Mathematical & Physical Foundations
Kepler's 3rd Law: T² = (4π² / G·M) · a³
Orbital Speed: v_orb ≈ √(G·M / a)
Escape Velocity: v_esc = √(2·G·M_p / R_p)
Thermal Speed: v_th = √(8·k_B·T_eq / π·m)
Jeans Atmospheric Escape Rule: A planetary body retains atmospheric gas over geological time (10⁹ yrs) if v_esc > 6 × v_th. If thermal velocity exceeds this threshold, atmospheric particles systematically escape into space.