The Starlink satellites are shaped like flat panels. The flat sides face zenith and nadir during normal operations. Their brightness is determined by the product of the solar illumination on the downward facing side of the panel multiplied by the area of that side projected toward the observer on Earth. This geometry leads to a unique brightness function that is not shared by other satellites. For example, the observed brightness is very sensitive to the solar elevation angle. There are circumstances where sunlight only illuminates the upward facing side of the satellite rendering it invisible to Earth-based observers. A brightness model depending on the solar aspect and the observer aspect of the flat panel, in addition to the satellite distance, is described. Absolute brightness is the only free parameter of the model, and it is taken to be that at a distance of 1,000 km when the solar and observer factors are unity. This model has been successfully fitted to a set of observed magnitudes. The absolute visual magnitude of a Starlink satellite as determined from this fitting is 4.1 +/- 0.1. The model could be used to determine the absolute magnitude of the Starlink satellite known as Dark Sat which has a special low-albedo coating.
The mean of 430 visual magnitudes of VisorSats adjusted to a distance of 550-km (the operational altitude) is 5.92 +/-0.04. This is the characteristic brightness of these satellites when observed at zenith. VisorSats average 1.29 magnitudes fainter than the original-design Starlink satellites and, thus, they are 31% as bright.
The mean of 830 visual magnitudes adjusted to a distance of 550 km (the operational altitude) is 4.63 +/-0.02. The data on DarkSat, the low-albedo satellite, indicate that it is fainter than the others by 1.6 magnitudes or 78%. However, there is considerable uncertainty in this value due to the small number of observations. Some satellites were observed to flare by 10,000 times their normal brightness. These statistics can serve as a baseline for assessing the reduced brightness of the VisorSat design for future Starlink satellites.
A large dataset of visual magnitudes for all three designs of Starlink satellites is analyzed. Brightness phase functions are derived for the Original, VisorSat and Post-VisorSat models. Similarities and differences between the functions for these spacecraft are noted. A metric called the characteristic magnitude is defined as the average brightness of a satellite when seen overhead at the end of astronomical twilight. When the phase functions are evaluated according to this metric, the characteristic magnitudes are: Original, 4.7; VisorSat, 6.2; and Post-VisorSat, 5.5.
Magnitudes for the VisorSat and Original-design types were analyzed separately and by time. Mean values are compared with those from other large-scale photometric studies, and some signficant differences are noted. The illumination phase functions for Starlink satellites indicate strong forward scattering of sunlight. They are also time-dependent on a scale of months and years. These phase functions improve the predictability of satellite magnitudes. A Starlink Brightness Function tailored to the satellite shape also improves magnitude predictions. Brightness flares lasting a few seconds are c…
A model of the brightness of the visorsat Starlink spacecraft is presented based on published information on the engineering design and from analysis of 131 observations of individual visorsats in late 2020. Comments are offered on the implications of this model on the visibility of visorsat spacecraft across the sky. This is an updated and expanded version of analysis published in Research Notes of the AAS (2020). An additional section has been added in this version to consider observations made in June 2021 which indicate brighter visorsat magnitudes.
The mean visual magnitude of OneWeb satellites at the standard satellite distance of 1,000 km is 7.18 +/-0.03 . When this value is adjusted to the nominal 1,200 km altitude of a OneWeb satellite in orbit it corresponds to magnitude 7.58 which is an indication of the mean brightness at zenith. The OneWeb satellites are fainter than the original Starlink satellites at a common distance. Preliminary data on the new and dimmer VisorSat design for Starlink suggests that they are still brighter than OneWeb at the satellites' respective operational altitudes.
A model that combines celestial geometry and atmospheric physics is used to calculate the dimming of artificial satellites as they enter and exit the Earth's shadow. Refraction of sunlight by the terrestrial atmosphere can illuminate a satellite while it is inside the eclipse region determined from geometry alone. Meanwhile, refraction combines with atmospheric absorption to dim the satellites for tens of km outside of that region. Spacecraft brightness is reduced more in blue light than in red because absorption of sunlight is stronger at shorter wavelengths. Observations from the MMT-9 robot…
We present observations of 23 Starlink satellites in the $g'$ bandpass, obtained from the Dominion Astrophysical Observatory's Plaskett 1.8 metre telescope. The targets include a mixture of satellites with and without brightness mitigation measures (i.e., visors). At the time of the observations (16 July 2021), Starlink satellites were sunlight throughout the night, and even with strict elevation and azimuth limits, there were over 800 candidate Starlink arcs. The satellites altogether have a median absolute brightness (550 km) of $\overline{H}_g^{550} =5.3$ mag. Dividing the targets into thos…
Starlink is a low-Earth orbit (LEO) satellite constellation operated by Space Exploration Technologies Corp. (SpaceX) which aims to provide global satellite internet access. Thus far, most photometric observations of Starlink satellites have primarily been from citizen scientists' visual observations without using quantitative detectors. This paper aims to characterize Starlink satellites and investigate the impact of mega constellations on ground-based astronomy, considering both the observed magnitude and two-line element (TLE) residuals. We collected 353 observations of 61 different Starlin…
Measuring photometric brightness is a common tool for characterizaing satellites. However, characterizing satellite mega-constellations and their impact on astronomy research requires a new approach and methodology. A few measurements of singular satellites are not sufficient to fully describe a mega-constellation and assess its impact on modern astronomical systems. Characterizing the brightness of a satellite mega-constellation requires a comprehensive measurement program conducting numerous observations over the entire set of critical variables. Utilizing Pomenis, a small-aperture and wide …
The brightness of Starlink satellites during orbit parking and orbit raising decreased significantly in 2020 when the operator modified their orientation. The mean apparent magnitude before the change was 3.90 +/- 0.18, while afterward it was 5.69 +/- 0.06. When magnitudes are adjusted to a standard distance of 1,000 km the means are 4.86 +/- 0.16 and 7.31 +/- 0.05. The difference at the standard distance indicates that spacecraft with adjusted roll angles are 90% fainter on average than the earlier ones.
