Skip to main content
SpringerLink
Log in

Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models

  • Published:
Space Science Reviews Aims and scope Submit manuscript

Abstract

During the past century Einstein’s theory of General Relativity gave rise to an experimental triumph; however, there are still aspects of this theory to be measured or more accurately tested. Today one of the main challenges in experimental gravitation, together with the direct detection of gravitational waves, is the accurate measurement of the gravitomagnetic field generated by the angular momentum of a body. Here, after a brief introduction on frame-dragging, gravitomagnetism and Lunar Laser Ranging tests, we describe the past measurements of frame-dragging by the Earth spin using the satellites LAGEOS, LAGEOS 2 and the Earth’s gravity models obtained by the GRACE project. We demonstrate that these measurements have an accuracy of approximately 10%.

We then describe the LARES experiment to be launched in 2010 by the Italian Space Agency for a measurement of frame-dragging with an accuracy of a few percent.

We finally demonstrate that a number of claims by a single individual, that the error budget of the frame-dragging measurements with LAGEOS-LAGEOS 2 and LARES has been underestimated, are indeed ill-founded.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • J.I. Andrès et al., Spin axis behavior of the LAGEOS satellites. J. Geophys. Res. 109, B06403–1-12 (2004)

    Article  Google Scholar 

  • N. Ashby, B. Shahid-Saless, Geodetic precession or dragging of inertial frames? Phys. Rev. D 42, 1118–1122 (1990)

    Article  ADS  Google Scholar 

  • B.M. Barker, R.F. O’Connel, The gravitational interaction: Spin, rotation, and quantum effects – A review. Gen. Relativ. Gravit. 11, 149–175 (1979)

    Article  ADS  Google Scholar 

  • P.L. Bender et al., The lunar laser ranging experiment. Science 182, 229–238 (1973)

    Article  ADS  Google Scholar 

  • B. Bertotti, I. Ciufolini, P.L. Bender, New test of general relativity: measurement of de Sitter geodetic precession rate for lunar perigee. Phys. Rev. Lett. 58, 1062–1065 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  • P.E. Ciddor, Refractive index of air: New equations for the visible and near infrared. Appl. Opt. 35(9), 1566–1573 (1996)

    Article  ADS  Google Scholar 

  • I. Ciufolini, Theory and experiments in General Relativity and other metric theories, Ph.D. Dissertation, Univ. of Texas, Austin, Pub. Ann Arbor, Michigan, 1984

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

    Article  ADS  Google Scholar 

  • I. Ciufolini, 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 Tapley et al. (1989)

    Article  ADS  Google Scholar 

  • I. Ciufolini, Gravitomagnetism and status of the LAGEOS III experiment. Class. Quantum Gravity 11, A73–A81 (1994)

    Article  ADS  Google Scholar 

  • I. Ciufolini, On a new method to measure the gravitomagnetic field using two orbiting satellites. Nuovo Cim. A 109, 1709–1720 (1996)

    Article  ADS  Google Scholar 

  • I. Ciufolini, The 1995–99 measurements of the Lense-Thirring effect using laser-ranged satellites. Class. Quantum Gravity 17, 2369–2380 (2000)

    Article  ADS  MATH  Google Scholar 

  • I. Ciufolini, in Proceedings of the I SIGRAV School on General Relativity and Gravitation, Frascati (Rome), September 2002, IOP, Bristol (2005), pp. 27–69

  • I. Ciufolini, On the orbit of the LARES satellite (2006). arXiv:gr-qc/0609081v1

  • I. Ciufolini, Dragging of inertial frames. Nature 449, 41–48 (2007a)

    Article  ADS  Google Scholar 

  • I. Ciufolini, A. Paolozzi, G. Sindoni, E.C. Pavlis, A. Gabrielli, Scientific Aspects of LARES mission, Proc. International Astronautical Congress 09.B4.2.9, Daejeon, Republic of Korea, 12–16 October 2009 (2009a)

  • I. Ciufolini, Frame-dragging, gravitomagnetism and lunar laser ranging. New Astron. (2009b). doi:10.1016/j.newast.2009.08.004

