Deriving the Average Change in Kinetic Energy of a Galaxy in Non-Relativistic Motion

Abstract

This study presents a novel approach to calculating the average change in kinetic energy of galaxies exhibiting non-relativistic motion. The methodology integrates the dynamics of total observed motion, which encompasses both peculiar and recessive motion, with the gravitational influence of neighboring galaxies. The peculiar motion is quantified through peculiar redshift, while recessive motion is described by Hubble’s Law. The total observed velocity is the sum of these two components. The research derives an expression for the average acceleration of a galaxy based on the change in its total observed redshift wavelength over time. Utilizing Newton’s Second Law of Motion, the average observed force and subsequent work done by this force is calculated. The work done by conservative forces, primarily gravitational forces exerted by neighboring galaxies, is also considered to determine the total work done on the galaxy. Results indicate that the average total observed force causing the motion of a galaxy is a non-conservative force, resulting from the combined effects of non-conservative forces responsible for peculiar and recessive motion. The change in potential energy due to gravitational interactions with neighboring galaxies is accounted for, leading to the formulation of the average change in kinetic energy. The conclusion of the paper provides a comprehensive expression for the average change in kinetic energy of a galaxy, factoring in the mass of the galaxy, the speed of light, the total observed redshift, the change in distance with respect to Earth, and the gravitational constant. This expression is significant for understanding the dynamics of galactic motion and the forces at play in a non-relativistic context.