Journal of Geodesy

, Volume 84, Issue 10, pp 605–624 | Cite as

The celestial mechanics approach: theoretical foundations

  • Gerhard Beutler
  • Adrian Jäggi
  • Leoš Mervart
  • Ulrich Meyer
Original Article

Abstract

Gravity field determination using the measurements of Global Positioning receivers onboard low Earth orbiters and inter-satellite measurements in a constellation of satellites is a generalized orbit determination problem involving all satellites of the constellation. The celestial mechanics approach (CMA) is comprehensive in the sense that it encompasses many different methods currently in use, in particular so-called short-arc methods, reduced-dynamic methods, and pure dynamic methods. The method is very flexible because the actual solution type may be selected just prior to the combination of the satellite-, arc- and technique-specific normal equation systems. It is thus possible to generate ensembles of substantially different solutions—essentially at the cost of generating one particular solution. The article outlines the general aspects of orbit and gravity field determination. Then the focus is put on the particularities of the CMA, in particular on the way to use accelerometer data and the statistical information associated with it.

Keywords

Celestial mechanics Orbit determination Global gravity field modeling CHAMP GRACE 

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References

  1. Altamimi Z, Collilieux X, Legrand J, Garayt B, Boucher C (2007) ITRF2005: a new release of the international terrestrial reference frame based on time series of station positions and Earth orientation parameters. J Geophys Res 112: B09401. doi:10.1029/2007JB004949 CrossRefGoogle Scholar
  2. Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M (1994) Extended orbit modeling techniques at the CODE processing center of the international GPS service for geodynamics (IGS): theory and initial results. Manuscr Geod 19: 367–386Google Scholar
  3. Beutler G (2005) Methods of celestial mechanics. Springer, BerlinGoogle Scholar
  4. Beutler G, Jäggi A, Hugentobler U, Mervart L (2006) Efficient satellite orbit modelling using pseudo-stochastic parameters. J Geod 80(7): 353–372. doi:10.1007/s00190-006-0072-6 CrossRefGoogle Scholar
  5. Beutler G, Jäggi A, Meyer U, Mervart L (2010) The celestial mechanics approach: application to data of the GRACE mission. J Geod. doi:10.1007/s00190-010-0402-6
  6. Biancale R, Balmino G, Lemoine J-M, Marty J-C, Moynot B, Barlier F, Exertier P, Laurain O, Gegout P, Schwintzer P, Reigber C, Bode A, König R, Massmann F-H, Raimondo J-C, Schmidt R, Zhu SY (2000) A new global Earth’s gravity field model from satellite orbit perturbations: GRIM5-S1. Geophys Res Lett 27(22): 3611–3614. doi:10.1029/2000GL011721 CrossRefGoogle Scholar
  7. Dach R, Hugentobler U, Meindl M, Fridez P (eds) (2007) The Bernese GPS Software Version 5.0. Astronomical Institute, University of BernGoogle Scholar
  8. Drinkwater M, Haagmans R, Muzi D, Popescu A, Floberghagen R, Kern M, Fehringer M (2006) The GOCE gravity mission: ESA’s first core explorer. ESA SP-627, ESA Publication Division, pp 1–7Google Scholar
  9. Flechtner F (2005) AOD1B product description document. Technical Report GRACE 327-750, JPL. http://podaac.jpl.nasa.gov/pub/grace/doc/newsletters/GRACE_SDS_NL_0401.pdf
  10. Förste C, Schmidt R, Stubenvoll R, Flechtner F, Meyer U, König R, Meumayer H, Biancale R, Lemoine JM, Bruinsma S, Loyer S, Barthelmes F, Esselborn S (2008) The GeoForschungszentrum Potsdam/Groupe de Recherche de Géodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C. J Geod 82(6): 331–346. doi:10.1007/s00190-007-0183-8 CrossRefGoogle Scholar
  11. Jäggi A, Beutler G, Hugentobler U (2006) Pseudo-stochastic orbit modeling techniques for low-Earth orbiters. J Geod 80(1): 47–60. doi:10.1007/s00190-006-0029-9 CrossRefGoogle Scholar
  12. Jäggi A (2007) Pseudo-stochastic orbit modeling of low Earth satellites using the Global Positioning System. Geodätisch-geophysikalische Arbeiten in der Schweiz, vol 73, Schweizerische Geodätische Kommission, Institut für Geodäsie und Photogrammetrie, Eidg. Technische Hochschule zürich, zürichGoogle Scholar
  13. Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beutler G (2009a) Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J Geod 83(12): 1145–1162. doi:10.1007/s00190-009-0333-2 CrossRefGoogle Scholar
  14. Jäggi A, Beutler G, Prange L, Meyer U, Mervart L, Dach R, Rummel R, Gruber T (2009b) Gravity field determination at AIUB: current activities. EGU General Assembly 2009, EGU2009-8714Google Scholar
  15. Jäggi A, Beutler G, Mervart L (2010a) GRACE gravity field determination using the celestial mechanics approach—first results. In: Mertikas S (ed) Gravity, geoid and Earth observation. Springer, Berlin, pp 177–184. doi:10.1007/978-3-642-10634-7-24
  16. Jäggi A, Beutler G, Meyer U, Mervart L, Prange L, Dach R (2010b) AIUB-GRACE02S—status of GRACE gravity field recovery using the celestial mechanics approach. In: International association of geodesy symposium (accepted)Google Scholar
