Mass Sensitivity or Gravimetric Satellites

A point mass on the surface of the Earth gives the highest frequency content for orbiting gravimetry, with  the maximum frequency for gradiometers or satellite-to-satellite tracking determined by orbital altitude.  Frequency-domain expressions are found for  measurements of a point-like source on the surface of the Earth.  The response of orbiting gradiometers such as GOCE and satellite-to-satellite tracking missions such as GRACE-FO are compared. The optimal signal-to-noise ratio as a function  of noise in the measurement apparatus is computed, and from that the minimum detectable mass is inferred. The point mass magnitude that gives signal-to-noise ratio = 3 is for GOCE  M_3=200 Gton and  for the laser ranging interferometer measurement on GRACE-FO  M_3= 0.5 Gton. For the laser ranging interferometer measurement, the optimal filter for detecting point-like masses has a passband of 1 to 20 mHz,  differing from the 0.3 to 20 mHz admittance filter of Ghobadi-Far et al. (2018), which is not specialized for detecting point-like masses. M_3 for  future GRACE-like missions with different orbital parameters and improved instrument sensitivity is explored, and the optimum spacecraft separation is found.