T_eq closed form: √2·S^(1/4)(1−α)^(1/4)/(2σ^(1/4)) (exact)

Closed-form evaluation of the zero-dimensional radiative-balance equilibrium. Setting absorbed solar πR²·S(1−α) = emitted longwave 4πR²·σT_eq⁴ and solving for T_eq yields the quartic root. Sympy canonical form: T_eq =…