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He studied tidal effects on the planets. In particular, using methods introduced by Laplace and Thomson, he discussed the effects of tidal action on the Sun-Earth-Moon system. One of his theories, namely that the Moon was pulled from a molten Earth early in its history by tidal action of the Sun, is now considered incorrect.
Darwin made a major study of the three-body problem in the case of the orbits of the Sun-Earth-Moon system. He also studied the stability of rotating fluids, again motivated by his interest in the Moon being formed in fluid form from a molten Earth. His conclusions that a pear shaped rotating mass is stable is today thought to be incorrect.
Despite the fact that we do not accept Darwin's conclusions today, he is important in being the first to apply mathematical techniques to study the evolution of the Sun-Earth-Moon system.
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