Zero-dimensional energy-balance model (Sellers 1969; Budyko 1969): a spherical planet of radius R intercepts solar irradiance S across its cross-section πR² with albedo α, reflecting fraction α and absorbing fraction (1−α); at equilibrium…
Stefan-Boltzmann energy balance: T_eq = [S(1−α)/(4σ)]^(1/4)
Related concepts
- Maxwell-Boltzmann distribution
- Boltzmann transport equation
- One-layer grey-atmosphere greenhouse: T_s = 2^(1/4)·T_e
- Planck feedback λ_P = 4σT_e³ ≈ 3.2 W/(m²·K)
- T_eq closed form: √2·S^(1/4)(1−α)^(1/4)/(2σ^(1/4)) (exact)
- T_eq = T_s · √(R_s/(2a)) · (1−A)^{1/4}: blackbody energy balance
- T_eq for (T_s, R_s/a, A)=(6000, 1/400, 0): 150√2 ≈ 212 K