Planetary Surface Temperatures from First Principles: Geometric Insights into Energy Balance and Implications for Habitable Exoplanets

Abstract

A previously overlooked relation governing planetary surface temperatures in terms of solar irradiance and top-of-atmosphere Bond albedo is identified. It reproduces the observed climates of Venus, Earth, and Titan, predicts condensation-level temperatures in the gas giants Jupiter, Saturn, Uranus, and Neptune, and extends naturally to rocky planets and large moons with substantial atmospheres. The relation encodes global energy conservation and highlights Bond albedo as a key bulk radiative constraint. Its central result is an empirical proportionality between Bond albedo and the fraction of outgoing longwave radiation returned downward by the atmosphere, termed the inner albedo. A geometric argument based on local beam-aligned parabolic wavefronts provides a rationale for a coefficient linked to the parabolic constant. Compared with classical one- or multi-layer models, the formulation achieves strong agreement using directly measurable quantities and no planet-by-planet tuning. Applied to exoplanets, it yields first-order estimates of equilibrium surface conditions across the habitable zone, suggesting that a substantial part of planetary temperature structure may be constrained by a simple relation among bulk radiative observables.