Milgrom 1983aAstrophys.J.270(1983)365 introduced a nonrelativistic
modification of Newtonian dynamics (MOND) at small accelerations, a < a_{0} , whereupon
the gravitational acceleration of a test particle is given by aμ(a/a_{0}) = a_{N}, where μ(x) is a function that interpolates between the Newtonian regime, μ(x) = 1, when x ≫1 and the MOND regime, μ(x) = x, when x ≪ 1. Milgrom 1983bAstrophys.J.270(1983)371 introduced the
interpolating function normally used for galaxy fitting,

where

and determined that the MOND acceleration was the order a_{0}
= cH_{0}/6, and proportional
to the Hubble constant, H_{0}, implying a cosmological connection to the modified dynamics. Milgroms acceleration has the solution:

which is written in terms of the Newtonian acceleration of a test particle at a separation, r,

where M(r) is the baryonic mass integrated within a sphere of radius, r.

In
§4.2 of the thesis, a_{0} is permitted to vary across the sample of 29 high and low surface brightness galaxies from the Ursa Major filament of galaxies, in order to compute the universal acceleration parameter, in Table 4.3, with the overall best-fitting results:

Because of the gross uncertainty in the mean results, the galaxy rotation curves of Figure 4.1 are one parameter best-fits by the
stellar mass-to-light ratio, applying the universal acceleration parameter,