Constraining the electric charges of some astronomical bodies in   Reissner-Nordstrom spacetimes and generic r^-2-type power-law potentials from   orbital motions
  We put model-independent, dynamical constraints on the net electric charge Q of some astronomical and astrophysical objects by assuming that their exterior spacetimes are described by the Reissner-Nordstroem metric, which induces an additional potential U_RN \propto Q^2 r^-2. Our results extend to other hypothetical power-law interactions inducing extra-potentials U_pert = r^-2 as well (abridged). 
Lorenzo Iorio
gr-qc hep-ph physics.space-ph