By plotting empirical chemical element abundances on Earth relative to the Sun and normalized to silicon versus their first ionization potentials, we confirm the existence of a correlation reported earlier. To explain this, we develop a model based on principles of statistical physics that predicts differentiated relative abundances for any planetary body in a solar system as a function of its orbital distance. This simple model is successfully tested against available chemical composition data from CI chondrites and surface compositional data of Mars, Earth, the Moon, Venus, and Mercury. We show, moreover, that deviations from the proposed law for a given planet correspond to later surface segregation of elements driven both by gravity and chemical reactions. We thus provide a new picture for the distribution of elements in the solar system and inside planets, with important consequences for their chemical composition. Particularly, a 4 wt% initial hydrogen content is predicted for bulk early Earth. This converges with other works suggesting that the interior of the Earth could be enriched with hydrogen.