Modelling Palomar Transients: Constraints from Reflection Geometry and Orbital Altitude
Recent searches of digitised photographic plates from the Palomar Observatory have uncovered tens of thousands of short-lived transients, each visible in only a single exposure. Their morphologies indicate sub-second flashes, consistent with specular reflections from highly reflective objects in near-Earth orbits. In this paper, we present a modelling study using geometric shadow modelling, Monte Carlo simulations, and photometric constraints to infer their physical properties. We examine the observed groupings and alignments, which appear to be consistent with sudden changes in attitude. Assuming a spherical-shell model, the angular profile of the measured transient deficit around the antisolar point is consistent with a population at characteristic altitudes of $\sim 20,000$--25,000 km. A complementary estimate, based on the altitude dependence of the global Earth-shadow deficit, yields a broader characteristic range of $\sim$ 20,000--35,000 km above Earth's surface, extending into the geosynchronous orbital (GSO) region. Under simplified geometric and photometric assumptions and assuming $\sim20{,}000$ to $35{,}786$ km above the Earth's surface, the inferred sizes of the specularly reflecting facets range from centimetre scales up to $\sim3$ m, with characteristic flash durations of $\sim320$ ms and slow rotation rates. We explore both natural and non-natural toy models consistent with the data, and provide constraints to guide future observational searches.