The second son of the eminent naturalist Charles Darwin, he became Plumian professor of astronomy and experimental philosophy at Cambridge University in 1883. His monumental analysis of tides, published in 1884, was based on the methods developed by Pierre-Simon Laplace and Lord Kelvin. In The Tides and Kindred Phenomena in the Solar System (1898), he discussed the effects of tidal friction on the Earth–Moon system and theorized that the Moon was formed from matter pulled away from the still-molten Earth by solar tides, a hypothesis now considered unlikely to be true. His great achievement was that he was the first to develop a theory of evolution for the Sun–Earth–Moon system based on mathematical analysis in geophysical theory.

Darwin made extensive studies of the orbits of three rotating bodies, such as the Sun–Earth–Moon system—i.e., he computed where each would be at a specific time. As part of his investigation of the origin of the Moon, he studied the shapes at which rotating masses of fluid become stable. His conclusion that a pear-shaped rotating fluid body is stable is now considered incorrect. Darwin became president of the Royal Astronomical Society in 1899 and of the British Association six years later. He was made Knight Commander of the Bath in 1905.