A confirmation of the general relativistic prediction of the Lense–Thirring effect

Article metrics


An important early prediction of Einstein's general relativity1,2,3 was the advance of the perihelion of Mercury's orbit, whose measurement provided one of the classical tests of Einstein's theory4. The advance of the orbital point-of-closest-approach also applies to a binary pulsar system5,6 and to an Earth-orbiting satellite3. General relativity also predicts that the rotation of a body like Earth will drag the local inertial frames of reference around it3,7, which will affect the orbit of a satellite8. This Lense–Thirring effect has hitherto not been detected with high accuracy9, but its detection with an error of about 1 per cent is the main goal of Gravity Probe B—an ongoing space mission using orbiting gyroscopes10. Here we report a measurement of the Lense–Thirring effect on two Earth satellites: it is 99 ± 5 per cent of the value predicted by general relativity; the uncertainty of this measurement includes all known random and systematic errors, but we allow for a total ± 10 per cent uncertainty to include underestimated and unknown sources of error.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: The ‘orbital gyroscope’ used to measure the Lense–Thirring effect.
Figure 2: Observed orbital residuals of the LAGEOS satellites.
Figure 3: Post-fit orbital residuals of the LAGEOS satellites.


  1. 1

    Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973)

  2. 2

    Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972)

  3. 3

    Ciufolini, I. & Wheeler, J. A. Gravitation and Inertia (Princeton Univ. Press, Princeton, New Jersey, 1995)

  4. 4

    Will, C. M. Theory and Experiment in Gravitational Physics 2nd edn (Cambridge Univ. Press, Cambridge, UK, 1993); The confrontation between general relativity and experiment. 〈http://relativity.livingreviews.org/Articles/lrr-2001-4/〉 (2001)

  5. 5

    Hulse, R. A. & Taylor, J. H. Discovery of a pulsar in a binary system. Astrophys. J. 195, L51–L53 (1975)

  6. 6

    Nordtvedt, K. Existence of the gravitomagnetic interaction. Int. J. Theor. Phys. 27, 1395–1404 (1988)

  7. 7

    Thorne, K. S., Price, R. H. & Macdonald, D. A. The Membrane Paradigm (Yale Univ. Press, New Haven, 1986)

  8. 8

    Lense, J. & Thirring, H. Uber den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z. 19, 156–163 (1918)

  9. 9

    Ciufolini, I. in A Relativistic Spacetime Odyssey, Proc. 25th Johns Hopkins Workshop on Current Problems in Particle Theory (eds Ciufolini, I., Dominici, D. & Lusanna, L.) 99–139 (World Scientific, Singapore, 2003)

  10. 10

    Fitch, V. L. et al. Review of Gravity Probe B (National Academic Press, Washington DC, 1995)

  11. 11

    Williams, J. G., Boggs, D. H., Dickey, J. O. & Folkner, W. M. in Proc. 9th Marcel Grossmann Meeting (eds Gurzadyan, V. G., Jantzen, R. T. & Ruffini, R.) 1797–1798 (World Scientific, Singapore, 2002)

  12. 12

    Shapiro, I. I., Reasenberg, R. D., Chandler, J. F. & Babcock, R. W. Measurement of the de Sitter precession of the Moon. Phys. Rev. Lett. 61, 2643–2646 (1988)

  13. 13

    Rees, M. J. in Black Holes in Binaries and Galactic Nuclei, Proc. ESO Workshop (eds Kaper, L., van den Heuvel, E. P. J. & Woudt, P. A.) 351–363 (Springer, Heidelberg, 2001)

  14. 14

    Genzel, R. et al. Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre. Nature 425, 934–937 (2003)

  15. 15

    LAGEOS scientific results. J. Geophys. Res. B 90, 9215–9438 (1985)

  16. 16

    Bender, P. & Goad, C. C. in Proc. 2nd Int. Symp. on the Use of Artificial Satellites for Geodesy and Geodynamics Vol. II (eds Veis, G. & Livieratos, E.) 145 (National Technical University of Athens, Athens, 1979)

  17. 17

    Reigber, C. et al. An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J. Geodyn. (in the press)

  18. 18

    Bertotti, B., Farinella, P. & Vokrouhlický, D. Physics of the Earth and the Solar System 2nd edn (Kluwer Academic, Dordrecht, 2003)

  19. 19

    Ciufolini, I. Measurement of the Lense-Thirring drag on high-altitude laser-ranged artificial satellites. Phys. Rev. Lett. 56, 278–281 (1986)

  20. 20

    Noomen, R., Klosko, S., Noll, C. & Pearlman, M. (eds) Toward millimeter accuracy. Proc. 13th Int. Laser Ranging Workshop (NASA CP 2003–212248, NASA Goddard, Greenbelt, MD, 2003)

  21. 21

    Pavlis, D. E. et al. GEODYN Systems Description Vol. 3 (NASA GSFC, Greenbelt, MD, 1998)

  22. 22

    McCarthy, D. The 1996 IERS Conventions (Observatoire de Paris, Paris, 1996)

  23. 23

    Rubincam, D. P. Yarkovsky thermal drag on LAGEOS. J. Geophys. Res. B 93, 13805–13810 (1988)

  24. 24

    Rubincam, D. P. Drag on the LAGEOS satellite. J. Geophys. Res. B 95, 4881–4886 (1990)

  25. 25

    Rubincam, D. P. & Mallama, A. Terrestrial atmospheric effect on satellite eclipses with application to the acceleration of LAGEOS. J. Geophys. Res. B 100, 20285–20290 (1995)

  26. 26

    Martin, C. F. & Rubincam, D. P. Effects of Earth albedo on the LAGEOS I satellite. J. Geophys. Res. B 101, 3215–3226 (1996)

  27. 27

    Andrés, J. I. et al. Spin axis behavior of the LAGEOS satellites. J. Geophys. Res. 109, B06403 (2004)

  28. 28

    Ray, R. D. A Global Ocean Tide Model from Topex/Poseidon Altimetry: GOT99.2 (NASA Tech. Memo. 209478, NASA GSFC, Greenbelt, MD, 1999)

  29. 29

    Ciufolini, I. A comprehensive introduction to the LAGEOS gravitomagnetic experiment. Int. J. Mod. Phys. A 4, 3083–3145 (1989)

  30. 30

    Ciufolini, I. et al. WEBER-SAT/LARES Study for INFN (Università di Lecce, Lecce, 2004)

  31. 31

    Ries, J. C., Eanes, R. J., Watkins, M. M. & Tapley, B. in LARES Phase A Study for ASI (ed. Ciufolini, I.) (Italian Space Agency, Rome, 1998)

Download references


We thank the International Laser Ranging Service (ILRS) for making available for our use the laser ranging data collected by their network, through their data service at CDDIS, NASA/Goddard, USA, and the GeoForschungsZentrum, Potsdam, Germany. E.C.P. acknowledges support from NASA. I.C. thanks R. Matzner and N. Cabibbo for comments. We thank R. Peron for reading the manuscript and, together with G. Chionchio, D. Lucchesi, D. Pavlis and F. Ricci, for computer support.

Author information

Correspondence to I. Ciufolini.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Supplementary Discussion

Error analysis and error budget of the measurement of the lense-thirring effect using the nodes of Lageos and Lageos 2. (DOC 45 kb)

Supplementary Figures 1S and 2S

Additional N-frequency fits of the lense-thirring effect. (DOC 256 kb)

Rights and permissions

Reprints and Permissions

About this article

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.