Semi-analytical propagation with drag computation and flow expansion using differential algebra

Abstract

Efficient long-term propagation of orbits is needed for e.g. the design of disposal orbits and analysis of their stability. Semi-analytical methods are suited for this as they combine accuracy and efficiency. However, the semi-analytical modelling of non-conservative forces is challenging and in general numerical quadrature is required to accurately average their effects, which reduces the efficiency of semi-analytical propagation. In this work we apply Differential Algebra (DA) for efficient evaluation of the mean element rates due to drag. The effect of drag is computed numerically in the DA arithmetic such that in subsequent integration steps the drag can be calculated by only evaluating a DA expansion. The method is tested for decaying low Earth and geostationary transfer orbits and it is shown that the method can provide accurate propagation with reduced computation time with respect to nominal semi-analytical and numerical propagation. Furthermore, the semi-analytical propagator is entirely implemented in DA to enable higher-order expansion of the flow that can be used for efficient propagation of initial conditions. The approach is applied to expand the evolution of a Galileo disposal orbit. The results show a large validity domain of the expansion which represents a promising result for the application of the method for e.g. stability analysis.

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Identifiers

ORCID for David, Jonathan Gondelach: orcid.org/0000-0002-8511-9523

ORCID for Hugh Lewis: orcid.org/0000-0002-3946-8757

ORCID for Alexander Wittig: orcid.org/0000-0002-4594-0368

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