We present the $g'$-, $R_{\rm c}$-, and $I_{\rm c}$-band magnitudes and associated colors of the Starlink's STARLINK-1113 (one of the standard Starlink satellites) and 1130 (Darksat) with a darkening treatment to its surface. By the 105 cm Murikabushi telescope/$\it{MITSuME}$, simultaneous multicolor observations for the above satellites were conducted four times: on April 10, 2020, May 18, 2020 (for Darksat), and June 11, 2020 (for Darksat and STARLINK-1113). We found that (1) $g'$-band apparent magnitudes of Darksat ($6.95~\pm~0.11-7.65~\pm~0.11$ mag) are comparable to or brighter than that …
We report studies on the mitigation of optical effects of bright low-Earth-orbit (LEO) satellites on Vera C. Rubin Observatory and its Legacy Survey of Space and Time (LSST). These include options for pointing the telescope to avoid satellites, laboratory investigations of bright trails on the Rubin Observatory LSST camera sensors, algorithms for correcting image artifacts caused by bright trails, experiments on darkening SpaceX Starlink satellites, and ground-based follow-up observations. The original Starlink v0.9 satellites are g ~ 4.5 mag, and the initial experiment "DarkSat" is g ~ 6.1 ma…
There is a growing concern about an impact of low-Earth-orbit (LEO) satellite constellations on ground-based astronomical observations, in particular, on wide-field surveys in the optical and infrared. The Zwicky Transient Facility (ZTF), thanks to the large field of view of its camera, provides an ideal setup to study the effects of LEO megaconstellations - such as SpaceX's Starlink - on astronomical surveys. Here, we analyze the archival ZTF observations collected between 2019 November and 2021 September and find 5301 satellite streaks that can be attributed to Starlink satellites. We find t…
Brightness Characterization and Modeling for Amazon Leo Satellites
IAU Centre for the Protection of the Dark and Quiet Sky（国际天文学联合会黑暗与宁静天空保护中心）；Instituto de Astrofísica de Canarias and Universidad de La Laguna（加那利群岛天体物理研究所和拉古纳大学）
Four observations of Starlink's LEO communication satellites, Darksat and STARLINK-1113, were conducted on two nights with two telescopes. The Chakana 0.6\,m telescope at the Ckoirama observatory (Chile) observed both satellites on 5\,Mar\,2020 (UTC) and 7\,Mar\,2020 (UTC) using a Sloan r' and Sloan i' filter, respectively. The ESO VISTA 4.1\,m telescope with the VIRCAM instrument observed both satellites on 5\,Mar\,2020 (UTC) and 7\,Mar\,2020 (UTC) in the NIR J-band and Ks-band, respectively. The calibration, image processing, and analysis of the Darksat images give r\,$\approx$\,5.6\,mag, i\…
Identifying and Measuring Satellite Streaks in DECam Images
Universidad Industrial de Santander（桑坦德工业大学）；IAU Centre for the Protection of the Dark and Quiet Sky, IAU-UAI Headquarters（国际天文学联合会保护黑暗与宁静天空中心，国际天文联合会总部）；University of Washington（华盛顿大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；Kavli Institute for Particle Astrophysics and Cosmology, Stanford University（卡弗里粒子天体物理与宇宙学研究所，斯坦福大学）
The impact of large-scale constellations of satellites, is a concern for ground-based astronomers. In recent years there has been a significant increase in the number of satellites in Low-Earth Orbit and this trend is set to continue. The large number of satellites increases the probability that one will enter the field of view of a ground-based telescope at the right solar angle to appear bright enough that it can corrupt delicate measurements. We present a new tool Astrosat that will project satellite orbits onto the RA/DEC coordinate system for a given observer location and time and field o…
We investigate a novel satellite avoidance strategy to mitigate the impact of large commercial satellite constellations in low-Earth orbit on the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We simulate the orbits of currently planned Starlink and OneWeb constellations ($\sim$40,000 satellites) to test how effectively an upgraded Rubin scheduler algorithm can avoid them, and assess how the overall survey is affected. Given a reasonably accurate satellite orbit forecast, we find it is possible to adjust the scheduler algorithm to effectively avoid some satellites. Overall, …
Observations of BlueWalker 3 (BW3) beginning on December 8 of this year indicate that its apparent brightness had decreased. We postulate that the orbital beta angle and resultant solar power considerations required an adjustment to the satellite attitude around that time. So, the nominally zenith facing side of the flat-panel shaped spacecraft, which supports the solar array, was tilted toward the Sun. Consequently, the nadir side, which is seen by observers on the ground, was mostly dark. Thus, BW3 has generally appeared faint and on some occasions was not seen at all. The amount of fading w…
