Testing Verlinde’s emergent gravity with the low acceleration gravitational anomaly observed in wide binary stars

Abstract

Recent binary orbit analysis by Chae, and independently by Hernandez shows the breakdown of Newtonian gravity in the weak gravity regime. Unlike the galaxy rotation curves, this result cannot be explained by dark matter as the scale concerned is much smaller than the galactic scale, which makes the gravitational acceleration contribution of the dark matter completely negligible. We propose to explain this binary orbit anomaly by Verlinde’s emergent gravity by correcting a minor error in Verlinde’s emergent gravity. We theoretically derive g2=gB2+gD2, which replaces Verlinde’s g=gB+gD, where g is the total gravitational acceleration, gB is the usual Newtonian gravitational acceleration due to baryonic matter, and gD is what Verlinde calls gravitational acceleration due to “apparent dark matter.” This correction yields 1.29 for the Verlinde to Newton-predicted acceleration ratio, at the Newton-predicted acceleration gpred=10−10.00m/s2, for which Chae reported gobs/gpred=1.37−0.21+0.25 for the observed to Newton-predicted acceleration ratio at the same Newton-predicted acceleration. With our earlier successful fitting of galaxy rotation curves, our study provides the observational test of Verlinde’s emergent gravity.