Determining the Exact Mass of M31 Using the Solar System

This paper focuses on clarifying the impact of an increase in radius on the flatness of the rotation curve in galaxies. This paper has three main objectives. First, a revision of Newtonian dynamics is proposed to explain the unexpectedly high velocity and flatness of the rotation curve of stars at the galaxy’s edge. This revision does not conflict with other applications of Newtonian dynamics. Secondly, it presents a calculation of how a decrease in the specified centripetal force with an increase in distance from the galactic center contributes to these phenomena. In regions of weak gravitational force, changes in specified centripetal force and velocity align with the revised Newtonian dynamics. It demonstrates that an increase in radius only significantly affects velocity reduction in regions of strong gravitational force near the galactic center, such as the Solar system. However, in regions of weak gravitational force far from the galactic center, radius increase minimally impacts velocity reduction, resulting in the flatness of the rotation curve. Thirdly, a law based on the Solar system is proposed to estimate the exact mass of the Andromeda galaxy (M31) using the average velocity of its stars, building on the insights gained from the first two objectives.