He worked on the mechanics of the Moon as a special case of the three-body problem.

The work hints at chaos in the system, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory.

His infinite series expression for finding the position of the Moon converged too slowly to be of practical use but was a catalyst in the development of functional analysis[3] and computer algebra.

[4] Delaunay became director of the Paris Observatory in 1870 but drowned in a boating accident near Cherbourg, France, two years later.

Peter Guthrie Tait in his book An Elementary Treatise on Quaternions edition 1867 on page 244 named Didonia in honour of Delaunay.