Improving the accuracy of general perturbations methods of spacecraft lifetime analysis

Using modern mathematic tool sets, various general perturbations methods such as the methods developed by the authors1,2, by Cook, King-Hele & Walker3 or by Griffin & French4 among others can be enhanced with the development of an average projected area model. A new method of determining the average projected area of a tumbling CubeSat is presented, which improves on the accuracy of the method recommended in Section 6.3 of the ISO standard 27852:2010(E)5. This enhancement can be applied to many different general perturbations methods and due to its simple mathematical nature it allows users to perform rapid Monte-Carlo analyses with thousands of permutations of the problem. Traditional numerical or even semi-analytical solutions would require a much greater length of time to produce an orbit lifetime prediction for a single permutation. 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% to within 5%. The enhancements are seen to outperform the ISO standard consistently and the ISO standard is seen to consistently overestimate the average projected area when considering non-cuboid spacecraft configurations, meaning that when applied to an orbit decay model it will consistently underestimate the orbit lifetime. However its worth lies not only in the improvement in accuracy but also in the time saved when considering space debris analysis or in initial mission design where many parameters may be unknown. In these situations the ability to swiftly provide solutions for thousands of permutations of the problem or to provide a range of predictions based on initial uncertainties and a confidence value for that range is invaluable. The enhanced solution has then been demonstrated using UKube-1 (COSPAR spacecraft identification 2014-037F) as a case study. It can be seen that the new method outperforms the ISO standard, with an error in the average projected area of 8.09% compared to the ISO standards 14.48%.