General perturbations methods for orbit propagation with particular application to orbit lifetime analysis

  • Emma Kerr

Student thesis: Doctoral Thesis


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 furthe
Date of Award8 Jan 2019
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorMalcolm Macdonald (Supervisor) & James Biggs (Supervisor)

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