Strong constraints on the gravitational law from Gaia DR3 wide binaries

We test Milgromian dynamics (MOND) using wide binary stars (WBs) with separations of 2-30 kAU. Locally, the WB orbital velocity in MOND should exceed the Newtonian prediction by approximate to 20 per cent at asymptotically large separations given the Galactic external field effect (EFE). We investigate this with a detailed statistical analysis of Gaia DR3 data on 8611 WBs within 250 pc of the Sun. Orbits are integrated in a rigorously calculated gravitational field that directly includes the EFE. We also allow line-of-sight contamination and undetected close binary companions to the stars in each WB. We interpolate between the Newtonian and Milgromian predictions using the parameter alpha(grav), with 0 indicating Newtonian gravity and 1 indicating MOND. Directly comparing the best Newtonian and Milgromian models reveals that Newtonian dynamics is preferred at 19 sigma confidence. Using a complementary Markov Chain Monte Carlo analysis, we find that alpha(grav) = -0 . 021(-0 . 045)(+0 . 065) , which is fully consistent with Newtonian gravity but excludes MOND at 16 sigma confidence. This is in line with the similar result of Pittordis and Sutherland using a somewhat different sample selection and less thoroughly explored population model. We show that although our best-fitting model does not fully reproduce the observations, an o v erwhelmingly strong preference for Newtonian gravity remains in a considerable range of variations to our analysis. Adapting the MOND interpolating function to explain this result would cause tension with rotation curve constraints. We discuss the broader implications of our results in light of other works, concluding that MOND must be substantially modified on small scales to account for local WBs.