Every observational test of gravitational light de ection since Eddington (1919)has treated the gravitating source as static. We extend this framework in two analyticallyand numerically validated directions, incorporating three robustness checks and a correctedform for the gravitomagnetic term.Part I (dynamically con ned energy and gravitomagnetic de ection). We derive the modi ed parallax correction coe cient κ(ξ,φ) in linearized GR via Born approximation withretarded- eld propagation. A new monopolar control test integrating null geodesics inthe Vaidya metric with a mass pro le M(t) ∝ tanh(t/τ) proves that spherically symmetric time-varying sources produce no rst-order gravitomagnetic de ection, ∆αgm = 0 atO(G1). The cancellation is exact and follows from an odd-times-even integrand argument.Gravitomagnetic de ection is therefore a direct signature of source anisotropy. For a sourcewith directional energy ux parametrized by β ( ux velocity), we establish numerically that:(i) ∆αgm ∝ β (linear, con rming the h0i origin); (ii) ∆αgm ∝ b−1 ( rst-order, not postNewtonian); (iii) the angular dependence is ∆αgm ∝ cos2φ, where φ is the angle betweenthe photon wavevector and the ux axis. The corrected coe cient is:κ(ξ,φ) = 41−e−ξκst+K(ξ)β cos2φκgm,ξ =τresc/R,where K(ξ) is tabulated numerically and peaks at ξ ≈ 0.5. This replaces the prior cotφcscφform, which arose from an incorrect angular projection in the retarded Green's function.Part II (stellar orbits near supermassive black holes). We identify and quantify a systematicin precision astrometry of S-stars around Sgr A* arising from SMBH-perturbed CMB reference frames (SachsWolfe and thermal SunyaevZel'dovich e ects). The uni ed parallaxcorrection is:pobs = pcl1 + κ(ξ,φ)εgrav(t) + 4εBH(b)F(b/rs) − Λ(βBH,yeff)Θeff(b,rs).Main falsi able prediction: for S2 at periastron, omitting the CMB correction produces|δd|/d ∼ 5 ×10−3 (δd ≈ 8pc), detectable by Gravity+ as a periastronapastron asymmetry.
Guilherme Moura Fernandes (Fri,) studied this question.