Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models

  • Ignazio CiufoliniEmail author
  • Erricos C. Pavlis
  • John Ries
  • Rolf Koenig
  • Giampiero Sindoni
  • Antonio Paolozzi
  • Hans Newmayer
Part of the Astrophysics and Space Science Library book series (ASSL, volume 367)


Dragging of Inertial Frames and gravitomagnetism are predictions of Einstein’s theory of General Relativity. Here, after a brief introduction to these phenomena of Einstein’s gravitational theory, we describe the method we have used to measure the Earth’s gravitomagnetic field using the satellites LAGEOS (LAser GEOdynamics Satellite), LAGEOS 2 and the Earth’s gravity models obtained by the spacecraft GRACE. We then report the results of our analysis with LAGEOS and LAGEOS 2, and with a number of GRACE (Gravity Recovery and Climate Experiment) models, that have confirmed this prediction of Einstein General Relativity and measured the Earth’s gravitomagnetic field with an accuracy of approximately 10%. We finally discuss the error sources in our measurement of gravitomagnetism and, in particular, the error induced by the uncertainties in the GRACE Earth gravity models. Here we both analyze the errors due to the static and time-varying Earth gravity field, and in particular we discuss the accuracy of the GRACE-only gravity models used in our measurement. We also provide a detailed analysis of the errors due to atmospheric refraction mis-modelling and to the uncertainties in measuring the orbital inclination. In the appendix, we report the complete error analysis and the total error budget in the measurement of gravitomagnetism with the LAGEOS satellites.


Satellite Laser Range Nodal Rate Gravity Field Model Zonal Harmonic Satellite Laser Range Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We gratefully acknowledge the support of ASI, the Italian Space Agency, grants I/043/08/0 and I/016/07/0.


  1. 1.
    Misner, C.W., Thorne, K.S., and Wheeler, J.A., Gravitation (Freeman, San Francisco, 1973).Google Scholar
  2. 2.
    Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).Google Scholar
  3. 3.
    Ciufolini, I., and Wheeler, J.A., Gravitation and Inertia (Princeton University Press, Princeton, New Jersey, 1995).Google Scholar
  4. 4.
    Will, C.M., Theory and Experiment in Gravitational Physics, 2nd edn (Cambridge Univ. Press, Cambridge, UK, 1993).Google Scholar
  5. 5.
    Will, C.M., The confrontation between general relativity and experiment. Living Rev. Rel. 9, 3 (2006); Scholar
  6. 6.
    Riess, A. et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998).ADSCrossRefGoogle Scholar
  7. 7.
    Perlmutter, S. et al., Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999).ADSCrossRefGoogle Scholar
  8. 8.
    Perlmutter, S., Supernovae, dark energy, and the accelerating universe. Phys. Today, 56, 53–59 (2003).CrossRefGoogle Scholar
  9. 9.
    Caldwell, R.R., Dark energy. Phys. World, 17, 37–42 (2004).Google Scholar
  10. 10.
    Adelberger, E., Heckel, B. and Hoyle, C.D., Testing the gravitational inverse-square law. Phys. World, 18, 41–45 (2005).Google Scholar
  11. 11.
    Amelino-Camelia, G., Ellis, J., Mavromatos, N.E., Nanopoulos, D.V. and Sarkar, S. Potential sensitivity of gamma-ray burster observations to wave dispersion in vacuo. Nature, 393, 763–765 (1998).ADSCrossRefGoogle Scholar
  12. 12.
    Dvali, G., Filtering gravity: modification at large distances? Infrared Modification of Gravity. In Nobel Symp. on Cosmology and String Theory and Cosmology, Proc. of Nobel Symposium 127, Sigtuna, Sweden, 2003 (eds Danielsson, U., Goobar, A. and Nilsson, B.) (World Scientific, Singapore, 2005). (Sigtuna, Sweden, August 2003); preprint at (2004).
  13. 13.
    Ciufolini, I. and Pavlis, E.C., A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature, 431, 958–960 (2004).ADSCrossRefGoogle Scholar
  14. 14.
    Ciufolini, I., Dragging of inertial frames. Nature, 449, 41–47 (2007).ADSCrossRefGoogle Scholar
  15. 15.
    Ries, J.C., Eanes, R.J. and Watkins. M.M., Confirming the frame-dragging effect with satellite laser ranging, 16th International Workshop on Laser Ranging, 13–17 October 2008, Poznan, Poland (2008).Google Scholar
  16. 16.
    Ciufolini, I. et al., The LARES space experiment: LARES orbit, error analysis and satellite structure. In this book: General Relativity and John Archibald Wheeler, eds. Ciufolini, I. and Matzner, R. (Springer Verlag, 2010).Google Scholar
  17. 17.
    Einstein, A., Letter to Ernst Mach. Zurich, 25 June 1913, in ref. [1] p. 544.Google Scholar
  18. 18.
