Large or bright satellite constellations: Effects on observations, including on the background sky brightness

This study evaluates the effect of proposed constellations -- ranging from current deployments to mega-constellations and very bright reflector concepts -- on direct trail losses, diffuse background, and scattered sky brightness. We use a numerical model for Mie and Rayleigh scattering in the V band, adapted from moonlight sky-brightness calculations and validated against observations of moonlight and stellar background light. This is combined with the SatConAnalytic package to quantify scattered light, diffuse light from undetected satellites, and direct losses from detected trails. Constellations comprising approximately 60,000 satellites that adhere to the V_550km > 7 recommendation exert a negligible effect on sky brightness, contributing only about 10^-4 of the natural dark sky. Conversely, mega-constellations with 10^6 satellites render trails pervasive. Bright satellites, such those from AST SpaceMobile, significantly impact saturating detectors even when their number is moderate. Extremely bright satellites pose a far more severe threat: a 5000-satellite Reflect Orbital-like constellation elevates the scattered sky background by 20%-30%, and a population of 50,000 increases it by 200%-300%. The constellations currently proposed for launch, over 1,700,000 objects and including satellites brighter than V_550km = 7, would substantially degrade observations. Maintaining satellite brightness below V_550km = 7 is important for all instruments, but critical for safeguarding saturating instruments, such as the VRO LSST camera and for limiting sky-background pollution. Even under this constraint, the total satellite population must remain below ~100,000 satellites to ensure that field-of-view losses do not exceed typical technical downtime.