Incorporating solar activity into general perturbations analysis of atmospheric friction

Kerr, Emma and Macdonald, Malcolm (2018) Incorporating solar activity into general perturbations analysis of atmospheric friction. Journal of Guidance, Control and Dynamics, 41 (6). pp. 1320-1336. ISSN 1533-3884 (

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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 new solar 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. These models are combined and applied to a well-known general perturbations method for satellite orbit lifetime analysis, which is first modified using modern mathematical tools to remove simplifications in the derivation. 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. Furthermore, the new method with applied atmospheric and solar activity models is found to compare favorably against other general and special perturbations methods, including third party, 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. A case study, the UKube-1 spacecraft, is presented and it is found that the spacecraft was inserted into an orbit 54km lower than required to comply with best-practice guidelines, and that with 1σ confidence its orbit will decay in June 2028 ± 2 years, and June 2028 ± 4 months if the next solar cycle is an average magnitude cycle.


Kerr, Emma ORCID logoORCID: and Macdonald, Malcolm ORCID logoORCID:;