    Mach, E., Die Mechanik in Ihrer Entwicklung Historisch Kritisch-Dargestellt (Brockhaus, Leipzig, 1912); transl. The Science of Mechanics (Open Court, La Salle, Illinois, 1960).Google Scholar
  19. 19.
    Barbour, J. and Pfister, H., eds., Mach’s Principle. From Newton’s Bucket to Quantum Gravity (Birkhauser, Boston, 1995).zbMATHGoogle Scholar
  20. 20.
    For implications of Mach principle and frame-dragging in cosmology see, e.g., chapter 4 of ref. [3] and Schmid, C., Cosmological gravitomagnetism and Machs principle. Phys. Rev. D, 74, 044031–1–18 (2006).Google Scholar
  21. 21.
    Friedländer, B. and Friedländer, I., Absolute und Relative Bewegung? (Simion-Verlag, Berlin, 1896).Google Scholar
  22. 22.
    Föppl, A., Überreinen Kreiselversuch zur messung der Umdrehungsgeschwindigkeit der Erde. Sitzb. Bayer. Akad. Wiss. 34, 5–28 (1904) Phys. Z. 5, 416; see also Föppl, A. Über Absolute und Relative Bewegung. Sitzb. Bayer. Akad. Wiss. 34, 383–95 (1904).Google Scholar
  23. 23.
    de Sitter, W., On Einstein’s theory of gravitation and its astronomical consequences. Mon. Not. Roy. Astron. Soc. 76, 699–728 (1916)ADSGoogle Scholar
  24. 24.
    Lense, J. and Thirring, H., Über den Einfluss der Eigenrotation der Zentralkorper auf die Bewegung der Planeten und Monde nach der Einsteinschen Phys. Z., 19, 156–163 (1918). See also English translation by Mashhoon, B., Hehl, F.W., Theiss, D.S. Gen. Relativ. Gravit., 16, 711–750 (1984).Google Scholar
  25. 25.
    Zeldovich, Ya.B. and Novikov, I.D., Relativistic Astrophysics, Vol. I, Stars and Relativity (Univ. Chicago Press, Chicago, 1971).Google Scholar
  26. 26.
    Landau, L.D. and Lifshitz, E.M., The Classical Theory of Fields, 3rd rev. English edn. (Pergamon, London, 1971).Google Scholar
  27. 27.
    Ciufolini, I. and Ricci, F., Time delay due to spin and gravitational lensing. Classical and Quantum Gravity, 19, 3863–3874 (2002).MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. 28.
    Ciufolini, I. and Ricci, F., Time delay due to spin inside a rotating shell. Classical and Quantum Gravity, 19, 3875–3881 (2002).MathSciNetADSzbMATHCrossRefGoogle Scholar
  29. 29.
    Ciufolini, I., Ricci, F., Kopekin, S. and Mashhoon, B. On the gravitomagnetic time delay. Phys. Lett. A, 308, 101–109 (2003).ADSCrossRefGoogle Scholar
  30. 30.
    Kerr, R.P., Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett., 11, 237–238 (1963).MathSciNetADSzbMATHCrossRefGoogle Scholar
  31. 31.
    Pugh, G.E., Proposal for a satellite test of the coriolis prediction of general relativity. Weapons Systems Evaluation Group Research Memorandum N. 11 (The Pentagon, Washington, 1959).Google Scholar
  32. 32.
    Schiff, L.I., Motion of a gyroscope according to Einstein’s theory of gravitation. Proc. Nat. Acad. Sci., 46, 871–82 (1960) and Possible new test of general relativity theory. Phys. Rev. Lett., 4, 215–7 (1960).Google Scholar
  33. 33.
    Bardeen, J.M. and Petterson, J.A., The Lense-Thirring effect and accretion disks around Kerr Black Holes. Astrophysical J., 195, L65–7 (1975).ADSCrossRefGoogle Scholar
  34. 34.
    Thorne, K.S., Price, R.H. and Macdonald, D.A., The Membrane Paradigm (Yale Univ. Press, NewHaven, 1986).Google Scholar
  35. 35.
    Schäfer, G., Gravitomagnetic effects. J. Gen. Rel. Grav., 36, 2223–2235 (2004).ADSzbMATHCrossRefGoogle Scholar
  36. 36.
    de Sitter, W., On Einstein’s theory of gravitation and its astronomical consequences. Mon. Not. R. Astron. Soc., 76, 699728 (1916).Google Scholar
  37. 37.
    Ashby, N. and Shahid-Saless, B., Geodetic precession or dragging of inertial frames? Phys. Rev. D, 42, 1118–22 (1990).ADSCrossRefGoogle Scholar
  38. 38.
    O’Connel, R.F., A Note on frame dragging. Class. Quant. Grav., 22, 3815–16 (2005).ADSCrossRefGoogle Scholar
  39. 39.