    Google Scholar 

  • I. Ciufolini, E.C. Pavlis, A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature 431, 958–960 (2004)

    Article  ADS  Google Scholar 

  • I. Ciufolini, E.C. Pavlis, 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 Astron. 10(8), 636–651 (2005)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  • I. Ciufolini et al., ASI-NASA Study on LAGEOS III, CNR, Rome, Italy, 1989

  • I. Ciufolini et al., Effect of particle drag on the LAGEOS node and measurement of the gravitomagnetic field. Nuovo Cim. B 105, 573–588 (1990)

    Article  ADS  Google Scholar 

  • I. Ciufolini, F. Chieppa, D. Lucchesi, F. Vespe, Test of Lense-Thirring orbital shift due to spin. Class. Quantum Gravity 14, 2701–2726 (1997a)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • I. Ciufolini, D. Lucchesi, F. Vespe, F. Chieppa, Measurement of gravitomagnetism. Europhys. Lett. 39, 359–364 (1997b)

    Article  ADS  Google Scholar 

  • I. Ciufolini, A. Paolozzi et al., LARES phase. A study for the Italian Space Agency, 1998a

  • I. Ciufolini, E.C. Pavlis, F. Chieppa, E. Fernandes-Vieira, J. Perez-Mercader, Test of general relativity and measurement of the Lense-Thirring effect with two Earth satellites. Science 279, 2100–2103 (1998b)

    Article  ADS  Google Scholar 

  • I. Ciufolini et al., Italian Space Agency Phase A Report on LARES, Italian Space Agency, ASI, Rome, 1998c

  • I. Ciufolini et al., INFN study on LARES/WEBER-SAT, 2004

  • I. Ciufolini, E.C. Pavlis, R. Peron, Determination of frame-dragging using Earth gravity models from CHAMP and GRACE. New Astron. 11, 527–550 (2006)

    Article  ADS  Google Scholar 

  • I. Ciufolini et al., Gravitomagnetism and its measurement with laser ranging to the LAGEOS satellites and GRACE Earth gravity models, in General Relativity and John Archibald Wheeler: Frame-Dragging, Gravitational-Waves and Gravitational Tests, ed. by I. Ciufolini, R. Matzner (Springer, Berlin, 2010a)

    Google Scholar 

  • I. Ciufolini et al., The LARES space experiment: LARES orbit, error analysis and satellite structure, in General Relativity and John Archibald Wheeler: Frame-Dragging, Gravitational-Waves and Gravitational Tests, ed. by I. Ciufolini, R. Matzner (Springer, Berlin, 2010b)

    Google Scholar 

  • I. Ciufolini, A. Anselmo et al., Effect of particle drag in the LARES experiment (2009c, to be published)

  • S.C. Cohen, P.J. Dunn, LAGEOS scientific results. J. Geophys. Res. B 90, 9215–9438 (1985)

    Article  ADS  Google Scholar 

  • L. Cugusi, E. Proverbio, Relativistic effects on the motion of Earth’s artificial satellites. Astron. Astrophys. 69, 321–325 (1978)

    ADS  Google Scholar 

  • W. Cui, S.N. Zhang, W. Chen, Evidence for frame dragging around spinning black holes in X-ray binaries. Astrophys. J. 492, L53–L58 (1998)

    Article  ADS  Google Scholar 

  • G. Felici, The meaning of systematic errors, a comment to “Reply to On the systematic errors in the Detection of the Lense-Thirring effect with a Mars orbiter”, by L. Iorio (2007). arXiv:gr-qc/0703020v1

  • R.S. Gross, Combinations of Earth orientation measurements: SPACE94, COMB94, and POLE94. J. Geophys. Res. 101(B4), 8729–8740 (1996)

    Article  ADS  Google Scholar 

  • G.C. Hulley, E.C. Pavlis, 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

    Article  Google Scholar 

  • International Earth Rotation Service (IERS) Annual Report, 1996. Observatoire de Paris, Paris, July 1997

  • L. Iorio, On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites. New Astron. 10, 603–615 (2005a)

    Article  ADS  Google Scholar 

  • L. Iorio, The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect with a new satellite. New Astron. 10, 616–635 (2005b)

