No Gravitational Anomaly in Wide Binaries from Forward Modeling of 3D Orbits

Recent work by Chae et al. (2026) reported a gravitational anomaly in 36 wide-binary pairs, finding a gravity boost factor of \(\gamma \equiv G_{\rm eff}/G_{\rm N} \approx 1.60_{-0.14}^{+0.17}\) at low accelerations, consistent with predictions from Modified Newtonian Dynamics (MOND). We reanalyze the same dataset using a hierarchical Bayesian model that infers a global \(\gamma\) across all systems while fitting three-dimensional orbital elements. Our model yields \(\gamma = 1.00^{+0.24}_{-0.19}\), consistent with Newtonian gravity (\(\gamma = 1\)). To identify the source of the discrepancy, we perform a test using an approach similar to Chae et al. (2026) , replacing the semi-major axis with a geometric de-projection of the observed projected separation. This test yields \(\gamma = 1.56^{+0.21}_{-0.18}\), closely matching the result of Chae et al. (2026). This shows that if the three-dimensional orbital separation is forward modelled using an independent semi-major axis parameter and then projected into the space of the observables, the relative velocities of wide binaries are consistent with Newtonian gravity.