Mass sensitivity of gravimetric satellites

Frequency-domain expressions are found for gradiometer and satellite-to-satellite tracking measurements of a point source on the surface of the Earth. The maximum signal-to-noise ratio as a function of noise in the measurement apparatus is computed, and from that the minimum detectable point mass is inferred. A point mass of magnitude M_3=100 Gt gives a signal-to-noise ratio of 3 when a GOCE-like gradiometer passes directly over the mass. On the satellite-to-satellite tracking mission GRACE-FO M_3=1.3 Gt for the microwave instrument and M_3=0.5 Gt for the laser ranging interferometer. The sensitivity of future GRACE-like missions with different orbital parameters and improved accelerometer sensitivity is explored, and the optimum spacecraft separation for detecting point-like sources is found. The future-mission benefit of improving the accelerometer sensitivity for measurement of non-gravitational disturbances is shown by the resulting reduction of M_3 to as small as 7 Mt for 500 km orbital altitude and optimized satellite separation of 900 km.