Darwin, the second son of the famous biologist Charles Darwin, was born at Down in England. He was educated at Clapham Grammar School, where the astronomer Charles Pritchard was headmaster, and Cambridge University. He became a fellow in 1868 and, in 1883, Plumian Professor of Astronomy, a post he held until his death. He was knighted in 1905.

His most significant work was on the evolution of the Earth–Moon system. His basic premise was that the effect of the tides has been to slow the Earth's rotation thus lengthening the day and to cause the Moon to recede from the Earth. He gave a mathematical analysis of the consequences of this, extrapolating into both the future and the past. He argued that some 4.5 billion years ago the Moon and the Earth would have been very close, with a day being less than five hours. Before this time the two bodies would actually have been one, with the Moon residing in what is now the Pacific Ocean. The Moon would have been torn away from the Earth by powerful solar tides that would have deformed the Earth every 2.5 hours.

Darwin's theory, worked out in collaboration with Osmond Fisher in 1879, explains both the low density of the Moon as being a part of the Earth's mantle, and also the absence of a granite layer on the Pacific floor. However, the theory is not widely accepted by astronomers. It runs against the Roche limit, which claims that no satellite can come closer than 2.44 times the planet's radius without breaking up; there are also problems with angular momentum. Astronomers today favor the view that the Moon has formed by processes of condensation and accretion. Whatever its faults, Darwin's theory is important as being the first real attempt to work out a cosmology on the principles of mathematical physics.