Propagation of atmospheric density errors to satellite orbits

We develop and test approximate analytic expressions relating time-dependent atmospheric density errors to errors in the mean motion and mean anomaly orbital elements. The mean motion and mean anomaly errors are proportional to the first and second integrals, respectively, of the density error. This means that the mean anomaly (and hence the in-track position) error variance grows with time as t3 for a white noise density error process and as t5 for a Brownian motion density error process. Our approximate expressions are accurate over a wide range of orbital configurations, provided the perigee altitude change is less than ∼0.2 atmospheric scale heights. For orbit prediction, density forecasts are driven in large part by forecasts of solar extreme ultraviolet (EUV) irradiance; we show that errors in EUV ten-day forecasts (and consequently in the density forecasts) approximately follow a Brownian motion process.