Aspects of Machian Gravity (II): Testing Theory against Rotation Curves of 175 SPARC Galaxies

Abstract: Machian Gravity (MG) presents a mathematical framework that captures the essence of Mach's principle. It was formulated to address the limitations of general relativity and provide a gravity theory founded on robust logical principles. Unlike the approach of modifying existing theories by introducing extra scalar and vector degrees of freedom to account for observational data, MG offers a more coherent alternative. Previous investigations have revealed MG's potential to explain diverse phenomena, such as galactic velocity patterns, galaxy cluster mass distribution, and cosmic expansion, without requiring additional dark components in the universe. This study applies the MG acceleration law to a wide array of galaxies sourced from the SPARC galactic database. Through meticulous analysis, we have determined the optimal parameters of the Machian gravity model for each individual SPARC galaxy, consequently fitting their distinctive rotational profiles. Similar to the Modified Newtonian Dynamics (MOND), our results suggest the presence of an acceleration scale linked to galaxies, governing their rotational behavior near the outer regions. Importantly, this acceleration scale exhibits variability across different galaxies, albeit typically remaining around the order of $10^{-8} {\rm cm/s^2}$.