Figure 3. This histogram shows the error in satellite position measured from 567 observations made by Pomenis (University of Arizona) in the northern summer and fall of 2020. The angular offset is the difference between the expected satellite position as calculated from the most timely TLE and the satellite’s astrometric position measured in the captured image. The majority of satellites were within a few arcminutes of their expected position, although the tail of the distribution extends beyond 2 degrees. This plot utilized the Supplemental TLEs provided on Celestrak.com; comparison with the standard issue TLEs did not show significant differences.
Overall, these observations demonstrate that the current TLE system is wholly inadequate for the needs of astronomers in predicting the trajectories of satellites across the night sky. This is particularly true immediately after orbital maneuvers when a new TLE isn’t released until hours later. With rapid orbital solution data sharing after an orbital maneuver along with error bars, a more robust forecast will be possible. This will allow observers to assign different probability distributions and confidence levels for different satellite densities and reflective magnitudes for a given patch of sky at a given time range — a critical capability, whether the goal is to image a specific satellite or avoid as many as possible.
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For optical astronomy, the reflective brightness of the satellite is also a critical factor. For ultra-sensitive detectors like the Vera C. Rubin Observatory LSST Camera, laboratory studies indicate that an optical magnitude of at least V ≈ 7 mag is needed to allow for non-linear image artefact correction to reduce the signal from the satellites to the same level as the background noise (Tyson et al., 2020). Darkening
