A new gravitational effect of a deformed mass

A new relativistic tidal effect of a deformed axisymmetric mass is described and the possibility of measuring it in an earth satellite is considered. The calculations show that the quadrupole moment of the earth causes a large secular relativistic contribution to the relative acceleration between two test masses placed in a satellite around the earth. Already after ≈10 hours of observation this new relativistic effect would exceed the corresponding newtonian quadrupole effect by a factor of 10.