Comparing Central Force Formulation in Newtonian and Special Theory of Relativity

Abstract

This research aims to give a comparison between classical mechanics and special relativity in term of formulating central force. We derive the Binet equation in relativistic form and find its solution. Then, we discuss the stability of the orbit and make several plots as well as the comparisons of kinematics variables by taking specific example namely circular orbit. Finally, we investigate the relativistic effect in Rutherford scattering by considering some variables including the closest distance and deflection angle. We believe this paper provides a good example for students about the difference between relativistic and classical central force.