently, ISS is the only artificial object with magnitude less than 0 while most of artificial objects have magnitude greater than 1. Second, the orbit of ISS is nearly circular with eccentricity about 0.0003. Typically, ELFIND is sufficient to find inclination, RAA node, and true longitude with only two observations if the orbit is nearly circular [7] which is consistent with our result. Using more than two observations will allow comparable results in all six classical elements. This can be conducted in two ways. First, ELFIND is used to produce an initial TLE using two observations and using the other set of two observations to refine the initial TLE. Relatively long exposure time of about 15 s is considered enough. Second, ELFIND is used to produce a TLE using three observations in which the orbit calculated will exactly fits the data. Being that strict, this technique should only be used carefully. Unless the observations are very close to the exact orbit, wild values for eccentricity and mean motion will result and the program may fail altogether if the three observations describe an impossible orbit [7]. To obtain the three observations, two streaks separated by less than 2 s are considered necessary. Each streak should be taken with short exposure time of less than 2 s. Short exposure time observations cannot be accomplished using image with wide focal of views (like the image used in this research). A typical DSLR camera (rather than a point-and-shoot camera) with long focal length e.g. 200mm placed on top of a tracking mount is preferred. Shorter exposure time (much less than 1 seconds) can only be conducted with a telescope. Small focal of view will allow dimmer objects to be captured and will be able to give a more homogeneous sky background which are useful in the subsequent analysis. A system which combines a Nikon 35mm lens with The Imaging Source DMK 41AU02.AS will provide an approximately 12° focal of view and is capable to detect a satellite with a magnitude up to 6.27 in 9.71 seconds exposure time [8].
CONCLUSION Reentry of artificial objects monitoring program in LAPAN is hindered by the incompleteness of the available TLE data from the internet. A research is currently conducted to generate the TLE of the observed objects using optical observations and astrometry. Preliminary results shows that analysis of a single image captured with modest instruments such as point-and-shoot camera and a tripod was sufficient to produce a TLE of the International Space Station (ISS) with a comparable result in semi-major axis, eccentricity, inclination, RAA Node, and true longitude. The high brightness of ISS and its nearly circular orbit were the primary factors in achieving the relatively accurate result of the study. More accurate results can be obtained by using more observations in two ways. First, by producing an initial TLE using two observations and using the other set of two observations to refine the initial TLE. Second, by producing a TLE using three observations in which the orbit calculated will exactly fits the data. The first technique is suitable for relatively long exposure time observations such as 15 seconds. On the other hand, the second technique is suitable for small exposure time observations of less than 2 seconds. A DSLR camera on tracking mount or a telescope is preferred for this technique.
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