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

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 semianalytical 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 higherorder 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

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

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 semianalytical 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 higherorder 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

Processing two line element sets to facilitate re-entry prediction of spent rocket bodies from geostationary transfer orbit

Predicting the re-entry of space objects enables the risk they pose to the ground population to be managed. The more accurate the re-entry forecast, the more cost-efficient risk mitigation measures can be put in place. However, at present, the only publicly available ephemerides (two line element sets, TLEs) should not be used for accurate re-entry prediction directly. They may contain erroneous state vectors, which need to be filtered out. Also, the object’s physical parameters (ballistic and solar radiation pressure coefficients) need to be estimated to enable accurate propagation. These estimates are only valid between events that change object’s physical properties, e.g. collisions and fragmentations. Thus, these events need to be identified amongst the TLEs. This paper presents the TLE analysis methodology, which enables outlying TLEs and space events to be identified. It is then demonstrated how various TLE filtering stages improve the accuracy of the TLE-based re-entry prediction