Observations and data reduction
CMOS - Sigma 0.135 m Observations
BW3 was observed on two nights (2022-11-12 UT and 2022-11-13 UT) from Tucson, Arizona, USA (Lat. 32.3740, Long. -111.0168) using a ZWO432 CMOS sensor attached to a Sigma 135 mm f/1.8 lens. The weather was photometric on the 12th and high cirrus on the 13th; therefore only the data from the 12th are reported. The data were collected by pointing the instrument at a star along the predicted track of the satellite. To avoid saturation, exposure times for BW3 were kept short (16 milliseconds), which created an additional challenge of insufficient signal-to-noise ratio (SNR) on background stars for photometric calibration. Five 15-second sidereal-tracked images of the same field were obtained before and after the satellite pass (10 images total) for photometric calibration.
The linear photometric correction used to convert from instrumental magnitude to GAIA G magnitude was calculated by using all solar type stars identified in the set of images after iterative sigma clipping, weighted by the individual flux measurement uncertainties (i.e., reciprocal of SNR). Solar-type stars are identified using the GAIA DR2 [1], and when multiple measurements of the same star are found across multiple images, a median flux and SNR is used in the fit. The RMS uncertainty quoted was calculated as the root-mean-squared error between the post-correction measured magnitudes of all solar-type stars in the images (no sigma clipping) and their published GAIA DR2 magnitudes. The Johnson V magnitudes were then converted from the GAIA G magnitudes [2].
Chakana, DDOTI, and Oukaïmeden Observations
Observations of BW3 were performed on two nights, 2022-11-09 UT and 2022-11-10 UT using the Chakana 0.6m telescope, located at the Ckoirama Observatory [3] in northern Chile (Lat: -24.089, Lon: -69.931). Observations used the Sloan g’ filter and used a 2x2 binning technique to reduce the CCD readout dead-time and increase the SNR of background stars, thereby improving the accuracy of the differential magnitude measurements of the satellite trail. The observing strategy used the standard ‘wait and catch’ technique while tracking in sidereel, where the telescope was positioned at the predicted RA and DEC derived from a LEO satellite ephemeris code[2] and the exposure began a few seconds before BW3 reached the predicted coordinates.
Observations of BW3 were also conducted on 2022 November 12, 14, 15, 18, 19, 20, 21, 22, and 23 UT with the Deca-Degree Optical Transient Imager (DDOTI) wide-field imager [4] at the Observatorio Astronómico Nacional on the Sierra de San Pedro Mártir, Baja California, Mexico (Lat. 31.0455, Long. -115.4658). DDOTI has six 28 cm telescopes on a common mount. Each telescope is equipped with an unfiltered 6k × 6k CCD, which gives a field of 3.4 × 3.4 degrees and a pixel scale of about 2 arcsec pixel-1. For the observations presented here, two of the telescopes were out of service for maintenance, and so the total field was about 7 × 7 degrees.
Further observations of BW3 were conducted on 2022 November 16 and 17 UT with a Takahashi telescope, Oukaïmeden Morocco (Lat. 31.2064, Long. -7.866). The observations used a CMOS camera and performed both two second exposures (2022-11-16) and one second exposures (2022-11-17). Sidereal tracking was used and the data allows for the extraction of the reflective brightness of BW3 and estimate the accuracy of the TLE used to predict the sky position.
The reduction, astrometric calibration, satellite trail detection and its analysis for the observations from Chakana, DDOTI, and Oukaïmeden were performed with the CLEOSat pipeline, a custom and open-source end-to-end Python pipeline for the processing and analysis of satellite trail observations [8].
The raw Flexible Image Transport System (FITS) image files were processed with ccdproc[3]. This includes subtracting the dark frame from each image to remove the instrumental signature as well as dividing by the average flat field to correct for non-uniform sensitivity across the chip.
