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Studying the albedos of the planets and moons of the Solar System dates backat least a century. Of particular interest is the relationship between thealbedo measured at superior conjunction, known as the ``geometric albedo", andthe albedo considered over all orbital phase angles, known as the ``sphericalalbedo". Determining the relationship between the geometric and sphericalalbedos usually involves complex numerical calculations and closed-formsolutions are restricted to simple reflection laws. Here we report thediscovery of closed-form solutions for the geometric albedo and integral phasefunction, which apply to any law of reflection that only depends on thescattering angle. The shape of a reflected light phase curve, quantified by theintegral phase function, and the secondary eclipse depth, quantified by thegeometric albedo, may now be self-consistently inverted to retrieve globallyaveraged physical parameters. Fully Bayesian phase curve inversions forreflectance maps and simultaneous light curve detrending may now be performeddue to the efficiency of computation. Demonstrating these innovations for thehot Jupiter Kepler-7b, we infer a geometric albedo of $0.25^{+0.01}_{-0.02}$, aphase integral of $1.77 \pm0.07$, a spherical albedo of $0.44^{+0.02}_{-0.03}$and a scattering asymmetry factor of $0.07^{+0.12}_{-0.11}$.

Closed-formed ab initio solutions of geometric albedos and reflected light phase curves of exoplanets