    Ciufolini, I., Frame-dragging, gravitomagnetism and lunar laser ranging, New Astronomy, 15, 332–337 (2010); see also Pavlis, E. and Ciufolini, I., Proc. of 15th International Laser Ranging Workshop, Camberra, Australia, October 16–20 (2006).Google Scholar
  40. 40.
    Bertotti, B., Ciufolini, I. and Bender, P.L., New test of general relativity: measurement of de Sitter geodetic precession rate for lunar perigee. Phys. Rev. Lett., 58, 1062–1065 (1987).MathSciNetADSCrossRefGoogle Scholar
  41. 41.
    Williams, J.G., Turyshev, S.G. and Boggs, D.H., Progress in lunar laser ranging tests of relativistic gravity. Phys. Rev. Lett., 93, 261101–1–4 (2004).Google Scholar
  42. 42.
    Barker, B.M. and O’Connel, R.F., The gravitational interaction: Spin, rotation, and quantum structured Williams, J.G., Newhall, X.X. and Dickey, J.O., Relativity parameters determined from lunar laser ranging. Phys. Rev. D, 53, 6730–6739 (1996).ADSCrossRefGoogle Scholar
  43. 43.
    GRAVITY PROBE-B update at:
  44. 44.
    Weisberg, J.M. and Taylor, J.H., General relativistic geodetic spin precession in binary pulsar B1913 + 16: mapping the emission beam in two dimensions. Astrophys. J., 576, 942–949 (2002).ADSCrossRefGoogle Scholar
  45. 45.
    Stairs, I.H., Thorsett, S.E. and Arzoumanian, Z., Measurement of gravitational spin-orbit coupling in a binary-pulsar system. Phys. Rev. Lett., 93, 141101–1–4 (2004).Google Scholar
  46. 46.
    Murphy, T.W. Jr., Nordtvedt, K. and Turyshev, S.G., Gravitomagnetic influence on gyroscopes and on the lunar orbit. Phys. Rev. Lett., 98, 071102–1–4 (2007).Google Scholar
  47. 47.
    Kopeikin, S.M., Comment on “Gravitomagnetic Influence on Gyroscopes and on the Lunar Orbit”. Phys. Rev. Lett., 98, 229001 (2007).ADSCrossRefGoogle Scholar
  48. 48.
    Murphy, T.W. Jr., Nordtvedt, K. and Turyshev, S.G., Murphy, Nordtvedt, and Turyshev Reply. Phys. Rev. Lett., 98, 229002 (2007).ADSCrossRefGoogle Scholar
  49. 49.
    Barker, B.M. and O’Connel, R.F., The gravitational interaction: Spin, rotation, and quantum effects. A review. Gen. Rel. Grav., 11, 149–175 (1979).Google Scholar
  50. 50.
    Khan, A.R. and O’Connell, R.F., Gravitational analogue of magnetic force. Nature 261, 480–481 (1976).ADSCrossRefGoogle Scholar
  51. 51.
    Ciufolini, I., Gravitomagnetism and status of the LAGEOS III experiment. Class. Quantum Grav., 11, A73–A81 (1994).ADSCrossRefGoogle Scholar
  52. 52.
    The curvature invariants have been calculated using MathTensor, a system for doing tensor analysys by computer, by Parker, L. and Christensen, S.M. (Addison-Wesley, Boston, 1994).Google Scholar
  53. 53.
    Nordtvedt, K., Lunar laser ranging: a comprehensive probe of post-Newtonian gravity. In: Gravitation: from the Hubble Length to the Planck Length, Proc. I SIGRAV School on General Relativity and Gravitation, Frascati, Rome, September 2002 (IOP, 2005) p 97–113.Google Scholar
  54. 54.
    Ciufolini, I., Measurement of the Lense-Thirring drag on high-altitude laser-ranged artificial satellites. Phys. Rev. Lett. 56, 278–281 (1986).ADSCrossRefGoogle Scholar
  55. 55.
    Ciufolini, I., A comprehensive introduction to the Lageos gravitomagnetic experiment: from the importance of the gravitomagnetic field in physics to preliminary error analysis and error budget. Int. J. Mod. Phys. A, 4, 3083–3145 (1989); see also: [56].ADSCrossRefGoogle Scholar
  56. 56.
    Tapley, B., Ries, J.C., Eanes, R.J., and Watkins, M.M., NASA-ASI Study on LAGEOS III, CSR-UT publication n. CSR-89-3, Austin, Texas (1989), and Ciufolini, I., et al., ASI-NASA Study on LAGEOS III, CNR, Rome, Italy (1989). See also: I. Ciufolini et al., INFN study on LARES/WEBER-SAT (2004).Google Scholar
  57. 57.
    Ries, J.C., Simulation of an experiment to measure the Lense-Thirring precession using a second LAGEOS satellite, Ph.D. dissertation. The University of Texas, Austin (1989).Google Scholar
  58. 58.
