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

TL;DR

This paper provides a comprehensive analytical framework for understanding how violations of the Strong Equivalence Principle affect the orbital dynamics of binary systems in a uniform external gravitational field, without simplifying assumptions.

Contribution

It derives general expressions for SEP-induced orbital element changes applicable to various scenarios, independent of specific SEP-violation theories.

Findings

The ratio of SEP precessions depends only on the binary’s pericenter and is independent of external field orientation.

Explicit formulas for changes in all Keplerian orbital elements are provided.

Results can be used to interpret and design SEP violation tests in astrophysical systems.

Abstract

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.