The Application of Unified Orbital Elements for Conic Orbits in Cislunar Orbit Prediction

When describing the motion of a spacecraft using traditional elliptical orbital elements, if its orbit changes from elliptical to hyperbolic, it becomes difficult to continue the calculation. In order to address this issue, improvements are made upon classical elliptical orbital elements, utilizing a set of orbital elements applicable to any conic section to integrate the equation of motion. The set of elements is applicable for any eccentricity $e⩾0$ and inclination $0⩽i<{180}^{\circ }$, with the singularity occurring only for $i={180}^{\circ }$. The basic conversion formulas and equations of perturbed motion are provided. Subsequently, orbit predictions for cislunar objects are conducted, and the results are compared with calculations using Cartesian. The findings indicate that the results obtained from these orbital elements are sufficiently accurate, and the computational efficiency is advantageous when the changes in the elements are not particularly drastic. In addressing the issue of the singularity at $i={180}^{\circ }$ that may arise in the practical application of orbital elements, various workarounds are proposed, including changing state variables and fixing integration step sizes, and their applicability is assessed.