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

Rights and responsibilities of individuals participating in medical research

Current geophysical knowledge of the planet Mercury is based upon observations from ground-based astronomy and flybys of the Mariner 10 spacecraft, along with theoretical and computational studies. Mercury has the highest uncompressed density of the terrestrial planets and by implication has a metallic core with a radius approximately 75% of the planetary radius. Mercury’s spin rate is stably locked at 1.5 times the orbital mean motion. Capture into this state is the natural result of tidal evolution if this is the only dissipative process affecting the spin, but the capture probability is enhanced if Mercury’s core were molten at the time of capture. The discovery of Mercury’s magnetic field by Mariner 10 suggests the possibility that the core is partially molten to the present, a result that is surprising given the planet’s size and a surface crater density indicative of early cessation of significant volcanic activity. A present-day liquid outer core within Mercury would require either a core sulfur content of at least several weight percent or an unusual history of heat loss from the planet’s core and silicate fraction. A crustal remanent contribution to Mercury’s observed magnetic field cannot be ruled out on the basis of current knowledge. Measurements from the MESSENGER orbiter, in combination with continued ground-based observations, hold the promise of setting on a firmer basis our understanding of the structure and evolution of Mercury’s interior and the relationship of that evolution to the planet’s geological history