Introduction Science is the belief in the ignorance of experts. Richard Feynman, What is Science? Fifteenth annual meeting of the National Science Teachers Association in 1966 The Earth rotation variations The rotation of the Earth not only rules social and biological life, but it is also at the crossroads of many scientific disciplines encompassing biology, geophysics and astronomy. Indeed, the rotation of the Earth determines biological cycles at quasi- daily periods (circadian cycles), our perception of the sky, duration of the ocean tides, and many geophysical processes like cyclone formation, oceanic currents, and the magnetic field. Owing to its tiny variability, almost imperceptible to our senses, con- cerning both the angular rate and the direction of the rotation axis, rotation of the Earth arouses great interest. First, for practical reasons: variations of the rotation of the Earth day after day modify astrometric pointing at a given sidereal instant and then influence measurements done by space geodetic techniques; processing these measurements, for instance for deriving the orbits of the implied satellite or for doing ground positioning, needs accurate estimates of these variations. More fundamentally, the Earth’s rotation changes reflect global geophysical properties and processes within the Earth. Thus, by analyzing the observed fluctuations, we can better come to know our planet. The progressive discovery of these fluctuations has a long history. In terms of observation techniques, three epochs can be distin- guished. The first, from Antiquity to the early classical science in the seventeenth century, is that of astrometric pointing to the naked eye, using instruments made of wood or metal (quarter circle for example). In the seventeenth century begins the telescopic age, benefiting a double technological breakthrough: angular measure- ments are not only much more precise, but they are dated more accurately thanks to Huygens invention of pendulum clocks, regulated by a stable pendulum period. This second era ended around 1960 with the advent of space and atomic clocks tech- nology: the astrometric pointing were abandoned in favor of ultra-precise measure- ments of flight time or frequencies of electromagnetic signals propagating over Earth scale distances.1 These technological advances, combined with the development of Newtonian mechanics first revealed the astronomical nature of the fluctuations of the Earth rotation, and at the end of nineteenth century interference of geophysical causes. 1 Or difference of flight time for the VLBI technique, yielding the time delay of a given radio wavefront at two remote antennas. https://doi.org/10.1515/9783110298093-203 XX | Introduction The Earth’s rotation: an astronomical theme until the nineteenth century By the end of the nineteenth century rotation of the Earth was still an astronomical discipline. As the precision of the angular measurements verged on 0.1 (about 1000 times the resolution power of human eye), the unique variation was the耠耠 precession– nutation of the rotation axis with respect to the starry sky. The precession—this gradual shift in the orientation of the Earth axis of rotation, which, similar to a precessing top, traces out a cone in a cycle of approximately 25800 years with a declination of 23°26 with respect to the ecliptic pole axis—had been discovered from the Antiquity (around耠 200 B.-C. by the Greek Hipparchus); the nutation—a composition of periodic oscillations with amplitude smaller than 20 and superimposed to the precession— was unveiled thanks to telescopic astrometry;耠耠 Bradley discovered its main component of 18.6 years in 1748. In the light of the new mechanics of Newton, precession and nutation result from the gravitational lunisolar forces on the Earth’s equatorial bulge. Even if the amplitude of each term is proportional to the Earth’s dynamical ellipticity, its cause is nonetheless astronomical. Geophysical breakthrough By the beginning of the nineteenth century Laplace investigated the influence of vari- ous terrestrial causes on the Earth’s angular velocity. However, the order of magnitude of the estimated effects was out of reach of the observation of his2 epoch. The geophys- ical breakthrough came where it was least expected. In 1750 Euler enlarged Newtonian mechanics to extended solid bodies, and from its new theorems could prove that the rotation pole freely moves with respect to the Earth’s surface with a period equal to the sidereal period divided by the Earth dynamical ellipticity [84].3 During 150 years, this polar motion was actively looked for in astronomical latitudes (angle between the true equator, perpendicular to rotation axis, and the local vertical). Finally, in 1891, Chandler [34, 35] related an oscillation of about 0.2 with a period of 430 days, not of 305 days, as expected. One year later, Newcomb耠耠 [162] explained how Earth’s non rigidity can lengthen the Euler period of 130 days. This allowed him to state that the solid Earth had an elasticity comparable to the steel one. From that moment Earth’s rotation became a means for inferring geophysical properties. In the same time an an- nual oscillation was discovered, with the half amplitude of the Chandler wobble [36]. So, after Lord Kelvin [119], Newcomb [163] and other scientists naturally assumed the role of seasonal air and water circulation in polar motion. 