**Authors:** Morgan Weinberg

Inspired by the continued success of MOND (Modified Newtonian Dynamics) in the prediction of galactic rotation curves, an attempt to derive the deep-MOND equation from known mechanics has resulted in a third explanation apart from MOND and dark matter. It is proposed that particle velocities follow the relation v = √(GM)r ^{-1/2 }+ √(a_{x})r^{1/2}, where a_{x} is a scalar accelerating field that is independent of mass. This yields the following relation for centripetal acceleration: a = (GM)r^{-2 }+ 2√(a_{x}GM)r^{-1 }+ a_{x}, which, at large radii, is nearly identical to the deep-MOND equation a = √(a_{0}GM)r^{-1}. When applied to a handful of galaxies, the velocity equation prefers an a_{x} on the order of 10^{-14} (km s^{-2}), which gives a good fit of velocity curves to observed values. It is posited that scalar field a_{x} is a result of local galactic expansion, such that a_{x} = cH_{g}, where H_{g} is the rate of expansion. For the Milky Way, it is estimated that H_{g} ≈ 9.3 E-4 (km s^{-1} kpc^{-1}). This rate would predict an increase of the astronomical unit of 14 (cm yr^{-1}), which compares well with the recently reported measurement of 15 ±4 (cm yr^{-1}).

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