GOCE: Gravitational Gradiometry in a Satellite

  • Reiner Rummel


Spring 2009 the satellite Gravity and steady-state Ocean Circulation Explorer (GOCE), equipped with a gravitational gradiometer, has been launched by European Space Agency (ESA). Its purpose is the detailed determination of the spatial variations of the Earth’s gravitational field, with applications in oceanography, geophysics, geodesy, glaciology, and climatology. Gravitational gradients are derived from the differences between the measurements of an ensemble of three orthogonal pairs of accelerometers, located around the center of mass of the spacecraft. Gravitational gradiometry is complemented by gravity analysis from orbit perturbations. The orbits are thereby derived from uninterrupted and three-dimensional GPS tracking of GOCE.The gravitational tensor consists of the nine second-derivatives of the Earth’s gravitational potential. These nine components can also be interpreted in terms of the local curvature of the field or in terms of components of the tidal field generated by the Earth inside the spacecraft. Four of the nine components are measured with high precision (10 − 11s − 2 per square-root of Hz), the others are less precise. Several strategies exist for the determination of the gravity field at the Earth’s surface from the measured tensor components at altitude. The analysis can be based on one, several or all components; the measurements may be regarded as time series or as spatial data set; recovery may take place in terms of spherical harmonics or other types of global or local base functions. After calibration GOCE entered into its first measurement phase in fall 2009. First results are expected to become available in summer 2010.