  17. Kim J (2000) Simulation study of a low-low satellite-to-satellite tracking mission. PhD Dissertation, The University of Texas at AustinGoogle Scholar
  18. Lemoine FG, Smith DE, Kunz L, Smith R, Pavlis NK, Klosko SM, Chinn DS, Torrence MH, Willamson RG, Cox CM, Rachlin KE, Wang YM, Kenyon SC, Salman R, Trimmer R, Rapp RH, Nerem RS (1997) The development of the NASA GSFC and NIMA joint geopotential model. In: Segawa J, Fujimoto H, Okubo S (eds) IAG symposia: gravity, geoid and marine geodesy. Springer, Berlin, pp 461–469Google Scholar
  19. Liu X (2008) Global gravity field recovery from satallite-to-satellite tracking data with the acceleration approach. Publications on Geodesy, Nederlandse Commissie voor Geodesie, Netherlands Geodetic Commission, No 68Google Scholar
  20. Liu X, Ditmar P, Siemes C, Slobbe DC, Revtova E, Klees R, Riva R, Zhao Q (2010) DEOS mass transport model (DMT-1) based on GRACE satellite data: methodology and validation. Geophys J Int. doi:10.1111/j.1365-246X.2010.04533.x
  21. Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: insight from FES2004. Ocean Dyn 56: 394–415CrossRefGoogle Scholar
  22. Mayer-Gürr T, Ilk KH, Eicker A, Feuchtinger M (2005) ITG-CHAMP01: a CHAMP gravity field model from short kinematical arcs of a one-year observation period. J Geod 78: 462–480CrossRefGoogle Scholar
  23. Mayer-Gürr T (2008) Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. Dissertation Schriftenreihe Institut für Geodäsie und Geoinformation No 9, University of BonnGoogle Scholar
  24. McCarthy DD, Petit G (eds) (2003) IERS conventions (2003), international Earth rotation and reference systems service (IERS). IERS Technical Note No. 32, Verlag des Bundesamtes für Karthographie und Geodäsie, Frankfurt am Main, 2004Google Scholar
  25. Montenbruck O, Garcia-Fernandez M, Williams J (2006) Performance comparison of semi-codeless GPS receivers for LEO satellites. GPS Solut 10(4): 249–261. doi:10.1007/s10291-006-0025-9 CrossRefGoogle Scholar
  26. Pail R, Metzler B, Lackner B, Preimesberger T, Höck E, Schuh W-D, Alkathib H, Boxhammer C, Siemes C, Wermuth M (2006) GOCE gravity field analysis in the framework of HPF: operational softwaresystem and simulation results. In: 3rd GOCE User workshop, Frascati, Italy, ESA SP-627, pp 249–256, 6–8 November 2006Google Scholar
  27. Prange L, Jäggi A, Beutler G, Mervart L, Dach R (2009) Gravity field determination at the AIUB—the celestial mechanics approach. In: Sideris MG (ed) observing our changing Earth. Springer, Berlin, pp 353–362. doi:10.1007/978-3-540-85426-5-42
  28. Prange L, Jäggi A, Bock H, Dach R (2010) The AIUB-CHAMP02S and the influence of GNSS model changes on gravity field recovery using spaceborne GPS. Adv Space Res 45(2): 215–224. doi:10.1016/j.asr.2009.09.020 CrossRefGoogle Scholar
  29. Reigber C, Jochmann H, Wünsch J, Petrovic S, Schwintzer F, Barthelmes F, Neumayer K H, König R, Förste C, Balmino G, Biancale R, Lemoine JM, Loyer S, Pérosanz F (2004) Earth gravity field and seasonal variability from CHAMP. In: Reigber C, Schwintzer P, Wickert J (eds) Earth observation from CHAMP—results from three years in orbit. Springer, Berlin, pp 25–30Google Scholar
  30. Seidelmann, PK (eds) (1992) Explanatory supplement to the astronomical almanac. University Science Books, Mill ValleyGoogle Scholar
  31. Strang G, Borre K (1997) Linear algebra, geodesy, and GPS. Wellesley-Cambridge Press, WellesleyGoogle Scholar
  32. Švehla D, Rothacher M (2004) Kinematic precise orbit determination for gravity field determination. In: Sansò F (eds) A window on the future of geodesy. Springer, Berlin, pp 181–188. doi:10.1007/3-540-27432-4-32
  33. Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins M (2004) GRACE measurements of mass variability in the Earth system. Science 305(5683): 503–505CrossRefGoogle Scholar
  34. Tapley BD, Ries J, Bettapour S, Chambers D, Cheng M, Condi F, Gunter B, Kang Z, Nagel P, Pastor R, Pekker T, Poole S, Wang F (2005) GGM02—an improved Earth gravity model from GRACE. J Geod 79: 467–478CrossRefGoogle Scholar
  35. Thomas JB (1999) An analysis of gravity-field estimation based on intersatellite dual-1-way biased ranging JPL Publication 98-15. http://podaac.jpl.nasa.gov/pub/grace/doc/newsletters/GRACE_SDS_NL_0401.pdf
  36. Touboul P, Willemenot E, Foulon B, Josselin V (1999) Accelerometers for CHAMP, GRACE and GOCE space missions: synergy and evolution. Boll Geofis Teor Appl 40: 321–327Google Scholar
  37. Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102: 5005–5017CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Gerhard Beutler
    • 1
  • Adrian Jäggi
    • 1
  • Leoš Mervart
    • 2
  • Ulrich Meyer
    • 1
  1. 1.Astronomical InstituteUniversity of BernBernSwitzerland
  2. 2.Institute of Advanced GeodesyCzech Technical UniversityPrague 6-DejviceCzech Republic

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