2 “J’ai discuté dans le cinquième livre de la Mécanique céleste l’influence des causes intérieures telles que les volcans, les tremblements de terre, les vents, les courants de la mer, etc., sur la durée de rota- tion de la terre; et j’ai fait voir au moyen du principe des aires que cette influence est insensible (…)” P.S. de Laplace, Exposition du système du monde, Sixth ed. (1827) p. 344. 3 Euler determined a flattening of about 1 230 from the available measurement of the epoch [83], so he found a period of about 230 sidereal days against 305 for the contemporaneous value of the so-called Euler period. / Introduction | XXI In the vein of a pioneering study by Hopkins in 1839 [76], Hough, Sloudsky and Henri Poincaré theorized the effect of a fluid core, still hypothetical, on the Earthro- tation at the dawn of the twentieth century. Assuming incompressible, homogeneous and non-viscous fluid contained in an ellipsoidal rigid cavity, Hough [116] and Sloud- sky [202] independently predicted a second free oscillation of the rotation pole, quasi- diurnal and retrograde in the terrestrial frame, resulting in a celestial nutation, of which the period is inversely proportional to the flattening of the fluid core. In 1910, Poincaré [172] showed how the terms of the nutation resonate at this period and there- fore differ from those of a rigid Earth. Discovery of variations in the rotation angular rate In the early twentieth century, it was proved that for the Earth the axis of rotation wobbles, but the diurnal rotation constituted a flawless clock until the 1920s: the suc- cession of seconds of the mean solar day (representing conventionally 1.00273 times the stellar rotation period assumed to be constant) realized the Universal Time (UT) with the convention that the mean sun passes the meridian of Greenwich at 12 hour UT. But, following the work of Newcomb and Spencer Jones (1926) [208], there was rec- ognized in the Length Of Day (LOD) a secular growth of about +1.6 ms per century and decadal fluctuations of a few milliseconds, which are interpreted by the dissipation ac- companying tidal deformations and core–mantle coupling, respectively. Then, in the 1930s, comparing UT with the time of quartz clocks which had just been developed, Stoyko found seasonal variations of about 20 ms, namely 0.5 ms in LOD, and it was immediately thought of in terms of the impact of seasonal atmospheric circulation. Advent of the Space Age and consequences In the period following the discovery of polar motion, instrumentation did not make substantial progress, and the quality of optical surveys was still affected by atmo- spheric turbulence. But regular observations of the latitude were then carried out over several observatories around the world to determine the terrestrial oscillations of the pole. And from 1900 to 1960, the temporal resolution going from months to weeks, the accuracy from grew from 0.03 to 0.01 . In the 1960s began the Space Age. Satel- lites, providing measurements of耠耠 the whole耠耠 Earth’s surface, enabled the determina- tion of overall physical properties of the solid Earth and its fluid envelope, in addi- tion to balloon or local surface measurements. Processing an increasing quantity of information was then made possible thanks to growing computer capabilities. This resulted in considerable progress in the measurement and modeling of meteorolog- ical, oceanographic and hydrological hazards. Analysis of satellite orbital perturba- tions also revolutionized our knowledge of the Earth’s gravity field on a large scale. From this epoch, “planetary” technology, such as Very Long Baseline Interferometry (VLBI), was developed to determine the shape of the Earth, its gravity field and its motions, and gradually replaced optical astrometry for ground positioning as well as XXII | Introduction for geodynamic studies. Space geodesy was born. In the 1980s, it addressed global deformations like tectonic drift. In 1985, it permitted to determine the Earth’s rotation irregularities 10 times more precisely than the optical astrometry does; this technique, downgraded, was abandoned in geodynamic studies and geodetic applications. This concomitant progress in the knowledge of Earth’s surface movements and mass re- distributions operating at its surface, or within it, confirmed the hypotheses made at the end of the nineteenth century. First, polar motion is indeed influenced by the at- mosphere, a little less by the oceans and inland waters (ice, snow, soil moisture and vegetation included). Second, from the 1980s the VLBI observations clearly have un- veiled the resonance of the lunisolar terms of the nutation at a 430 day period, in 1986 a non-tidal nutation was discovered at this period and immediately attributed to the corresponding free mode.