Degravitation, Orbital Dynamics and the Effective Barycentre

In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined for the first time in [13-16] and originates from the quest of finding a mechanism that is able to degravitate the vacuum energy on cosmological scales. We suggest in this manuscript a precise covariant coupling model which acts like a high-pass filter with a macroscopic distance filter scale $\sqrt{\Lambda}$. In the context of this specific theory of gravity we review some cosmological aspects before we briefly recall the effective relaxed Einstein equations outlined for the first time in [1]. We present a general procedure to determine the gravitational potentials for a far away wave zone field point. Moreover we work out the modified orbital dynamics of a binary-system as well as the effective 1.5 post-Newtonian barycentre for a generic $n$-body system. We notice that it is always possible to recover the corresponding general relativistic results in the limit of vanishing nonlocal modification parameters.