SCIENCE CHINA Technological Sciences, Volume 61 , Issue 2 : 204-211(2018) https://doi.org/10.1007/s11431-016-9096-6

Atmospheric density determination using high-accuracy satellite GPS data

More info
  • ReceivedOct 25, 2016
  • AcceptedJul 12, 2017
  • PublishedJan 18, 2018


Atmospheric drag is the main source of error in the determination and prediction of the orbit of low Earth orbit (LEO) satellites; however, empirical models that are used to account for this often have density errors of around 15%–30%. Atmospheric density determination has thus become an important topic for researchers. Based on the relationship between the atmospheric drag force and the decay of the semi-major axis of the orbit, we derived atmospheric density along the trajectory of challenging mini-satellite payload (CHAMP) satellite with its rapid science orbit (RSO) data. Three primary parameters—the ratio of cross-sectional area to mass, the drag coefficient, and the decay of the semi-major axis caused by atmospheric drag—were calculated. We also analyse the source of the error and made a comparison between the GPS-derived and reference density. The result for December 2, 2008, showed that the mean error of the GPS-derived density could be decreased from 29.21% to 9.20%, if the time span adopted for the process of computation was increased from 10 min to 50 min. The result for the entire month of December indicated that a density precision of 10% could be achieved, when the time span meets the condition that the amplitude of the decay of the semi-major axis is much greater than its standard deviation.

Funded by

National High Technology Research and Development Program(2015AA7033102B)

State Key Laboratory of Aerospace Dynamics(2016ADL-DW0304)


This work was supported by the National High Technology Research and Development Program (Grant No. 2015AA7033102B) and the State Key Laboratory of Aerospace Dynamics (Grant No. 2016ADL-DW0304).


[1] Jacchia L. New Static Models of the Thermosphere and Exosphere with Empirical Temperature Profiles. SAO Special Report #313, 1970. Google Scholar

[2] Hedin A E. MSIS-86 thermospheric model. J Geophys Res, 1987, 92: 4649-4662 CrossRef ADS Google Scholar

[3] Picone J M, Hedin A E, Drob D P, et al. NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues. J Geophys Res, 2002, 107: SIA 15-1-SIA 15-16 CrossRef ADS Google Scholar

[4] Bowman B R, Kent Tobiska W, Marcos F A, et al. The JB2006 empirical thermospheric density model. J Atmos Sol-Terrestrial Phys, 2008, 70: 774-793 CrossRef ADS Google Scholar

[5] Storz M F, Bowman B R, Branson M J I, et al. High accuracy satellite drag model (HASDM). Adv Space Res, 2005, 36: 2497-2505 CrossRef ADS Google Scholar

[6] King-Hele D G. Methods of determining air density from satellite orbits. Ann Geophys, 1966, 22: 40–52. Google Scholar

[7] King-Hele D G. Satellite Orbits in an Atmosphere: Theory and Application. London: Blackie, 1987. Google Scholar

[8] Bowman B R, Marcos F A, Kendra M J. A method for computing accurate daily atmospheric density values from satellite drag data. In: Space Flight Mechanics Meeting. Maui, 2004. Google Scholar

[9] Hoots F R, Roehrich R L. Models for Propagation of NORAD Element Sets. Spacetrack Report 3, Alexandria, 1988. Google Scholar

[10] Picone J M, Emmert J T, Lean J L. Thermospheric densities derived from spacecraft orbits: Accurate processing of two-line element sets. J Geophys Res, 2005, 110: A03301 CrossRef ADS Google Scholar

[11] Lean J L, Picone J M, Emmert J T, et al. Thermospheric densities derived from spacecraft orbits: Application to the Starshine satellites. J Geophys Res, 2006, 111: A04301. Google Scholar

[12] Cefola P J, Proulx R J, Nazarenko A I, et al. Atmospheric density correction using two line element sets as the observation data. Adv Astronaut Sci, 2003, 116: 1953–1978. Google Scholar

[13] Doornbos E, Klinkrad H, Visser P. Use of two-line element data for thermosphere neutral density model calibration. Adv Space Res, 2008, 41: 1115-1122 CrossRef ADS Google Scholar