The reduced FITS-images were then calibrated to be able to map the positions of sources on the detector to their celestial coordinates on the sky. The positions of sources on the detector were extracted using photutils[4]. For reference, a catalogue of stellar sources, with known and precise positions on the sky, was compiled from the GAIA DR3 [9,10] catalogue via astroquery [11]. The required transformation, i.e., the scale, rotation, and translation to match both coordinate systems, was then determined by applying a phase correlation algorithm to the distances and angles calculated between each source from both catalogues to determine the location of the peak in the cross-correlation spectrum yielding the correction to the World Coordinate System (WCS) information in the FITS-header.
To identify the satellite trail(s) in the observations, first a sharpen filter was applied to the image to increase contrast and facilitate detection of fainter trails. Then, a source detection algorithm was used to create a segmentation map containing all sources, including trails, 1-sigma above the background in the sharpened image. The resulting segments were filtered, retaining only the most eccentric segments (e>0.99).
To identify and characterise the satellite trail(s), we followed the approach for line segment detection using the Hough transform [12]. In this approach, a voting procedure is performed that associates a set of lines in the x-y image space to a pair of values in the Θ-⍴ plane, also referred to as Hough space, and given a voting angle in the image space, this voting distribution is analysed. Regarding the corresponding column in Hough space, voting along the distance axis is considered as being a random variable, and voting values in cells of the discrete Hough space are considered as forming a probability distribution. The statistical characteristics of this probability distribution are used to fit a quadratic polynomial curve and a linear curve whose coefficients yielded the direction, length, and width of a line segment as well as the midpoint of a line segment, respectively.
The magnitude of the trail was estimated using aperture photometry by comparing the instrumental magnitude of the trail to the well-known magnitudes of a set of comparison stars in the image [13]. To estimate the optimum aperture at which most of the light from the source is captured, while minimising contamination from the sky background and unrelated sources, first, the SNR for different aperture sizes was measured. The aperture radius at which the S/N is maximised was then multiplied by a factor to allow for any error in centroiding and was used as the new aperture radius for the image. Additionally, the magnitude correction required to compensate for the flux lost due to a finite aperture size was determined by calculating the ratio of fluxes in the optimum aperture and a larger standard aperture. The average value and standard deviation of the resulting distribution of magnitude corrections were then taken as the aperture correction and applied to all sources measured with standard aperture size during aperture photometry.
Steward Observatory Observations
Figure 2 shows the apparent brightness of BW3 after deployment as observed by the Steward Observatory SSA astrograph on nine different passes on nine different nights in November and December 2022. The Steward Observatory SSA astrograph is a unique system specifically created to observe Earth-orbiting satellites and space debris [5]. The system resides in a portable trailer-mounted enclosure which was stationed at the Mt. Lemmon SkyCenter near Tucson, Arizona (Lat. 32.4420, Long. -110.7893), for the reported observations.
The astrograph tracked BW3 as it passed overhead and continually recorded images at a rate of approximately one image every five seconds. All observations utilised a Johnson-Cousins V filter. On the first two observed passes (2022-11-11 UT and 2022-11-12 UT), BW3 saturated the detector and the brightest measurements from these two passes should be considered an upper bound on the visual magnitude (i.e., the satellite was at least this bright). Subsequent observations utilised a shorter exposure time and were defocused to avoid saturation.
We processed the images and produced calibrated photometric measurements with a suite of software created for The Steward Observatory LEO Satellite Photometric Survey [14]. When tracking the satellite, the background stars are severely streaked and extracting astrometric or photometric references is all but impossible. Instead, we used other sidereal observations from the same night to create an airmass extinction model and determine the photometric zero point for each observation of the tracked satellite. Figure 2 shows the correlation of apparent brightness with on-sky position and that BW3 typically appears brighter than 4th magnitude across most of the sky.
Ōtehīwai Mt John observations
Eight passes of BW3 were observed on 2022 December 14 through 17 with the 1.8 m MOA-II telescope at the University of Canterbury’s Mt John Observatory on Ōtehīwai Mt John, Takapō, Aotearoa New Zealand (Lat. -43.9857, Long. 170.4651). Images were acquired with sidereal tracking with MOA-cam3 [15] (1.32° × 1.65° FOV, 0.57 “/px) in the broadband MOA-R filter (632-860 nm) [15]. Each pointing was selected based on that day’s TLE from Celestrak via Heavens-Above[5], with the shutter opening timed so that the satellite was predicted to cross the camera’s 2.2 deg2 field of view at the midpoint of the exposure. Conditions were often cloudy and windy for the entire run, with some stretches of photometric conditions with seeing of 2-3” (Table 1).
