Smooth Bi-Polynominal Interpolation of Jacchia 1971 Atmospheric Densities For Efficient Satellite Drag Computation

Abstract

The atmospheric drag on low-Earth orbiting satellites is one of the dominant forces affecting the spacecraft motion. As the drag depends on the atmospheric density along the spacecraft path, the modeling of the complex properties and dynamics of the Earths atmosphere is a challenging task of modern precision orbit determination. A variety of more or less complicated atmosphere models have been established within the last decades, with typical density differences for different models of about 20% at 300 km height, even increasing at higher altitudes. It is remarkable that the accuracy of empirical drag models has not significantly improved during the past two decades (Marcos et al. 1989). The well-known algorithm of the Jacchia 1971 model is established as a standard and has therefore been used as starting point for the development of a density model, that reproduced the original Jacchia density values over the full altitude and temperature regime to better than 8% while improving the run-time by a factor of 9. To this end a bi-polynomial fit of the density values w.r.t. altitude and exospheric temperature has been performed, that replaces Jacchias numerical integration of the barometric and diffusion equations. The altitude and temperature regimes have been divided in 8 separate sections, where polynomials of order 5 in temperature and 6 height have been obtained using a constrained least-squares fit that assures a smooth variation of the density with varying height. In a similar way a constrained fit of the Helium number density has been performed to compute the seasonal-latitudinal corrections due to Helium. Finally, the developed model is compared to a variety of different density models in terms of density differences and computational effort.