The heights for the time measurement and the time for the heights measurement

Measuring the time is something essential to humans: all our activities are marked by atomic clocks found in research laboratories, in companies and in many satellites above us. In this context, a common International Time scale has been necessary for several centuries. With the advent of new frequency standards, the accuracy obtainable has increased, reaching values of about 2 × 10-16. To achieve this kind of accuracy, it is necessary to make some corrections, including one for the relativistic effect caused by the altitude at which the clocks are found. Therefore, the importance of having correct and precise measurements of geodetic heights becomes fundamental in increasing the accuracy in time determination. Today, the precision of geodetic and metrological measurements are becoming comparable, making the measurement of time for the determination of height differences interesting: this involves the use of atomic optical clocks for the futuristic 'relativistic geodesy'. The measure of the geodetic height becomes, therefore, an element whose importance increases as much as the desired accuracy in time determination. Today, the precision of geodetic and metrological measurements are becoming comparable, making the measuring of time for the determination of height differences interesting: this involves the use of atomic optical clocks for the futuristic 'relativistic geodesy'. This work aims to demonstrate how it is possible to couple geodetic and atomic measurements, by addressing and solving problems due to heights determinations of some metrological sites and considering different geoid models.