    Ciufolini, I., On a new method to measure the gravitomagnetic field using two orbiting satellites. Nuovo Cimento A, 109, 1709–1720 (1996).ADSCrossRefGoogle Scholar
  59. 59.
    Ciufolini, I. et al., Measurement of dragging of inertial frames and gravitomagnetic field using laser-ranged satellites. Nuovo Cimento A, 109, 575–590 (1996).ADSCrossRefGoogle Scholar
  60. 60.
    Ciufolini, I., Chieppa, F., Lucchesi, D. and Vespe, F., Test of Lense-Thirring orbital shift due to spin. Class. and Quantum Grav., 14, 2701–2726 (1997). See also: Ciufolini, I., Lucchesi, D., Vespe, F., and Chieppa, F., Measurement of gravitomagnetism. Europhys. Lett., 39, 359–364 (1997).Google Scholar
  61. 61.
    Ciufolini, I., Pavlis, E.C., Chieppa, F., Fernandes-Vieira, E. and Perez-Mercader, J., Test of general relativity and measurement of the Lense-Thirring effect with two Earth satellites. Science, 279, 2100–2103 (1998).ADSCrossRefGoogle Scholar
  62. 62.
    Cohen, S.C. and Dunn, P.J., eds., LAGEOS Scientific Results. J. Geophys. Res., 90 (B11), 9215 (1985).ADSCrossRefGoogle Scholar
  63. 63.
    Bender P. and Goad, C.C., The use of satellites for geodesy and geodynamics, in: Veis, G., Livieratos, E. (Eds.), Proceedings of the Second International Symposium on the Use of Artificial Satellites for Geodesy and Geodynamics, Vol. II. National Technical University of Athens, p. 145 (1979).Google Scholar
  64. 64.
    Reigber, Ch., Schwintzer, P., Neumayer, K.-H., Barthelmes, F., König, R., Förste, Ch., Balmino, G., Biancale, R., Lemoine, J.-M., Loyer, S., Bruinsma, S., Perosanz, F. and Fayard, T., The CHAMP-only Earth Gravity Field Model EIGEN-2. Advan. Space Res., 31(8), 1883–1888 (2003), doi: 10.1016/S0273–1177(03)00162–5.ADSCrossRefGoogle Scholar
  65. 65.
    Reigber, C., Schmidt, R., Flechtner, F., Koenig, R., Meyer, U., Neumayer, K.H., Schwintzer, P. and Zhu, S.Y., An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. Geodynamics, 39, 1–10 (2005). The EIGEN-GRACE02S gravity field coefficients and their calibrated errors are available at:
  66. 66.
    Förste, C., Flechtner, F., Schmidt, R., Stubenvoll, R., Rothacher, M., Kusche, J., Neumayer, K.-H., Biancale, R., Lemoine, J.-M., Barthelmes, F., Bruinsma, J., Koenig, R., Meyer, U., EIGEN-GL05C – A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. General Assembly European Geosciences Union, Vienna, Austria, 2008, J. Geophys. Res. Abstracts, 10, No. EGU2008-A-06944 (2008).Google Scholar
  67. 67.
    Förste, C., Schmidt, R., Stubenvoll, R., Flechtner, F., Meyer, U., Konig, R., Neumayer, H., Biancale, R., Lemoine, J.-M., Bruinsma, S., Loyer, S., Barthelmes, F. and Esselborn, S., The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C. J. Geodesy, 82, 6, 331–346 (2008).ADSCrossRefGoogle Scholar
  68. 68.
    Förste, C., Flechtner, F., Schmidt, R., Meyer, U., Stubenvoll, R., Barthelmes, F., Köenig, R., Neumayer, H., Rothacher, M., Reigber, Ch. Biancale, R., Bruinsma, S., Lemoine, J.M., Raimondo, J.C., A New High Resolution Global Gravity Field Model Derived From Combination of GRACE and CHAMP Mission and Altimetry/Gravimetry Surface Gravity Data. EGU General Assembly 2005, Vienna, Austria, 24–29, April 2005.Google Scholar
  69. 69.
    Tapley, B., Ries, J., Bettadpur, S., Chambers, D., Cheng, M., Condi, F., Gunter, B., Kang, Z., Nagel, P., Pastor, R., Pekker, T., Poole, S., and Wang, F., GGM02 An improved Earth gravity field model from GRACE. J. Geod., 79, 467–478 (2005). The GGM02 gravity model is available at: ADSCrossRefGoogle Scholar
  70. 70.
    Tapley, B., Ries, J., Bettadpur, S., Chambers D., Cheng, M., Condi, F., Poole, S., The GGM03 Mean Earth Gravity Model from GRACE. Eos Trans. AGU 88(52), Fall Meet.Suppl., Abstract G42A-03 (2007).Google Scholar
  71. 71.
