Precision Orbit Derived Total Density

O PERATIONAL orbit determination and orbit prediction experience suggests that the extreme upper atmosphere is more variable than the factors included in atmospheric density models commonly used in orbit propagation. Unmodeled atmospheric density variations can greatly impact the orbit determination process and add kilometers of error to orbit predictions. The motivation for this research is to improve orbit determination and prediction by improving density models and to better measure and understand thermospheric and exospheric density variations, especially variations with time scales shorter than those of the empirical models typically used for atmospheric drag calculations. This paper represents afirst step toward those long-term goals, which will process precision orbit data from multiple satellites simultaneously. Atmospheric density modeling has long been one of the greatest uncertainties in the dynamics of low-Earth-orbit satellites. Accurate density calculations are required to provide meaningful estimates of the atmospheric drag perturbing satellite motion. These effects increase with lower altitude orbits, higher effective area, and lower mass satellites. McLaughlin [1] gave an introduction to the neutral atmosphere and the time varying effects on the density of the thermosphere and exosphere. The effects include diurnal variations, solar rotation, the solar cycle, winds and tides, gravity waves, long-term climate change, and magnetic storms and substorms. The authors hope to increase understanding of the variations in neutral density that are important for satellite drag. Vallado [2] gave an introduction to the basic density variations and to the density models most commonly used in orbit determination. A more comprehensive introduction to the space environment and the neutral atmosphere can be found in Hargreaves [3]. Sabol and Luu [4] gave a summary of the drivers of atmospheric density variations and some of the problems associated with the temporal resolution of various proxies used in empirical density models. Marcos et al. [5] presented an overview of ongoing research to address the inaccuracies in satellite drag modeling. There are two major types of research ongoing to address these problems. The first is dynamic calibration of the atmosphere (DCA) and the second is use of satellites with accelerometers to measure the nonconservative accelerations, including drag. DCA involves estimating density corrections to a given atmospheric density model based upon the observed motion of satellites. The work of Storz et al. [6] and Bowman et al. [7,8] on the High Accuracy Satellite Drag Model (HASDM), Cefola et al. [9], Yurasov et al. [10,11], andWilkins et al. [12,13] are all examples of approaches to provide corrections to atmospheric density models. In each case, the observations from a group of satellites are used to estimate large-scale corrections to an existing atmospheric density model. The approaches have shown the ability to provide a general improvement to a baseline atmospheric density model. The DCA approaches have several disadvantages, however. First, the approaches are designed to run internal to a particular orbit determination scheme. This means that users of other orbit determination schemes have to rely on that system to provide atmospheric density correction updates. In addition, the atmospheric density corrections are only applicable to a certain point in time. Thus, one must have access to the entire archive of density corrections applicable to a given problem. A second limitation of DCA approaches to date is that the corrections have limited spatial and temporal resolution. The corrections do allow the models to better represent effects with temporal resolution of several hours to days, but not temporal effects with shorter time scales.Most dynamic atmospheric density models use a daily solar flux and averaged 3 h geomagnetic indices as input values to address solar and geomagnetic activity. Using these values limits the ability of the models to represent changes in the atmosphere that occur within the averaging interval of the input data. Although the original Russian DCAwork used radar observations, most current DCA approaches use two-line element sets of a large number of low-Earth-orbit objects as observations to develop atmospheric corrections in a DCA scheme. Unfortunately, relying on two-line element sets reduces the accuracy of the corrections and provides limited temporal resolution. HASDM [6–8] relies on the actual radar observations of low-Earthorbit satellites, but even this accuracy is lower than that available from precision orbit ephemerides (POEs) or satellite laser ranging (SLR). In addition, the radar observations are not generally available. The second major type of research related to improving atmospheric density knowledge is using satellites with accelerometers to measure nonconservative forces, which can then be used to estimate density. This represents the opposite extreme from using two-line element sets in terms of accuracy and total data availability. The accelerometer data provide a way to separate the gravitational forces from the nonconservative forces such as drag, solar radiation pressure, and Earth radiation pressure. Then by using accurate radiation pressure models, the drag acceleration can be determined Presented as Paper 2009-6951 at theAIAA/AASAstrodynamics Specialist Conference, Honolulu, HI, 18–21 August 2008; received 12 October 2009; revision received 22 June 2010; accepted for publication 31 July 2010. Copyright © 2010 by Craig A. McLaughlin. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0022-4650/11 and $10.00 in correspondence with the CCC. Assistant Professor, Department of Aerospace Engineering, 2120 Learned Hall, 1530 West 15th Street. Senior Member AIAA. Graduate Research Assistant, Department of Aerospace Engineering; currently Ph.D. Student, University of Alabama in Huntsville. Member AIAA. Graduate Research Assistant, Department of Aerospace Engineering, 2120 Learned Hall, 1530 West 15th Street. Member AIAA. JOURNAL OF SPACECRAFT AND ROCKETS Vol. 48, No. 1, January–February 2011