The ballistic free-fall absolute gravimeter FG5#202  Accuracy : g ( g = 9, 8xx xxx xX m/s²)  1 µgal [= 10 nm/s²]  Vertical displacement of 3 mm at the Earth’s surface (free air correction)  ~ 50 in the world ~ 130 cm

Interferometer The FG5 absolute gravimeter Constructive & destructive interferences : When the falling mass runs /2, an interference fringe appears and is detected by a photodiode  Distance measurement Free fall on 20 cm during 0.2 s : fringes, with frequency sweeping from 0 to 6 MHz The time intervals between the occurrence of each fringe are measured by a Rb oscillator (or Cs if available) Free falling Mass (corner cube) Iodine stabilized He-Ne Laser (  633 nm) Inertial Reference corner cube Dropping chamber (vacuum ~10 -4 Pa) /2 + + = = Superspring : long period insulation spring that provides the inertial reference frame Gravimeter: © Micro-g LaCoste, animations: M. Van Camp

 The following equation of motion is fitted to the data x i, t i : -  is the vertical gravity gradient (~ -30 nm/s²/cm), - c the speed of light, - x 0 the initial position, - v 0 the initial velocity, - g 0 the initial acceleration. Free fall : data processing

1. Geophysics : Determination of the Geoid (represents the average level of the seas and their prolongation under the continents) Tectonic deformations & Post-glacial rebound Influence of atmosphere, cryosphere & hydrosphere Structure of the Earth’s interior Geology & mineral resource exploration 2. Metrology : Calibration of relative gravimeters Force and pressure standards: e.g. pressure transducers Watt balance: to relate the kilogram to a natural constant Why determining g ?

International prototype K (  1 kg) Goal : to replace the K base unit (K  1 kg) Metrology : the redefinition of “K”: the Watt balance experiment  “The kilogram is a mass whose equivalent energy equals the energy of a collection of photons whose frequencies sum to Hz (mc² = h )” … Where g is a key factor !

Metrology: the Watt balance (METAS) 1st : Weighing mode : mg = I. G(B, l) G(B, l) = “geometrical factor”, difficult to measure. m g v = U I = k h f J ² (f J = Josephson’s frequency) U, I determined using Josephson junctions and the quantised Hall effect (von Klitzing) standards v measured by laser interferometry  Using a Watt balance, best measurement of the Planck’s constant with an uncertainty of (Williams et al., 1998)  Planck’s constant as a consequence of the definition of the kilogram. 2nd : Velocity mode : U = v. G(B, l) v © METAS

International prototype K (  1 kg) … Where h is fixed, g a key factor and the Watt balance a practical realization of the kilogram Metrology: the redefinition of “K” using the Watt balance  “The kilogram is a mass whose equivalent energy equals the energy of a collection of photons whose frequencies sum to Hz (mc² = h )”  Museum ! © METAS © BIPM

Geophysics: Absolute gravity measurements at the Membach station (Eupen) : 40 nm/s² 1 year - 6 ± 1 nm / s² / yr  ± 0.5 mm/yr (free air + Bouguer) Confirmed by GPS measurements to drops  ~ 1 to 8 days

Cam-driven absolute gravimeter : compacter, much shorter cycle: 200 drops / minute (FG5 : 6 drops / minute). Atomic absolute gravimeters (atoms = test masses, but due to their quantum nature, also used as matter-wave to carry out interferometric measurements of the effect of gravity on the atoms). Comparison with FG5 provided best confirmation of the equivalence principle between a quantum and macroscopic object [Peters, Chung & Chu, 1999]. Satellite measurements: resolution of 100 to 200 km and precision at the 10 µm /s² level (10 -6 g). The Future

…and with g Without g... Gravity is as important in physics as in the everyday live !