    Mayer-Guerr, T., Eicker, A., Ilk, K.H., ITG-Grace02s: A GRACE Gravity Field Derived from Short Arcs of the Satellites Orbit. Proc. of the 1st International Symposium of the International Gravity Field Service “Gravity Field of the Earth”, Istanbul (2007).Google Scholar
  72. 72.
    Mayer-Guerr, T., ITG-Grace03s: The latest GRACE gravity field solution computed in Bonn. presentation at GSTM + SPP, 15–17 Oct 2007, Potsdam.Google Scholar
  73. 73.
    The JEM models were provided by JPL-Caltech.Google Scholar
  74. 74.
    International Earth Rotation Service (IERS) Annual Report, 1996. Observatoire de Paris, Paris (July 1997).Google Scholar
  75. 75.
    Rubincam, D.P., Yarkovsky thermal drag on LAGEOS. J. Geophys. Res., 93 (B11), 13803–13810 (1988).ADSCrossRefGoogle Scholar
  76. 76.
    Rubincam, D.P., Drag on the LAGEOS satellite. J. Geophys. Res., 95 (B11), 4881–4886 (1990).ADSCrossRefGoogle Scholar
  77. 77.
    Rubincam, D.P., and Mallama, A. Terrestrial atmospheric effects on satellite eclipses with application to the acceleration of LAGEOS. J. Geophys. Res., 100 (B10), 20285–20990 (1995).ADSCrossRefGoogle Scholar
  78. 78.
    Martin, C.F., and Rubincam, D.P., Effects of Earth albedo on the LAGEOS I satellite. J. Geophys. Res., 101 (B2), 3215–3226 (1996).ADSCrossRefGoogle Scholar
  79. 79.
    Andrès, J.I. et al., Spin axis behavior of the LAGEOS satellites. J. Geophys. Res., 109, B06403–1–12 (2004).Google Scholar
  80. 80.
    Gross, R.S., Combinations of Earth orientation measurements: SPACE94, COMB94, and POLE94. J. Geophys. Res., 101 (B4), 8729–8740 (1996).ADSCrossRefGoogle Scholar
  81. 81.
    Pavlis, D.E. et al., GEODYN operations manuals, contractor report, Raytheon, ITSS, Landover MD (1998).Google Scholar
  82. 82.
    Ries, J.C., Eanes R.J. and Tapley, B.D., Lense-Thirring precession determination from laser ranging to artificial satellites. In: Nonlinear Gravitodynamics, the Lense-Thirring Effect, Proc. III William Fairbank Meeting (World Scientific, Singapore, 2003) pp. 201–211.Google Scholar
  83. 83.
    Ciufolini, I., Frame-dragging and its measurement. In: Gravitation: from the Hubble Length to the Planck Length, Proc. I SIGRAV School on General Relativity and Gravitation, Frascati, Rome, September 2002 (IOP, 2005) pp. 27–69.Google Scholar
  84. 84.
    Ciufolini, I., Theory and experiments in general relativity and other metric theories, Ph.D. Dissertation, Univ. of Texas, Austin (Pub. Ann Arbor, Michigan, 1984).Google Scholar
  85. 85.
    Peterson, G.E., Estimation of the Lense-Thirring precession using laser-ranged satellites. Ph. Dissertation, Univ. of Texas, Austin, (1997).Google Scholar
  86. 86.
    Ries, J.C., Eanes, R.J., Tapley, B.D. and Peterson, G.E., Prospects for an improved Lense-Thirring test with SLR and the GRACE gravity mission. In: Toward Millimeter Accuracy Proc. 13th Int. Laser Ranging Workshop, Noomen, R., Klosko, S., Noll, C. and Pearlman, M. eds., (NASA CP 2003212248, NASA Goddard, Greenbelt, MD, 2003).Google Scholar
  87. 87.
    Pavlis, E.C., Geodetic contributions to gravitational experiments in space. In: Recent Developments in General Relativity, Genoa 2000, R. Cianci, et al., eds. (Springer-Verlag, Milan, 2002) pp. 217–233.CrossRefGoogle Scholar
  88. 88.
    Rubincam, D.P., General relativity and satellite orbits: the motion of a test particle in the Schwarzschild metric. Celest. Mech., 15, 21–33 (1977).ADSCrossRefGoogle Scholar
  89. 89.
    Cugusi, L. and Proverbio, E., Relativistic effects on the motion of Earth’s artificial satellites. Astron. Astroph., 69, 321–325 (1978).ADSGoogle Scholar
  90. 90.
    Yilmaz, H., Proposed test of the nature of gravitational interaction. Bull. Am. Phys. Soc., 4, 65 (1959).Google Scholar
  91. 91.
    Van Patten, R.A., Everitt, C.W.F., Possible Experiment with two counter–orbiting drag–free satellites to obtain a new test of Einstein’s general theory of relativity and improved measurements in geodesy. Phys. Rev. Lett., 36, 629–32 (1976).ADSCrossRefGoogle Scholar
  92. 92.
