Multi-year stacking searches for solar system bodies

Digital tracking detects faint solar system bodies by stacking many images along hypothesized orbits, revealing objects that are undetectable in every individual exposure. Previous searches have been restricted to small areas and short time baselines. We present a general framework to quantify both sensitivity and computational requirements for digital tracking of nonlinear motion across the full sky over multi-year baselines. We start from matched-filter stacking and derive how signal-to-noise ratio (SNR) degrades with trial orbit mismatch, which leads to a metric tensor on orbital parameter space. The metric defines local Euclidean coordinates in which SNR loss is isotropic, and a covariant density that specifies the exact number of trial orbits needed for a chosen SNR tolerance. We validate the approach with Zwicky Transient Facility (ZTF) data, recovering known objects in blind searches that stack thousands of images over six years along billions of trial orbits. We quantify ZTF's sensitivity to populations beyond 5 au and show that stacking reaches most of the remaining Planet 9 parameter space. The computational demands of all-sky, multi-year tracking are extreme, but we demonstrate that time segmentation and image blurring greatly reduce orbit density at modest sensitivity cost. Stacking effectively boosts medium-aperture surveys to the Rubin Observatory single-exposure depth across the northern sky. Digital tracking in dense Rubin observations of a 10 sq. deg field is tractable and could detect trans-Neptunian objects to 27th magnitude in a single night, with deep drilling fields reaching fainter still.