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We analytically work out several effects which a violation of the StrongEquivalence Principle (SEP) induces on the orbital motion of a binary systemconstituted of self-gravitating bodies immersed in a constant and uniformexternal field. We do not restrict to the small eccentricity limit. Moreover,we do not select any specific spatial orientation of the external polarizingfield. We explicitly calculate the SEP-induced mean rates of change of all theosculating Keplerian orbital elements of the binary, the perturbation of theprojection of the binary orbit onto the line-of-sight, the shift of the radialvelocity, and the range and range-rate signatures and as well. We find that theratio of the SEP precessions of the node and the inclination of the binarydepends only on and the pericenter of the binary itself, being independent onboth the magnitude and the orientation of the polarizing field, and on thesemimajor axis, the eccentricity and the node of the binary. Our results, whichdo not depend on any particular SEP-violating theoretical scheme, can beapplied to quite general astronomical and astrophysical scenarios. They can beused to better interpret present and future SEP experiments, especially whenseveral theoretical SEP mechanisms may be involved, and to suitably design newdedicated tests.

A uniform treatment of the orbital effects due to a violation of the Strong Equivalence Principle in the gravitational Stark-like limit