    Ciufolini, I., Paolozzi, A., et al., LARES phase A study for ASI (1998).Google Scholar
  93. 93.
    Lucchesi, D.M., Reassessment of the error modelling of non–gravitational perturbations on LAGEOS 2 and their impact in the Lense–Thirring determination. Part I. Planet. Space Sci., 49, 447–463 (2001).ADSCrossRefGoogle Scholar
  94. 94.
    Pavlis, E.C. and Iorio, L., The impact of tidal errors on the determination of the Lense-Thirring effect from satellite laser ranging. Int. J. Mod. Phys. D, 11, 599–618 (2002).ADSCrossRefGoogle Scholar
  95. 95.
    Lemoine, F.G., Kenyon, S.C., Factor, J.K., Trimmer, R.G., Pavlis, N.K., Chinn, D.S., Cox, C.M., Klosko, S.M., Luthcke, S.B., Torrence, M.H., Wang, Y.M., Williamson, R.G., Pavlis, E.C., Rapp, R.H. and Olson, T.R., The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, Maryland (July 1998).Google Scholar
  96. 96.
    NRC, Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and Its Fluid Envelope (National Academy Press, Washington D.C., 1997).Google Scholar
  97. 97.
    Pavlis, E.C., Improvements to geodesy from gradiometers and drag-free satellites. In: Proc. 1st W. Fairbank Memorial Conference on Gravitational Relativistic Experiments in Space, M. Demianski and C.W.F. Everitt, eds., (World Scientific, 1993).Google Scholar
  98. 98.
    Reigber, Ch., Flechtner, F., Koenig, R., Meyer, U., Neumayer, K., Schmidt, R., Schwintzer, P., and Zhu, S., GRACE Orbit and Gravity Field Recovery at GFZ Potsdam – First Experiences and Perspectives. Eos. Trans. AGU, 83(47), Fall Meet. Suppl., Abstract G12B-03 (2002).Google Scholar
  99. 99.
    Perosanz, F., Loyer, S., Lemoine, J.M.L., Biancale, R., Bruinsma, S. and Vales, N., CHAMP accelerometer evaluation on two years mission. Geophys. Res. Abstracts, 5 (CD), Abstract EAE03-A-06989 (2003).Google Scholar
  100. 100.
    Tapley, B.D., The GRACE mission: status and performance assessment. Eos. Trans. AGU, 83(47), Fall Meet. Suppl., Abstract G12B-01 (2002).Google Scholar
  101. 101.
    Watkins, M.M., Yuan, D., Bertiger, W., Kruizinga, G., Romans, L. and Wu, S., GRACE gravity field results from JPL. Eos. Trans. AGU, 83(47), Fall Meet. Suppl., Abstract G12B-02 (2002).Google Scholar
  102. 102.
    Rummel, R., GOCE – its status and promise. Geophys. Res. Abstracts, Vol. 5 (CD), Abstract EAE03-A-09628 (2003).Google Scholar
  103. 103.
    Kaula, W.M., Theory of Satellite Geodesy, (Blaisdell, Waltham, 1966).Google Scholar
  104. 104.
    Lucchesi, D.M., Reassessment of the error modelling of non-gravitational perturbations on LAGEOS 2 and their impact in the Lense–Thirring determination. Part II. Planet. Space Sci., 50, 1067–1100 (2002).ADSCrossRefGoogle Scholar
  105. 105.
    Yoder, C.F., Williams, J.G., Dickey, J.O., Schutz, B.E., Eanes, R.J. and Tapley, B.D., Secular variations of Earth’s gravitational harmonic J2 coefficient from Lageos and nontidal acceleration of Earth rotation. Nature, 303, 757–62 (1983).ADSCrossRefGoogle Scholar
  106. 106.
    Cheng, M.K., Shum, C.K. and Tapley, B., Determination of long-term changes in the Earth’s gravity field from satellite laser ranging observations. J. Geophys Res., 102 (B10), 22377–22390 (1997).ADSCrossRefGoogle Scholar
  107. 107.
    Cheng, M.K. and Tapley, B.D., Temporal variations in J2 from analysis of SLR data. In: Proc. 12th International Workshop on Laser Ranging (2000).Google Scholar
  108. 108.
    Cheng M.K. and Tapley B.D., Variations in the Earth’s oblateness During the Past 28 years. J. Geophys. Res., 109, B09402 (2004) doi: 10,1029/2004JB003028.ADSCrossRefGoogle Scholar
  109. 109.
    Cheng, M.K., Tapley, B.D., Secular variations in the low degree zonal harmonics from 28 years of SLR data. Eos Trans. AGU, 85(47), Fall Meet. Suppl., Abstract G31C-0801.Google Scholar
  110. 110.
    Ciufolini, I. and Pavlis, E.C., On the Measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to “On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites” by L. Iorio. New Astr., 10, (8), 636–651 (2005).Google Scholar
  111. 111.
