Machian Gravity: Modeling Rotation Curves and Radial Acceleration in the SPARC Galaxy Sample

This paper investigates the potential of Machian Gravity (MG), a five-dimensional theory of gravity, to explain the acceleration law governing rotationally bound systems, in particular spiral galaxies. MG was proposed as a framework capable of accounting for a range of astrophysical and cosmological phenomena – including galactic rotation curves, mass distributions in galaxy clusters, and cosmic expansion – without invoking additional dark components. In this study, we apply the MG acceleration law to a large sample of galaxies drawn from the SPARC database. Through a detailed analysis, we determine the optimal MG parameters for each individual galaxy, successfully fitting their observed rotation curves. Similar to Modified Newtonian Dynamics (MOND), our results indicate the existence of a characteristic acceleration scale associated with galactic dynamics, which regulates rotational behavior in the outer regions. Notably, this acceleration scale varies from galaxy to galaxy, but typically remains of order ${10}^{-8}\mathrm{c}\mathrm{m}\mathrm{/}{\mathrm{s}}^2$.