Propagation of Forecast Errors from the Sun to LEO Trajectories: How Does Drag Uncertainty Affect Conjunction Frequency?

Atmospheric drag is the largest source of error in the prediction of trajectories of most objects in low-Earth orbit, and solar variability is the largest source of error in upper atmospheric density forecasts. There is thus a need to accurately propagate solar forecast uncertainty to atmospheric density uncertainty and thence to satellite position uncertainty. Furthermore, the collective position uncertainty of the low-Earth Orbit (LEO) population determines the frequency of conjunctions that must be assessed in order to avoid collisions. To maintain Space Situational Awareness of the growing LEO population, the number of conjunctions must be kept at a manageable level to avoid being overwhelmed by false alarms. This criterion can be used to define solar and atmospheric forecast accuracy requirements. In this paper, we examine how solar forecast errors grow with increasing forecast time, and how this uncertainty maps to atmospheric density uncertainty as a function of altitude. We then develop analytical approximations of the mapping from density uncertainty to in-track position uncertainty, as a function of perigee height, orbital eccentricity, ballistic coefficient, background atmospheric conditions, and forecast time. Finally, we estimate the conjunction frequency between operational LEO satellites and the entire LEO population (separately considering objects larger than 10 cm and objects larger than 1 cm), based on the statistical distributions of the key orbital parameters (perigee height, eccentricity, inclination and ballistic coefficient) and assumed solar and density forecast uncertainties. 1
In the Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference, 9-12 Sep 2014, Maui, HI. Supported in part by ONR.