    Cox, C.M., Klosko, S.M. and Chao, B.F., Changes in Ice-Mass Balance inferred from time variation of the geopotential observed through SLR and Doris tracking. In: Gravity, Geoid and Geodynamics 2000, International Association of Geodesy (IAG) Symposia Vol. 123, M.G. Sideris, ed. (Springer, 2000).Google Scholar
  112. 112.
    Devoti, R., Luceri, V., Rutigliano, P., Sciappreta, C. and Bianco, G., Time series of low degree zonals obtained analyzing different geodetic satellites. Bollettino di Geofisca Teorica ed Applicata, 40, 353–358, (1999).Google Scholar
  113. 113.
    Pavlis, E.C., Dynamical Determination of Origin and Scale in the Earth System from Satellite Laser Ranging. In: Vistas for Geodesy in the New Millennium, Proc. 2001 International Association of Geodesy Scientific Assembly, Budapest, Hungary, September 2–7, 2001, J. Adam and K.P. Schwarz, eds. (Springer-Verlag, New York, 2002) pp. 36–41.Google Scholar
  114. 114.
    Schmidt, R., Flechtner, F., Koenig, R., Meyer, U., Neumayer, K.H., Schwintzer, P., Zhu, S.Y., An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J. Geodyn., 39, 1–10 (2005).CrossRefGoogle Scholar
  115. 115.
    Tapley, B.D. et al., Lageos Laser Ranging Contributions to Geodynamics, Geodesy and Orbital Dynamics. In: Contributions of Space Geodesy to Geodynamics: Earth Dynamics. Geodyn. Ser., 24, 147–174, D.E. Smith and D.L. Turcotte, eds., AGU Washington, D.C. (1993).Google Scholar
  116. 116.
    Tapley, B.D., Chambers, D.P., Bettadpur, S., and Ries, J.C., Large scale ocean circulation from the GRACE GGM01 geoid. Geophys. Res. Lett., 30 (22), 2163 (2003)–1–4 doi: 10.1029/2003GL018622.Google Scholar
  117. 117.
    Cazenave, A., Geogut, P. and Ferhat, G., Secular variations of the gravity field from Lageos 1, Lageos2 and Ajisai. In: Global Gravity Fields and its temporal variations, Int. Assoc. of. Geod. Symp., Vol. 116 (Springer-Verlag, New York, 1996) p 141–151.Google Scholar
  118. 118.
    Cheng, M.K., Eanes, R.J., Shum, C.K., Schutz, B.E. and Tapley, B.D., Temporal variation in low degree zonal harmonics from starlette orbit analysis. Geophys. Res. Lett., 16, 393–396, (1989)ADSCrossRefGoogle Scholar
  119. 119.
    Cheng, M.K., Eanes, R.J., Shum, C.K., Time-varying gravitational effects from analysis off measurements from geodetic satellite. EoS Trans. AGU, 74(43), Fall Meet., Suppl., 196 (1993)Google Scholar
  120. 120.
    Eanes, R.J. and Battadpur, S., Temporal variability of Earth’s gravitational field from satellite laser ranging observations. In: Global Gravity Field and its Temporal Variations, Int. Assoc. of Geod. Symp., Vol. 116, 30–41 (Springer-Verlag, New York, 1996).Google Scholar
  121. 121.
    Gegout, P., and Cazenave, A., Geodynamic parameters derived from 7 years of laser data on Lageos. Geophys. Res. Lett., 18, 1729–1742 (1991).ADSCrossRefGoogle Scholar
  122. 122.
    Ivins, E.R., Sammis, C.G. and Yoder, C.F., Deep mantle viscous structure with prior estimate and satellite constraint. J. Geophys. Res., 98, 4579–4609 (1993).ADSCrossRefGoogle Scholar
  123. 123.
    Mitrovica, J.X. and Peltier, W.R., Present-day secular variations in the zonal harmonics of Earth’s geopotential. J. Geophys. Res., 98, 4509–4526 (1993).ADSCrossRefGoogle Scholar
  124. 124.
    Nerem, R.S., and Klosko, S.M., Secular variations of the zonal harmonics and polar motion as geophysical constraints. In: Global Gravity Field and its Temporal Variations, Int. Assoc. of Geod. Symp. Vol. 116, 152–163 (Springer-Verlag, New York, 1996).Google Scholar
  125. 125.
    Nerem, R.S., Chao, A.Y., Chan, J.C., Klosko, S.M., Pavlis, N.K. and Williamson, R.G., Temporal variations of the Earth’s gravitational field from satellite laser ranging to Lageos. J. Geophys. Res. Lett., 20, 595–598 (1993).ADSCrossRefGoogle Scholar
  126. 126.