European Space Agency Spherical Harmonic Coefficient Star Sensor Gravitational Gradient Tidal Acceleration 
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  1. Albertella A, Rummel R (2009) On the spectral consistency of the altimetric ocean and geoid surface: a one-dimensional example. J Geodesy 83(9):805–815CrossRefGoogle Scholar
  2. Baur O (2007) Die Invariantendarstellung in der Satellitengradiometrie, DGK, Reihe C, Beck, MünchenGoogle Scholar
  3. Baur O, Grafarend EW (2006) High performance GOCE gravity field recovery from gravity gradient tensor invariants and kinematic orbit information. In: Flury J, Rummel R, Reigber Ch, Rothacher M, Boedecker G, Schreiber U (eds) Observation of the earth system from space. Springer, Berlin, pp 239–254CrossRefGoogle Scholar
  4. Baur O, Cai J, Sneeuw N (2009) Spectral approaches to solving the polar gap problem. In: Flechtner F, Mandea M, Gruber Th, Rothacher M, Wickert J, Güntner A, Schöne T (eds) System earth via geodetic-geophysical space techniques. Springer, BerlinGoogle Scholar
  5. Brockmann JM, Kargoll B, Krasbutter I, Schuh WD, Wermuth M (2009) GOCE data analysis: from calibrated measurements to the global earth gravity field. In: Flechtner F, Mandea M, Gruber Th, Rothacher M, Wickert J, Güntner A, Schöne T (eds) System earth via geodetic-geophysical space techniques. Springer, BerlinGoogle Scholar
  6. Bunge H-P, Richards MA, Lithgow-Bertelloni C, Baumgardner JR, Grand SP, Romanowiez BA (1998) Time scales and heterogeneous structure in geodynamic earth models. Science 280:91–95CrossRefGoogle Scholar
  7. Carroll JJ, Savet PH (1959) Gravity difference detection. Aerospace Eng 18:44–47Google Scholar
  8. Colombo O (1989) Advanced techniques for high-resolution mapping of the gravitational field. In: Sansò F, Rummel R (eds) Theory of satellite geodesy and gravity field determination. Lecture notes in earth sciences, vol 25. Springer, Heidelberg, pp 335–369Google Scholar
  9. Eicker A, Mayer-Gürr T, Ilk KH, Kurtenbach E (2009) Regionally refined gravity field models from in- situ satellite data. In: Flechtner F, Mandea M, Gruber Th, Rothacher M, Wickert J, Güntner A, Schöne T (eds) System earth via geodetic-geophysical space techniques. Springer, BerlinGoogle Scholar
  10. ESA (1999a) Introducing the “Living Planet” Programme—The ESA strategy for earth observation. ESA SP-1234. ESA Publication Division, ESTEC, Noordwijk, the NetherlandsGoogle Scholar
  11. ESA (1999b): Gravity field and steady-state ocean circulation mission. Reports for mission selection, SP-1233 (1). ESA Publication Division, ESTEC, Noordwijk, the Netherlands.
  12. ESA (2006) The changing earth—New scientific challenges for ESA’s Living Planet Programme. ESA SP-1304. ESA Publication Division, ESTEC, Noordwijk, the NetherlandsGoogle Scholar
  13. Falk G, Ruppel W (1974) Mechanik, Relativität, Gravitation. Springer, BerlinGoogle Scholar
  14. Freeden W, Gervens T, Schreiner M (1998) Constructive approximation on the sphere. Oxford Science Publications, OxfordzbMATHGoogle Scholar
  15. Ganachaud A, Wunsch C, Kim M-Ch, Tapley B (1997) Combination of TOPEX/POSEIDON data with a hydrographic inversion for determination of the oceanic general circulation and its relation to geoid accuracy. Geophys J Int 128: 708–722CrossRefGoogle Scholar
  16. Hager BH, Richards MA (1989) Long-wavelength variations in Earth’s geoid: physical models and dynamical implications, Phil Trans R Soc Lond A 328:309–327CrossRefGoogle Scholar
  17. Jäggi A (2007) Pseudo-stochastic orbit modelling of low earth satellites using the global positioning system. Geodätisch – geophysikalische Arbeiten in der Schweiz, 73Google Scholar
  18. Johannessen JA, Balmino G, LeProvost C, Rummel R, Sabadini R, Sünkel H, Tscherning CC, Visser P, Woodworth P, Hughes CH, LeGrand P, Sneeuw N, Perosanz F, Aguirre-Martinez M, Rebhan H, Drinkwater MR (2003) The European gravity field and steady-state ocean circulation explorer satellite mission: its impact on geophysics. Surv Geophys 24:339–386CrossRefGoogle Scholar
  19. Kaban MK, Schwintzer P, Reigber Ch (2004) A new isostatic model of the lithosphere and gravity field. J Geodesy 78:368–385CrossRefGoogle Scholar
  20. Kusche J, Klees R (2002) Regularization of gravity field estimation from satellite gravity gradients. J Geodesy 76:359–368CrossRefGoogle Scholar
  21. LeGrand P, Minster J-F (1999) Impact of the GOCE gravity mission on ocean circulation estimates. Geophys Res Lett 26(13):1881–1884CrossRefGoogle Scholar
  22. Lithgow-Bertelloni C, Richards MA (1998) The dynamics of cenozoic and mesozoic plate motions. Rev. Geophys. 36(1):27–78CrossRefGoogle Scholar
  23. Losch M, Sloyan B, Schröter J, Sneeuw N (2002) Box inverse models, altimetry and the geoid; problems with the omission error. J Geophys Res 107(C7):10.1029Google Scholar
  24. Martinec Z (2003) Green’s function solution to spherical gradiometric boundary-value problems. J Geodesy 77:41–49zbMATHCrossRefGoogle Scholar
  25. Marussi A (1985) Intrinsic geodesy. Springer, BerlinGoogle Scholar
  26. Maximenko N, Niiler P, Rio M-H, Melnichenko O, Centurioni L, Chambers D, Zlotnicki V, Galperin B (2009) Mean dynamic topography of the ocean derived from satellite and drifting buoy data using three different techniques. J Atmos Ocean Technol 26:1910–1919CrossRefGoogle Scholar
  27. Migliaccio F, Reguzzoni M, Sansò F (2004) Space-wise approach to satellite gravity field determination in the presence of coloured noise. J Geodesy 78:304–313CrossRefGoogle Scholar
  28. Misner CW, Thorne KS, Wheeler JA (1970) Gravitation. Freeman, San FranciscoGoogle Scholar
  29. Moritz H, Hofmann-Wellenhof B (1993) Geometry, relativity, geodesy. Wichmann, KarlsruheGoogle Scholar
  30. Nutz H (2002) A unified setup of gravitational observables. Dissertation, Shaker Verlag, AachenGoogle Scholar
  31. Ohanian HC, Ruffini R (1994) Gravitation and spacetime. Norton & Comp., New YorkzbMATHGoogle Scholar
  32. Pail R, Plank R (2004) GOCE gravity field processing strategy. Stud Geophys Geod 48:289–309CrossRefGoogle Scholar
  33. Rummel R (1986) Satellite gradiometry. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy. Lecture notes in earth sciences. vol 7. Springer, Berlin, pp 317–363, ISBN (Print) 978-3-540-16809-6, doi:10.1007/BFb0010135Google Scholar
  34. Rummel R, van Gelderen M (1992) Spectral analysis of the full gravity tensor. Geophys J, Int 111:159–169CrossRefGoogle Scholar
  35. Rummel R (1997) Spherical spectral properties of the earth’s gravitational potential and its first and second derivatives. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid. Lecture notes in earth sciences, vol 65. Springer, Berlin, pp 359–404, ISBN 3-540-62636-0Google Scholar
  36. Rummel R, Balmino G, Johannessen J, Visser P, Woodworth P (2002) Dedicated gravity field missions—principles and aims. J Geodyn 33/1–2: 3–20CrossRefGoogle Scholar
  37. Schreiner M (1994) Tensor spherical harmonics and their application in satellite gradiometry. Dissertation, Universität KaiserslauternGoogle Scholar
  38. Stubenvoll R, Förste Ch, Abrikosov O, Kusche J (2009) GOCE and its use for a high-resolution global gravity combination model. In: Flechtner F, Mandea M, Gruber Th, Rothacher M, Wickert J, Güntner A, Schöne T (eds) System earth via geodetic-geophysical space techniques. Springer, BerlinGoogle Scholar
  39. Švehla D, Rothacher M (2004) Kinematic precise orbit determination for gravity field determination. In: Sansò F (ed) The proceedings of the international association of geodesy: a window on the future of geodesy. Springer, Berlin, 181–188Google Scholar
  40. Wells W C (ed) (1984) Spaceborne gravity gradiometers. NASA conference publication 2305, Greenbelt, MDGoogle Scholar
  41. Wunsch C, Gaposchkin EM (1980) On using satellite altimetry to determine the general circulation of the oceans with application to geoid improvement. Rev Geophys 18:725–745CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Reiner Rummel
    • 1
  1. 1.Institut für Astronomische und Physikalische GeodäsieTechnische Universität MünchenMünchenGermany

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