  We analytically work out several effects which a violation of the Strong
Equivalence Principle (SEP) induces on the orbital motion of a binary system
constituted of self-gravitating bodies immersed in a constant and uniform
external field. We do not restrict to the small eccentricity limit. Moreover,
we do not select any specific spatial orientation of the external polarizing
field. We explicitly calculate the SEP-induced mean rates of change of all the
osculating Keplerian orbital elements of the binary, the perturbation of the
projection of the binary orbit onto the line-of-sight, the shift of the radial
velocity, and the range and range-rate signatures and as well. We find that the
ratio of the SEP precessions of the node and the inclination of the binary
depends only on and the pericenter of the binary itself, being independent on
both the magnitude and the orientation of the polarizing field, and on the
semimajor axis, the eccentricity and the node of the binary. Our results, which
do not depend on any particular SEP-violating theoretical scheme, can be
applied to quite general astronomical and astrophysical scenarios. They can be
used to better interpret present and future SEP experiments, especially when
several theoretical SEP mechanisms may be involved, and to suitably design new
dedicated tests.