    Rubincam, D.P., Postglacial rebound observed by Lageos and the effective viscosity of the Lower mantle. J. Geophys. Res., 89, 1077–1087 (1984).ADSCrossRefGoogle Scholar
  127. 127.
    Trupin, A., Meier, M.F. and Wahr, J., Effects of the melting glaciers on the Earth’s rotation and gravity field: 1965–1984. Geophys. J. Int., 108, 1–15 (1992).ADSCrossRefGoogle Scholar
  128. 128.
    Cox, C.M. and Chao, B., Detection of a large-scale mass redistribution in the terrestrial system since 1998. Science, 297, 831 (2002).ADSCrossRefGoogle Scholar
  129. 129.
    Ciufolini, I., Pavlis, E.C. and Peron, R., Determination of frame-dragging using Earth gravity models from CHAMP and GRACE. New Astron., 11, 527–550 (2006).ADSCrossRefGoogle Scholar
  130. 130.
    Eanes, R.J., A study of temporal variations in Earth’s gravitational field using Lageos-1 laser ranging observations. Ph. D. dissertation, Univ. of Texas at Austin (1995)Google Scholar
  131. 131.
    Iorio, L., On the impact of the atmospheric drag on the LARES mission, arXiv:0809.3564v2, see also: arXiv:0809.3564v1 (2008).Google Scholar
  132. 132.
    Iorio, L., Will the recently approved LARES mission be able to measure the Lense-Thirring effect at 1 %? Gen. Relativ. Gravit. 41, 1717–1724 (2009) doi: 10.1007/s10714-008-0742-1; see also: arXiv:0803.3278v5 [gr-qc] (2008).ADSzbMATHCrossRefGoogle Scholar
  133. 133.
    Iorio, L., An assessment of the systematic uncertainty in present and future tests of the Lense-Thirring effect with satellite laser ranging. Space Sci. Rev. 148, 363–381 (2009); see also: arXiv:0809.1373v2 [gr-qc] (2008).ADSCrossRefGoogle Scholar
  134. 134.
    Iorio, L., On some critical issues of the LAGEOS/LAGEOS II Lense-Thirring experiment. arXiv:0710.1022v1 [gr-qc].Google Scholar
  135. 135.
    Ciufolini, I., Paolozzi, A., Pavlis, E.C., Ries, J.C., Koenig, R., Matzner, R.A., Sindoni G., and Neumayer, H. Towards a one percent measurement of frame-dragging by spin with satellite laser ranging to LAGEOS, LAGEOS 2 and LARES and GRACE gravity models. Space Sci. Rev., 148, 71–104 (2009).ADSCrossRefGoogle Scholar
  136. 136.
    Lucchesi, D.M., The impact of the even zonal harmonics secular variations on the Lense-Thirring effect measurement with the two Lageos satellites. Int. J. of Mod. Phys. D, 14, 1989–2023 (2005).ADSzbMATHCrossRefGoogle Scholar
  137. 137.
    Ciddor, P.E., Refractive index of air: New equations for the visible and near infrared. Applied Optics, 35, 1566–1573 (1996).ADSCrossRefGoogle Scholar
  138. 138.
    Hulley, G.C. and Pavlis, E.C., A ray-tracing technique for improving Satellite Laser Ranging atmospheric delay corrections, including the effects of horizontal refractivity gradients. J. Geophys. Res., 112, B06417–1-19 (2007), doi:10.1029/2006JB004834.Google Scholar
  139. 139.
    Mendes, V.B., Prates, G., Pavlis, E.C., Pavlis, D.E. and Langley, R.B., Improved mapping functions for atmospheric refraction correction in SLR. Geophysical Res. Lett., 29, 1414–1-4 (2002), doi:10.1029/2001GL014394.Google Scholar
  140. 140.
    Mendes, V.B. and Pavlis, E.C., High-accuracy zenith delay prediction at optical wavelengths. Geophys. Res. Lett., 31, L14602–1-5 (2004), doi:10.1029/2004GL020308.Google Scholar
  141. 141.
    Tapley, B.D., Bettadpur, S., Watkins, M., and Reigber, C., The gravity recovery and climate experiment: Mission overview and early results. Geophysical Res. Lett., 31, L09607 (2004) doi: 10.1029/2004GL019920.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Ignazio Ciufolini
    • 1
    Email author
  • Erricos C. Pavlis
    • 2
  • John Ries
    • 3
  • Rolf Koenig
    • 3
  • Giampiero Sindoni
    • 4
  • Antonio Paolozzi
    • 4
  • Hans Newmayer
    • 3
  1. 1.Dip. Ingegneria dell’InnovazioneUniversità del Salento and INFN Sezione di LecceLecceItaly
  2. 2.Joint Center for Earth Systems TechnologyUniversity of Maryland, Baltimore CountyMarylandUSA
  3. 3.Center for Space ResearchUniversity of Texas at AustinAustinUSA
  4. 4.GFZ German Research Centre for GeosciencesPotsdamGermany

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