Reduction of instrumental signatures for dark current and flatfielding, and photometric calibration of field stars to SkyMapper Southern Sky Survey DR1.1 [16] (Vizier: CDS/II/358/smss) to establish zeropoints was made with Pouākai[6], with astrometric calibration via astrometry.net [17].
Images acquired back-to-back were subtracted. Circular aperture photometry was applied at 0.005 s intervals along the TLE-predicted satellite trail. As the TLE did not match, we made a Gaussian fit to the normalised counts to spatially offset the TLE onto the trail centre. MOA-R is a substantially wider bandpass filter than Johnson V, but assuming BW3 is a Solar-neutral reflector, we applied an image-specific offset to the MOA-R zeropoints; thereby transforming the MOA-R photometry to the Johnson-V magnitudes reported here.
Video observations from Leiden
Video observations on BW3 were conducted from Leiden, the Netherlands (Lat. 52.1540, Long. 4.4908), on the evenings of September 21, 24 and 29, and on December 8, 2022. These observations yielded both photometry [18], and astrometry (this study).
The camera used is a sensitive WATEC 902H2 Supreme Low Light Level CCTV camera, equipped with a Pentax 1.2/50 mm lens and filming at 25 frames/second. This camera/lens combination has a 5.5 x 7.4 degree FOV at a scale of 35.4” pixel-1: the typical astrometric accuracy is about half of that.
The PAL signal output from the camera was fed into a GPSBoxsprite-2 GPS time-inserter which imprinted each video frame with a 1PPS time signal, allowing timekeeping at the millisecond level. The signal was next digitised by an EZcap dongle and recorded in AAV format on a laptop using OccuRec[7]. The video frames were astrometrically solved on a frame-by-frame basis with TANGRA software[8], using the UCAC-4 star catalogue as a reference.
From n=2086 astrometric observations obtained on four separate nights, an average angular difference between the TLE-predicted positions and observed astrometric positions of 3.5 arcmin was determined.
Visual observations
Visual observations were made from 2022-10-03 UT and 2023-01-16 UT from sites near Tulsa, Oklahoma, USA. The observer has 20+ years of tracking satellites, has seen 8,000+ unique objects, reported 25,000+ passes and thousands of brightness estimates of satellites and variable stars[9]. In some cases, hand-held binoculars were used. Data was gathered on 23 occasions [6]. Pass predictions were obtained for the observer's two sites (Lat. +36.139 Long. -95.983 and Lat. +35.831 Long. -96.141) from Heavens-above.com[10]. At a minimum, the location, expected time of observation, and reliable limiting brightness must be known, bearing in mind that moving objects may appear visually dimmer than predicted. Observable passes were selected, with low elevation passes, ones in deep twilight, or at unfavourable phase angles were discarded.
Suitable comparison stars were chosen to provide brightness measurements. A newly launched satellite does not always match the predictions, especially in brightness and often in timing (see TLE accuracy section). Comparison stars to estimate magnitudes were suitably bright for the stage of twilight during observations, and alternate stars were chosen in case the pass was off track or early/late. All comparison star magnitudes used were obtained from the extended Hipparcos catalogue [19].
The object was observed as it passed the stars selected, so that direct comparison could be made. Any significant brightness variations, such as flashing or flaring, were also recorded at that time. Before deployment of the phased array antenna on 2022-11-10 UT, the visual magnitude of BW3 was 6.1 ± 0.2, versus 2.4 ± 0.2 after deployment of the array. The range corrected magnitudes were calculated using -5 log(range/500 km) and are shown in Figure 1 and is the brightness of the object when viewed with a range equal to the orbital height (i.e. at local zenith with airmass=1) at 500 km and fully lit.
