Orbit Elements from Kepler Solutions in Projective Coordinates

TL;DR

This paper introduces a novel set of eight orbit elements derived from Kepler solutions in projective coordinates, providing a singularity-free framework for analyzing perturbed two-body dynamics, including J2 perturbations.

Contribution

It develops a new set of orbit elements from Kepler solutions in projective coordinates, applicable to arbitrarily-perturbed two-body problems, with verified numerical results.

Findings

Elements are singularity-free except in rectilinear motion.

The method accurately models J2-perturbed two-body dynamics.

Numerical verification confirms the robustness of the approach.

Abstract

Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are singularity-free in all cases besides rectilinear motion (when angular momentum vanishes). The classic J2-perturbed two-body problem is developed and used for numerical verification.