We consider a binary system made of self-gravitating bodies embedded in a constant and uniform external field \boldsymbol { g } .
We analytically work out several orbital effects induced by a putative violation of the Strong Equivalence Principle ( SEP ) due to \boldsymbol { g } . In our calculation , we do not assume e \sim 0 , where e is the binary ’ s orbit eccentricity .
Moreover , we do not a priori choose any specific preferred spatial orientation for the fixed direction of \boldsymbol { g } . Our results do not depend on any particular SEP-violating theoretical scheme . They can be applied to general astronomical and astrophysical binary systems immersed in an external constant and uniform polarizing field .