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High precision Superconductivity Gravity Gradiometers (SGG) are powerfultools for relativistic experiments. In this paper, we work out the tidalsignals in non-dynamical Chern-Simons modified gravity, which could be measuredby orbiting SGGs around Earth. We find that, with proper orientations ofmulti-axes SGGs, the tidal signals from the Chern-Simons modification can beisolated in the combined data of different axes. Furthermore, for three-axesSGGs, such combined data is the trace of the total tidal matrix, which isinvariant under the rotations of SGG axes and thus free from axis pointingerrors. Following nearly circular orbits, the tests of the parity-violatingChern-Simons modification and the measurements of the gravitomagnetic sector inparity-conserving metric theories can be carried out independently in the sametime. A first step analysis on noise sources is also included.

Testing Chern-Simons modified gravity with orbiting superconductive gravity gradiometers --- The non-dynamical formulation