Determination of Gravitational Potential at Ground Using Optical-Atomic Clocks on Board Satellites and on Ground Stations and Relevant Simulation Experiments

Abstract

The general relativity theory provides a potential way to directly determine the gravitational potential (GP) difference by comparing the running rate or vibration frequencies of two optical-atomic clocks located at two stations. Recently we proposed an approach referred to as satellite frequency signal transmission based on the Doppler canceling technique or tri-frequency combination technique to determine the GP difference between a satellite and a ground site via exchanging microwave signals. Here, as an extension of our previous study, we aim to formulate determination of GP at ground stations and establish simulation experiments in different cases, including determining the GP at a ground station via one or more satellites and determining the GP difference between two ground stations via one or more satellites. Concerning each case we made simulating experiments, and results show that the precision of the GP at a ground station and that of the GP difference between two stations, determined via one satellite, are, respectively, about 0.383 and 0.454 m2/s2, assuming the clocks with inaccuracy of about 1 × 10 - 18 (s/s) level are available. If more satellites equipped with ultra-high-precise clocks are available, the precision of the determined GP (difference) at ground stations can be further improved.