Abstract: In this paper, we study the Quality of Surveillance of Low Earth Orbit (LEO) satellite constellations in orbit edge computing platforms, with a focus on monitoring and detecting unpredictable intruding targets. We are primarily interested in targets for precision agriculture and climate monitoring purposes, ranging from natural events such as tornados and flooding, to human-induced phenomenon, such as forest fires and crop monitoring. Targets may be static or mobile. We develop an analytical model that seeks to predict performance attributes of the surveillance. The model takes into account tunable system parameters, such as the number of satellites and their altitude, thereby allowing us to decide the best constellation configuration for different purposes. The results from the analytical model validate the feasibility of using LEO constellation for surveillance purposes and illustrate how model-guided parameter tuning can significantly enhance the monitoring performance in precision agriculture and climate monitoring applications.