Our work focuses on plasma discharges produced in various planetary atmospheres. This process can create luminescent emissions at low currents and low temperatures: glow and corona discharges. The parallel plate geometry used in Townsend’s theory lets us develop a theoretical formalism, with explicit solutions for the critical voltage effectively reproducing experimental Paschen curves. Here, we present a generalization of the classic parallel plate configurations to concentric spherical and coaxial cylindrical geometries in Earth, Mars, Titan, and Venus atmospheres. We show that glow coronæ form more easily in Mars’s low-pressure, CO2-rich atmosphere than in Earth’s high-pressure, N2-rich atmosphere. Additionally, we present breakdown criteria for Titan and Venus, two planets where discharge processes have been postulated. We further demonstrate that critical voltage minima occur at 0.5 cm⋅Torr for all three investigated geometries, suggesting easier initiation around millimeter-size particles in dust and water clouds. Townsend breakdown can transition to streamer and leader discharges with higher current densities and/or temperatures. Time permitting, we will introduce how our FRActal Model of Electrical Discharges (FraMED) can be readily adapted and tested to study extraterrestrial lightning and Transient Luminous Events.