Precession and Nutation of the Earth

International audiencePrecession and nutation of the Earth originate in the tidal forces exerted by the Moon, the Sun, and the planets on the equatorial bulge of the Earth. Discovered respectively in the 2nd century B.C. by Hipparcus and in the 18th century by Bradley, their existence and characteristics were deduced theoretically by Newton for the precession and by d'Alembert for the nutation. After a historical review we explain, both in an intuitive manner and by simple calculations, the gravitational origin and the main characteristics of the precession-nutation. Then we describe in detail two fundamental theories, one using the Lagrangian formalism, the other the Hamiltonian one. A large final part is devoted to successive improvements of the precession-nutation theory in the last decades, both when considering the Earth as a rigid body and when taking into account the small effects of non-rigidity