A Use of Elliptic Complex Numbers in Newtonian Gravity

Abstract

In this study, we used the fact that unit circle for elliptic numbers is an ellipse to model motion of a planet around a star. For that purpose we first have given a standard derivation of elliptic orbits in Newtonian two-body problem. Then we translated the variables found in the coordinates where the origin is at the focus of the ellipse to elliptic number parameters where the origin is at the center of the ellipse. We noted that a similar argument may be used to model hyperbolic orbits in Newtonian gravity with hyperbolic numbers. However it seems that modelling parabolic orbits is not possible within the context of p-complex numbers.