IMPROVING AND EXPANDING PRECISION ORBIT DERIVED ATMOSPHERIC DENSITIES

Abstract

Atmospheric drag is the most uncertain non-conservative force acting on a low Earth orbiting satellite. The existing atmospheric density models are not accurate enough to model the variations in density, which significantly affect the drag on satellites since drag is directly proportional to atmospheric density. In this research, precision orbit ephemerides (POE) are used as measurements in an optimal orbit determination scheme to estimate corrections to baseline atmospheric density models. These corrections improve the drag estimates, which in turn improve orbit determination and prediction and also provide a better understanding of the upper atmosphere. The POE are used as measurements in a sequential measurement and filtering scheme using the Orbit Determination Tool Kit (ODTK) software, which provides the orbit determination. Five atmospheric density models are available in ODTK, which are used as baseline atmospheric density models to which corrections are made in the orbit determination. These density models are Jacchia 1971, Jacchia-Roberts, CIRA 1972, MSISE 1990, and NRLMSISE 2000. The user has the option to specify the ballistic coefficient (BC) correlated half-life and density correlated half-life. These half-lives are usually given values of 1.8, 18, or 180 minutes. If all five baseline density models are used along with three different combinations of ballistic coefficient and density correlated half-lives, then this would result in forty-five different cases. All the forty-five cases are examined in some studies and only a selected few are examined in others, the details of which are given in the appropriate sections. The POE derived densities are validated by comparing them with accelerometer derived densities for satellites which have accelerometers onboard, such as the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE). The trend in the variation is compared quantitatively by calculating the cross correlation between the POE and accelerometer derived densities, and the magnitude is compared by calculating the root mean square between the two. The accelerometer derived densities for both CHAMP and GRACE are available from Sean Bruinsma of CNES and also from Eric Sutton of the United States Air Force Research Laboratory, and are used in this research. The effect of different functions of geomagnetic planetary amplitude (ap) as an input in orbit determination to estimate atmospheric density was investigated. The three different functions of input are 3-hourly ap step functions, linear interpolated ap functions, and ap osculating spline functions. These three different types of functions were used as inputs for all the forty-five different combinations obtained by using the five different baseline atmospheric density models and three different combinations of ballistic coefficient and density correlated half-lives as stated earlier, and POE derived density was estimated for both CHAMP and GRACE. The POE derived densities were compared with the accelerometer derived densities by calculating the CC and RMS. To create continuous data sets of POE derived densities that span a period of one week, the linear weighted blending technique was used to blend the 14 hour POE derived densities in their overlap periods. CIRA 1972 was used as the baseline atmospheric density model and a BC correlated half-life of 1.8 minutes and density correlated half-life of 180 minutes were used as inputs in ODTK to generate these POE derived density estimates. These one week continuous POE derived densities showed better correlation with accelerometer derived densities than HASDM densities for both CHAMP and GRACE. The average cross-sectional area of the satellite that is normal to the velocity vector, the area facing the Sun, and the area facing the Earth, were determined so that these areas could be used to estimate the atmospheric drag, the force due to solar radiation pressure, and the force due to Earth radiation pressure (infrared and Earth albedo). This was done for both TerraSAR-X and ICESat. For TerraSAR-X, the area normal to the velocity vector was assumed be a constant and equal to the frontal area, and the area facing the Earth was also assumed to be constant. However, the area facing the Sun varied with time. The average area facing the Sun for a period of 14 hours and also the annual average area were calculated and used to calculate the POE derived densities. The POE derived densities calculated using these two different average areas facing the Sun were found to be very similar. Since TerraSAR-X does not have an accelerometer onboard, the POE derived densities could not be compared with accelerometer derived densities, but instead were compared with Jacchia-71 densities since this was also one of the outputs from ODTK. The POE derived densities were also compared with NRLMSISE 2000 densities. The attitude of ICESat as a function of beta angle was given in the literature and so was the average area of each side of the satellite when it was modeled as a rectangular box with two solar panels. This information was used to estimate the 30-hour average area normal to the velocity vector, area facing the Earth, and area facing the Sun, for ICESat. The POE derived densities using these areas were estimated by ODTK and compared with the Jacchai-71 density model.