On possibilities of improving the accuracy of the geocentric gravitational constant GM by combining SLR and atomic clocks measurements

Nowadays, the geocentric gravitational constant GM is determined by solving equations of motion for trajectories of artificial satellites measured by Satellite Laser Ranging (SLR). The estimated value of GM and its uncertainty 398600441.8 ± 0.8×10⁶ m³s⁻² are currently adopted by the International Astronomical Union. In this study, we investigate possibility of improving the accuracy of GM by integrating atomic clocks measurements with SLR. The functional model defines GM in terms of geopotential differences observed by atomic clocks at two points in space and their distance measured by SLR. Two types of observation equations are established. The first equation defines geopotential differences with respect to the geoidal geopotential value W0. The second equation defines distances with respect to the geocentric position of ground-based station determined from GNSS measurements. With the improving stability of atomic clocks to 10⁻¹⁸, it will be possible to measure geopotential differences with the accuracy ±0.1 m²s⁻² (equivalent to ±1 cm in terms of the geoidal heights), while SLR measurements can currently be carried out with sub-centimetre accuracy under optimal conditions and applying advanced corrections and numerical procedures. Taking into consideration both, accuracy characteristics and their expected improvement, we conduct sensitivity analysis to assess accuracy requirements needed to improve the accuracy GM (±0.8 × 10⁶ m³s⁻²). Error analysis indicates that combination of relativistic measurements with SLR cannot currently improve the accuracy of GM due to insufficient stability of atomic clocks. Nevertheless, the accuracy improvement by an order of magnitude might be feasible in the feature if relativistic measurements are carried out by atomic clocks with stability 10⁻²⁰ (or better), while also achieving sub-millimetre accuracy of SLR. In this way, integration of relativistic measurements with SLR could improve the current accuracy of GM, while the critical aspect is determination of the geoidal geopotential value W0 with sub-millimetre accuracy in terms of geoidal heights that could be achievable.