Launch Vehicle Adapter Brightness Measurement
On the evening of 2022-11-10 UT coordinated simultaneous observations of BW3 were attempted using both the Chakana 0.6 m telescope, Ckoirama, Antofagasta, Chile (Lat: -24.089, Lon: -69.931), and the 0.9 m telescope at Cerro Tololo Interamerican Observatory (CTIO), Chile (Lat: -30.165, Lon: 289.185 E). Due to the low elevation (< 25 degree) of the apex of the forecasted sky-track observed from CTIO, only a single position for which both telescopes were able to point to was selected to perform a simultaneous observation, with the exposures starting at 23:54:56.70 (UT) and 23:54:55.22 (UT) for the two telescopes, respectively. The images are given in Figure 3 and show that from Ckoirama’s view point, only a single track is detected, while from CTIO two tracks are seen. This provides a rare opportunity to triangulate the position of the BW3’s LVA in relation to BW3. The sky-projected angular separation in the CTIO image is measured to be 26.8 arcsec. When combined with a range of 1201 km, it provides a sky-projected separation of 78.1 ± 8.8 m. Making the assumption that the sky-projected separation lies along the line of sight from the Chakana telescope (hence a single track detected), we calculate the geocentric coordinates () of both BW3 and the LVA, where the difference is found to be -55.95 m , -52.30 m , -15.3 m . This value is then converted to longitude, latitude, and altitude, where we find that at 23:55:00 (UT) the LVA position is Lat: -24.041053, Lon: -78.672693, Alt: 524.31 km whilst for BW3 Lat: -24.041074, Lon: -78.672101, Alt: 524.27 km. As a check, we calculate the RA and DEC from both Ckoirama and CTIO for the LVA and compare these with the RA and DEC of BW3. We find that the difference in RA and DEC for Ckoirama is zero, as expected as the LVA and BW3 follow the same track, while for CTIO the difference equates to 26.8 arcsec (Δ RA = 24.8 arcsec, Δ Dec = 10.2 arcsec). Additional observations from Ckoirama, one prior and three afterwards, showed that the last three images in the sequence contained two trails (Figure 3, lower panels). The sky-projected angular separation is seen to be increasing: an angular separation of 2.2 ± 1.5 arcsec at 23:56:00 (UT); then by 23:57:00 (UT), an angular separation of 8.2 ± 2.9 arcsec is observed; while by 23:58:00 (UT), this has increased to 14.8 ± 3.8 arcsec. This translates to a sky-projected separation of 9 ± 3 m, 19 ± 4 m and 42 ± 6 m using the range between BW3 and Ckoirama of 920.31 km, 962.5 km and 1167.0 km, respectively, at the time of the observations. However, the first image (23:54:00 UT) shows a single track, indicating that the measured angular separation observed in the final three images is a combination of changing viewpoints, separation velocity, and angular rotation velocity. The first two images from the Chakana telescope are in the west (AZ: 252.2° and 268.9°), while the CTIO observation and subsequent Chakana observations which clearly show the two trails are towards the north and north-west (AZ: 311.2°, 327.0°, and 349.0°). Without a second simultaneous observation, it is not possible to calculate the orbital velocity of the LVA, and therefore determine how much of the observed sky-projected angular separation is due to a changing viewpoint.
TLE accuracy
The coordinates (ɑ, δ) of the midpoint of the observed satellite trails of BW3 were obtained using the LEOSat pipeline. The pipeline uses observations and TLEs to detect and analyse satellite trails. Given the TLE, the pipeline provides magnitudes and coordinates of the trails by performing astrometric and photometric calibrations and so measures the observed trail length. In addition the pipeline uses the pyorbital package[11] to perform orbital calculations (utilising the SGP4 simplified perturbation model) to determine the RA and DEC of a satellite for given times. Measurements of the TLE spatial and temporal accuracy require datasets that contain at least one end point of the satellite trail. Satellite trails are point sources spread over a specific length due to the satellite’s angular velocity. For datasets where there are no endpoints (i.e. small FoV detectors), it is only possible to measure the spatial accuracy of the TLE, due to the fact that it is not possible to precisely know the satellite’s position as a function of time (i.e. the point source could be at any point along the trail for any given time in the exposure timestamp).
