Chronometric geodesy: methods and applications

The theory of general relativity was born more than one hundred years ago, and since the beginning has striking prediction success. The gravitational redshift effect discovered by Einstein must be taken into account when comparing the frequencies of distant clocks. However, instead of using our knowledge of the Earth’s gravitational field to predict frequency shifts between distant clocks, one can revert the problem and ask if the measurement of frequency shifts between distant clocks can improve our knowledge of the gravitational field. This is known as chronometric geodesy. Since the beginning of the atomic time era in 1955, the accuracy and stability of atomic clocks were constantly ameliorated, with around one order of magnitude gained every ten years. Now that the atomic clock accuracy reaches the low (10^{-18}) in fractional frequency, and can be compared to this level over continental distances with optical fibres, the accuracy of chronometric geodesy reaches the cm level and begins to be competitive with classical geodetic techniques such as geometric levelling and GNSS/geoid levelling. Moreover, the building of global timescales requires now to take into account these effects to the best possible accuracy. In this chapter we explain how atomic clock comparisons and the building of timescales can benefit from the latest developments in physical geodesy for the modelization and realization of the geoid, as well as how classical geodesy could benefit from this new type of observable, which are clock comparisons that are directly linked to gravity potential differences.