Generalized Fractional Two Body Problem

Abstract

The two body problem using the fractional calculus is reformulated. The fractional equation of motion of two body problem is constructed and then solved. The integrals of motion are re-investigated. A very new conclusion about the trajectory on which the motion of the center of mass takes place is revealed. The center of mass moves along a nonlinear path regardless the index of the fractional derivative except at alfa = 1. The classical results of two body problem are verified when alfa = 1. The specific angular momentum and total energy are conserved. But the potential of the point mass is corrected with a numerical factor given by equation (2.16) in the text.