Bond albedo Created 2026-09-24 Updated 2026-11-05
The Bond albedo is the fraction of total incident radiant power that a body reflects, summed over outgoing directions and over the incident spectrum. The absorbed fraction is . It is a global energy-budget quantity, so it appears directly in the planetary equilibrium temperature and must lie between zero and one for a passive reflecting body.
A bright appearance from one direction does not determine Bond albedo. Geometric albedo measures full-phase brightness, and the planetary phase integral supplies the angular weighting needed to connect that brightness to reflected power at a given wavelength. The spectral weighting also depends on the illuminating star: the same reflecting material need not absorb the same fraction of light from hot and cool stars.
The geometric albedo compares the planet's reflected brightness at full phase with that of a perfectly reflecting Lambertian surface in the form of a flat disc of the same projected area, illuminated by the same incident flux. The Bond albedo is the fraction of total incident stellar power reflected in all directions and over all wavelengths. They need not be equal: the planetary phase integral and the incident spectral weighting connect them.
For a blackbody star, the incident flux at orbital distance is
Assume negligible intrinsic luminosity, thermal emissivity one, and efficient day-night heat redistribution giving uniform emission over the whole planet. The absorbed and emitted powers are
Using the Stefan–Boltzmann law gives the planetary equilibrium temperature
For a representative emitting area encoded by a stellar flux redistribution factor , the equivalent expression is
with for global uniform emission and for uniform dayside-only emission. The Bond albedo, rather than the geometric albedo, belongs in the energy budget. Internal heat, wavelength-dependent emissivity and imperfect redistribution require corresponding modifications.