# Orbital Lifetime Predictions

Orbital Lifetime Predictions: An assessment of model-based ballistic coefficient estimations and adjustment for temporal drag coefficient variations

Author Contributor Faculty Department Date2017-06-01

AbstractThe ballistic coefficient β of a satellite indicates the influence atmospheric drag has on the orbital decay of said satellite. The method developed in this study estimates the ballistic coefficients of 1U CubeSats by analysing both its historical TLE data and the density it experienced along its trajectory according to the empirical density model NRLMSISE-00. In parallel the same is done for a spherical satellite with an already known ballistic coefficient, given the object is experiencing near-similar atmospheric conditions as that of the CubeSat. Any density error associated with NRLMSISE-00 along that trajectory is consecutively largely mitigated, resulting in an improved model-dependent estimated ballistic coefficient for the CubeSat. This procedure is iterated upon with a batch of 60+ CubeSats, leading to a single procedure capable of estimating the ballistic coefficient of a large group of objects. The estimated β are consecutively adjusted for the epoch- and altitude-dependent drag coefficient, performed analytically as a function of ambient gas-composition and spacecraft geometry. Additionally, an investigation in the computation of the energy accommodation coefficient α, an essential variable for the CD computation, is performed, assessing whether a constant α = 0.8 can be assumed or if Langmuir’s adsorption model based on the ambient presence of atomic oxygen wouldn’t be more suited. When subjecting the estimated and adjusted β values to a propagator build in TUDAT, based on Runge-Kutta-Fehlberg 7(8), and comparing them to their actual orbits, prediction improvements of up to 40% are observed compared to regular non-adjusted β values for CubeSats re-entering the atmosphere. For CubeSats orbiting Earth above 500 km, improvements between 5% and 15% are observed. The research furthermore highlighted the sensitivity of the iterative process and the orbital element selection criteria through which satellite pairs are assumed to have near-similar atmospheric conditions – the tighter the selection criteria the better the quality of the β estimations were, though at the cost of fewer β estimations to occur. Overall, it can be concluded that the β estimation method can be applied on a scale covering multiple satellites, potentially growing to a global ballistic coefficient estimation model which could also include space debris. Improvements to orbital lifetime predictions are primarily seen in the lower parts of LEO. Furthermore, the adjustment for the variable drag coefficient proved most useful for the CubeSats above 500 km, given Langmuir’s adsorption model was used. For the lower orbits, Langmuir’s adsorption model lost its accuracy and an adaptation of Langmuir’s model which considers an object’s historical orbit data is suggested.

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