This paper proposes a model for the origin of the gravitational constant G and the influence of universal matter distribution on local gravitational dynamics. In Section I, I argue that it is plausible that the century-old relation of is in fact a precise relation. From this relation and the observed Hubble constant H0, I derive a model for the universe with estimates for the radius Ru, mass Mu and density ρu of the observable universe. Using these estimates, I propose a relativistic equation to calculate the cosmological redshift using gravitational potentials. Based on this model, I propose in Section II a possible origin of the galaxy rotational velocity discrepancy and the specific value of the Modified Newtonian Dynamics (MOND) constant a0. I derive an equation to predict the modified acceleration of typical galaxies, galaxy clusters, and dwarf galaxies which relies solely on the local baryonic mass distribution and the distribution of mass within the observable universe. Finally, in Section III, I present an interesting finding which emerges from applying my equation for galaxies to a system of a proton and an electron on the 1s orbital. I find that I can use the function of my model to precisely calculate the value of the fine structure constant to a high degree of precision.