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Title: General perturbations methods for orbit propagation with particular application to orbit lifetime analysis
Author: Kerr, Emma
ISNI:       0000 0004 8502 8263
Awarding Body: University of Strathclyde
Current Institution: University of Strathclyde
Date of Award: 2018
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The average number of spacecraft launched per year has recently and rapidly increased, a trend largely the result of the increased use of small and micro-satellites, platforms such as the CubeSat. This growth trend is unlikely to reverse in the near-term. To mitigate the risk that spacecraft pose to the availability and accessibility of the space environment, space debris mitigation standards currently recommend that spacecraft be removed from low-Earth orbit within 25 years of end-of-mission. In order to prove compliance with these standards, spacecraft operators must demonstrate the evolution of their spacecraft's orbit through the use of orbit propagation software. The aim of this thesis is to improve understanding and accuracy of general perturbations methods for orbit propagation. This thesis tackles this challenge from two different angles. Firstly, the general perturbations method itself is derived using modern mathematical toolsets. Secondly, the input parameters are addressed, these include atmospheric density and ballistic coefficient. A new parameter is introduced, termed the density index, which enables the solar activity cycle to be captured in a new analytical atmospheric density model. Consequentially, a newsolar activity model is developed that uses a single independent variable per solar cycle to describe the solar activity across that cycle, as indicated by the F10.7 index. This density index is applied to a new analytical spherically-symmetrical model for atmospheric mass density. When combined with the newly derived general perturbations method for orbit propagation, validation against historical data shows an improvement in orbit lifetime estimates from an average error of 50.44 percent with a standard deviation of 24.96 percent, to an average error of 3.46 percent with a standard deviation of 3.25 percent when compared with the method developed by King-Hele and co-authors including an averaged atmospheric mass density (not including solar activity effects). Furthermore, the new method with the new analytical spherically-symmetrical atmospheric model and solar activity models applied is found to compare favourably against other general and special perturbations methods, including thirdparty, and commercial software, the most accurate of which was found to have an average error of 6.63 percent and standard deviation of 7.00 percent. The spherically-symmetrical atmospheric model is also extended to include an analytical non-spherically-symmetrical atmospheric density companion model. This improvement allows the method to be applied with confidence to highly inclined orbits and special cases such as sun-synchronous orbits where the inclusion of the effects of atmospheric oblateness and the diurnal bulge will be particularly significant. Using a case study of a sun-synchronous satellite a comparison is drawn between the models, showing that by capturing the effects of a non-spherically-symmetrical atmosphere the orbit lifetime predicted could be up to 10 percent different than when using the spherically-symmetrical model. It is noted that the inclusion of the non-spherically-symmetrical model is less important than the inclusion of the solar activity model. A new method of determining the average projected area of a randomly tumbling CubeSat is presented, which improves on the accuracy of the method recommended in Section 6.3 of the ISO standard 27852:2010(E). For the range of CubeSat configurations presented it can be seen that the new method improves the error in the average projected area from, approximately 27 percent to within 5 percent. It is of particular note that the ISO standard is found to consistently overestimate the average projected area when considering noncuboid spacecraft configurations, meaning that when applied to an orbit decay model it will consistently underestimate the orbit lifetime. A further improvement to the general perturbations method is suggested, using spacecraft orbit decay tracking data to inform orbit predictions. The decay data is used to derive the ballistic coefficient input parameter in order to make the method independent from error inthis input. The accuracy of the method including decay data is validated against the original method using historical data. Finally, some applications of the developed methods are presented, including launch window selection, and post operations predictions. The most notable result of the presented applications is, however, in collision risk analysis. A popular de-orbit concept due to its simplicity is drag augmentation, the use of a deployable surface to increase atmospheric friction. Such concepts have received notable attention, with various funding bodies and licensing authorities supporting technology and flight demonstrations, as well as in the specialist and popular media. However, studies lack a full analysis of the implications of increasing projected area on collision risk, focusing principally on time to de-orbit and assuming a direct correlation with collision risk. Using the volume swept (equivalent to area-time product) during de-orbit as a metric for collision risk it is shown that, contrary to the widely held belief, drag augmentation typically increases collision risk. It is shown that if applied in the worst-case scenario, specifically at the wrong time during the solar activity cycle, drag augmentation can increase the collision risk by an order of magnitude. The legal implications of this are briefly considered, and it is shown that spacecraft operators who inappropriately deploy a drag augmentation device could be argued liable for any subsequent on-orbit collision. As such the viability of drag augmentation as a simple, low-cost end-of missionspacecraft removal device is diminished and it is anticipated that licensing authorities need to reconsider future and prior approval to deploy such devices.
Supervisor: Macdonald, Malcolm Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral