An Alternative Explanation of Non-Newtonian Galactic Rotation Curves

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 + √(ax)r1/2, where ax is a scalar accelerating field that is independent of mass. This yields the following relation for centripetal acceleration: a = (GM)r-2 + 2√(axGM)r-1 + ax, which, at large radii, is nearly identical to the deep-MOND equation a = √(a0GM)r-1. When applied to a handful of galaxies, the velocity equation prefers an ax 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 ax is a result of local galactic expansion, such that ax = cHg, where Hg is the rate of expansion. For the Milky Way, it is estimated that Hg ≈ 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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[v1] 2018-01-22 00:16:21

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