A generalization of the equinoctial orbital elements

TL;DR

This paper introduces a new set of generalized orbital elements that improve satellite propagation accuracy when perturbing forces are derived from a potential, extending the classical equinoctial elements.

Contribution

The paper presents six generalized orbital elements applicable under perturbing forces from a potential, with explicit transformation Jacobians and demonstrated improved satellite propagation.

Findings

Enhanced accuracy in satellite orbit propagation.

Explicit Jacobian matrices for transformations.

Significant improvement over classical equinoctial elements.

Abstract

We introduce six quantities that generalize the equinoctial orbital elements when some or all the perturbing forces that act on the propagated body are derived from a disturbing potential. Three of the elements define a non-osculating ellipse on the orbital plane, other two fix the orientation of the equinoctial reference frame, and the last allows one to determine the true longitude of the body. The Jacobian matrices of the transformations between the new elements and the position and velocity are explicitly given. As a possible application we investigate their use in the propagation of Earth's artificial satellites showing a remarkable improvement compared to the equinoctial orbital elements.