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Having great accuracy in the range and range rate measurements,he GRACEmission and the planed GRACE Follow On mission can in principle be employed toplace strong constraints on certain relativistic gravitational theories. Inthis paper, we work out the range observable of the non-dynamical Chern-Simonsmodified gravity for the Satellite-to-Satellite Tracking (SST) measurements. Wefind out that a characteristic time accumulating range signal appears innon-dynamical Chern-Simons gravity, which has no analogue found in the standardparity-preserving metric theories of gravity. The magnitude of thisChern-Simons range signal will reach a few times of $\chi cm$ for each freeflight of these SST missions, here $\chi$ is the dimensionless post-Newtonianparameter of the non-dynamical Chern-Simons theory. Therefore, with the 12years data of the GRACE mission, one expects that the mass scale$M_{CS}=\frac{4\hbar c}{\chi a}$ of the non-dynamical Chern-Simons gravitycould be constrained to be larger than $1.9\times10^{-9}eV$. For the GRACE FOmission that scheduled to be launched in 2017, the much stronger bound that$M_{CS}\geq5\times10^{-7}eV$ is expected.

european physical journal. c, particles and fields

Signature of biased range in the non-dynamical Chern-Simons modified  gravity and its measurements with satellite-satellite tracking missions:  Theoretical studies