Higher-order composition of short- and long-period effects for improving analytical ephemeris computation

TL;DR

This paper extends Brouwer's solution to second order and composes multiple transformations into one, significantly speeding up analytical ephemeris computations by reducing evaluation time.

Contribution

It introduces a novel method of composing mean-to-osculating transformations into a single step, enhancing computational efficiency in orbit theory.

Findings

Evaluation efficiency improved by at least 33%.

Single transformation reduces computational complexity.

Extension of Brouwer's solution to second order.

Abstract

The construction of an analytic orbit theory that takes into account the main effects of the Geopotential is notably simplified when splitting the removal of periodic effects in several stages. Conversely, this splitting of the analytical solution into several transformations reduces the evaluation efficiency for dense ephemeris output. However, the advantage is twofold when the different parts of the mean-to-osculating transformation are composed into a single transformation. To show that, Brouwer's solution is extended to the second order of the zonal harmonic of the second degree by the sequential elimination of short- and long-period terms. Then, the generating functions of the different transformations are composed into a single one, from which a single mean-to-osculating transformation is derived. The new, unique transformation notably speeds up the evaluation process, commonly improving evaluation efficiency by at least one third with respect to the customary decomposition of the analytical solution into three different parts.