[14] Keating G M, Tolson R H, Bradford M S. Evidence of long term global decline in the Earth's thermospheric densities apparently related to anthropogenic effects. Geophys Res Lett, 2000, 27: 1523-1526 CrossRef ADS Google Scholar

[15] Emmert J T, Picone J M, Lean J L, et al. Global change in the thermosphere: Compelling evidence of a secular decrease in density. J Geophys Res, 2004, 109: A02301 CrossRef ADS Google Scholar

[16] Emmert J T, Picone J M, Meier R R. Thermospheric global average density trends, 1967–2007, derived from orbits of 5000 near-Earth objects. Geophys Res Lett, 2008, 35: L05101 CrossRef ADS Google Scholar

[17] Vallado D A. Fundamentals of Astrodynamics and Applications. New York: Spring, 2007. Google Scholar

[18] Cook G E. Satellite drag coefficients. Planet Space Sci, 1965, 13: 929-946 CrossRef ADS Google Scholar

[19] Moe M M, Wallace S D, Moe K. Recommended drag coefficients for aeronomic satellites. Geophys Monogr Ser, 1995, 87: 349–356. Google Scholar

[20] Bowman B R. True satellite ballistic coefficient determination for HASDM. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Monterey, 2002, 774–793. Google Scholar

[21] Emmert J T, Meier R R, Picone J M, et al. Thermospheric density 2002–2004: TIMED/GUVI dayside limb observations and satellite drag. J Geophys Res, 2006, 111: A10S16. Google Scholar

[22] Maley P D, Moore R G, King D J. Starshine: A student tracked atmospheric research satellite deployed from the space shuttle, IAF-99-P.1.01. In: Proceeding of the 50th International Astronautical Federation Congress. Amsterdam, 1999. Google Scholar

[23] Bowman B R, Moe K. Drag coefficient variability at 175–500 km from the orbit decay analysis of spheres, AAS 2005-257. In: AAS/AIAA Astrodynamics Specialist Conference. Lake Tahoe, 2005. Google Scholar

[24] Ren T, Miao J, Liu S, et al. Research on thermospheric densities derived from two-line element sets (in Chinese). Chin J Space Sci, 2014, 34: 426–433. Google Scholar

[25] Bettadpur S. GRACE Product Specification Document, Rev 4.2. Technical Report. Austin: Centre for Space Research, The University of Texas at Austin, 2004. Google Scholar

[26] Sang J, Bennett J C, Smith C H. Estimation of ballistic coefficients of low altitude debris objects from historical two line elements. Adv Space Res, 2013, 52: 117-124 CrossRef ADS Google Scholar

[27] Sang J, Smith C, Zhang K. Towards accurate atmospheric mass density determination using precise positional information of space objects. Adv Space Res, 2012, 49: 1088-1096 CrossRef ADS Google Scholar

  • Figure 1

    Example of cross-sectional area on December 21, 2008.

  • Figure 2

    (Color online) Three possible situations for the decay of the semi-major axis of CHAMP. Red lines are the linear fitting curve with the correction coefficient (denoted by cc) written above.

  • Figure 3

    Time series of CD of CHAMP (top panel) and GRACE-A (bottom panel) provided by the University of Colorado. The CD values are all greater than the common value of 2.1 or 2.2.

  • Figure 4

    Time series of altitude (black line) and change rate of semi-major axis caused by atmospheric drag (red line) for CHAMP on December 21, 2008. The change rate ranges from −2.5×10−4 to −1.0×10−3, so the mean value is −6.25×10−4, corresponding to the minimum time interval of about 48 min.

  • Figure 5

    Mean error of GPS-derived density (black lines) with respect to the reference value (red lines) under different time intervals. The mean error (ME) value is shown at the top left corner.

  • Figure 6

    Comparison of the mean error between the NRLMSISE-00 model (five black lines) and the GPS-derived (other five colored lines) density under different time intervals.

  • Table 1   value of CHAMP from year 2002 to 2008

















  • Table 2   Primary characteristics of the ANDE twin satellites

    ANDE Castor

    ANDE Pollux


    350 km

    350 km








    50 kg

    25 kg

Copyright 2020  CHINA SCIENCE PUBLISHING & MEDIA LTD.  中国科技出版传媒股份有限公司  版权所有

京ICP备14028887号-23       京公网安备11010102003388号