To select coordinates along the sky-track of BW3 on each pass, the BW3 TLEs used to predict BW3 orbital ephemerides and therefore the sky position was used to provide a predicted track in the image. This provides an opportunity to measure the accuracy of the TLEs of BW3 for the observations in which at least one end point of the trail is visible. This provides a boundary condition when integrating the angular velocity over the trail length to obtain the position as a function of time of a moving source. The total error (σtle) is the quadrature sum of the spatial (σr) and temporal errors (σt),
σtle is calculated using the difference between the RA and DEC predicted by the TLE at the midpoint of the observation (ɑtle, δtle) and the RA and DEC (ɑobs, δobs) of BW3 in the image, when two endpoints are observed. When only one end of the trail is visible, the RA and DEC of this point is used instead. σr is simply the length of the line of intersection between (ɑobs, δobs) and (ɑtle, δtle), which lies perpendicular to both the observed and extrapolated TLE-predicted trails. σt is then found using Eq. 1. This process allows the sign of σt to dictate whether the predicted TLE position leads (positive) or lags behind (negative) the satellite. The results show that while below an elevation of 20°, |σt| = 2.38 ± 0.42 s where the quoted uncertainty is the 1-σ distribution. While when above 20° elevation, this reduces to |σt| = 0.18 ± 0.06 s.
To determine the confidence of the large error measured from the Takahashi data, all known instrumental uncertainties were examined. To examine the how the propagation of the uncertainties in the orbital equations used by pyorbital, some of the data was compared to TLE predictions using skyfield[12]. The predicted positions between the two models differ on average by 30 arcsec, which alone can not explain the large 24 ± 6 arcmin difference between the measured BW3 position and that predicted by the TLE. The next set of errors can come from the accuracy of the telescope location. A set of models were created with random changes in the location of the telescope by up to 150 m and the resultant changes in the predicted sky position from the TLE were recorded and found to be on average ± 1.2 arcmin. The third possible source of uncertainty is from the instrument timing uncertainty. For professional telescopes such the DDOTI this is < 100 ms. If a conservative error budget of 1 s is assumed for the Takahashi data, it creates a positional uncertainty of ± 10.7 arcmin. Taking these additional errors and applying them to the Takahashi data measurements gives a TLE-measurement accuracy of 24 ± 11 arcmin, meaning that using the worst case instrumental, telescope position, and orbital equation uncertainties, a minimum TLE accuracy is found to be > 13 arcmin.
The TLE errors are shown in Figure 4 and hint that the timing errors are dependent on elevation. For sensitive detectors such as those of the Simonyi Survey Telescope's camera of Vera C. Rubin Observatory, having low-accuracy ephemeris predictions of bright (V<7) artificial satellites will be a major concern. It will prevent the avoidance of satellites which are too bright for minimisation of the impacts of electronic ghosts and non-linear image artefacts by correction to at least the background level [20].
Another source of error of the TLE accuracy is the amount of time passed since the TLE epoch. As the TLE provides position and velocity vectors, for a single point in time (the TLE epoch) the accuracy will depend on how far forward in time the prediction is. Therefore by comparing the accuracy as a function of time elapsed since the different TLE epochs and the time of the observations we determine that the decay rate of the TLE accuracy is 1.1 ± 0.6 arcmin hr-1, when using all available data. However, when only the data collected from higher elevations (> 20°) is used a lower decay rate of 0.4 ± 0.2 arcmin hr-1 is found (see Figure 4).
[2] https://github.com/CLEOsat-group/satellite-tracking
[3] https://ccdproc.readthedocs.io/en/
[4] https://photutils.readthedocs.io/en/stable/
[5] https://www.heavens-above.com/
[6] https://github.com/CheerfulUser/Pouakai
[7] http://www.hristopavlov.net/OccuRec/OccuRec.html
[8] http://www.hristopavlov.net/Tangra3/
[10] https://www.heavens-above.com/
[11] https://github.com/pytroll/pyorbital
[12] https://pypi.org/project/skyfield/
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