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Reflections from objects in Earth orbit can produce sub-second, star-like optical flashes similar to astrophysical transients. Reflections have historically caused false alarms for transient surveys, but the population has not been systematically studied. We report event rates for these orbital flashes using the Evryscope Fast Transient Engine, a low-latency transient detection pipeline for the Evryscopes. We select single-epoch detections likely caused by Earth satellites and model the event rate as a function of both magnitude and sky position. We measure a rate of $1800^{+600}_{-280}$ sky$^{-1}$ hour$^{-1}$, peaking at $m_g = 13.0$, for flashes morphologically degenerate with real astrophysical signals in surveys like the Evryscopes. Of these, $340^{+150}_{-85}$ sky$^{-1}$ hour$^{-1}$ are bright enough to be visible to the naked eye in typical suburban skies with a visual limiting magnitude of $V\approx4$. These measurements place the event rate of orbital flashes orders of magnitude higher than the combined rate of public alerts from all active all-sky fast-timescale transient searches, including neutrino, gravitational-wave, gamma-ray, and radio observatories. Short-timescale orbital flashes form a dominating foreground for un-triggered searches for fast transients in low-resolution, wide-angle surveys. However, events like fast radio bursts (FRBs) with arcminute-scale localization have a low probability ($\sim10^{-5}$) of coincidence with an orbital flash, allowing optical surveys to place constraints on their potential optical counterparts in single images. Upcoming satellite internet constellations, like SpaceX Starlink, are unlikely to contribute significantly to the population of orbital flashes in normal operations.