    Article  ADS  Google Scholar 

  • L. Iorio, Evidence of the gravitomagnetic field of Mars. Class. Quantum Gravity 23, 5451–5454 (2006)

    Article  ADS  MATH  Google Scholar 

  • L. Iorio, On some critical issues of the LAGEOS/LAGEOS II Lense-Thirring experiment (2007). arXiv:0710.1022v1 [gr-qc]

  • L. Iorio, On the impact of the atmospheric drag on the LARES mission. arXiv:0809.3564v2 (2008a); see also: arXiv:0809.3564v1

  • L. Iorio, An assessment of the systematic uncertainty in present and future tests of the Lense-Thirring effect with satellite laser ranging (2008b). arXiv:0809.1373v2 [gr-qc]

  • L. Iorio, 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]

    Article  ADS  MATH  Google Scholar 

  • W.M. Kaula, Theory of Satellite Geodesy (Blaisdell, Waltham, 1966)

    Google Scholar 

  • A.R. Khan, R.F. O’Connell, Gravitational analogue of magnetic force. Nature 261, 480–481 (1976)

    Article  ADS  Google Scholar 

  • S.M. Kopeikin, Comment on “Gravitomagnetic Influence on Gyroscopes and on the Lunar Orbit”. Phys. Rev. Lett. 98, 229001–1 (2007)

    Article  ADS  Google Scholar 

  • K. Krogh, Iorio’s “high-precision measurement” of frame-dragging with the Mars Global Surveyor. Class. Quantum Gravity 24, 5709–5715 (2007)

    Article  ADS  Google Scholar 

  • D.M. Lucchesi, 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)

    Article  ADS  Google Scholar 

  • D.M. Lucchesi, Reassessment of the error modelling of non-gravitational perturbations on LAGEOS II and their impact in the Lense-Thirring determination. Part II. Planet. Space Sci. 50, 1067–1100 (2002)

    Article  ADS  Google Scholar 

  • D.M. Lucchesi, The impact of the even zonal harmonics secular variations on the Lense-Thirring effect measurement with the two Lageos satellites. Int. J. Mod. Phys. D 14, 1989–2023 (2005)

    Article  ADS  MATH  Google Scholar 

  • D.M. Lucchesi, A. Paolozzi, A cost effective approach for LARES satellite, in XVI AIDAA, Palermo, September 2001, pp. 1–14. Paper no. 111

  • C.F. Martin, D.P. Rubincam, Effects of Earth albedo on the LAGEOS I satellite. J. Geophys. Res. 101(B2), 3215–3226 (1996)

    Article  ADS  Google Scholar 

  • V.B. Mendes, E.C. Pavlis, High-accuracy zenith delay prediction at optical wavelengths. Geophys. Res. Lett. 31, L14602–1-5 (2004). doi:10.1029/2004GL020308

    Article  Google Scholar 

  • V.B. Mendes, G. Prates, E.C. Pavlis, D.E. Pavlis, R.B. Langley, Improved mapping functions for atmospheric re-fraction correction in SLR. Geophys. Res. Lett. 29, 1414–1-4 (2002). doi:10.1029/2001GL014394

    Article  Google Scholar 

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

    Google Scholar 

  • T.W. Murphy Jr., K. Nordtvedt, S.G. Turyshev, Phys. Rev. Lett. 98, 071102–1-4 (2007a)

    ADS  Google Scholar 

  • T.W. Murphy Jr., K. Nordtvedt, S.G. Turyshev, Phys. Rev. Lett. 98, 229002–1 (2007b)

    ADS  Google Scholar 

  • R. Noomen, S. Klosko, C. Noll, M. Pearlman (eds.), Toward Millimeter Accuracy in NASA CP 2003-212248. Proc. 13th Int. Laser Ranging Workshop (NASA Goddard, Greenbelt, 2003)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • K. Nordtvedt, LARES and tests on new long ranges forces, in LARES phase. A study for the Italian Space Agency (1998), pp. 34–38

  • R.F. O’Connell, A note on frame dragging. Class. Quantum Gravity 22, 3815–3816 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • A. Paolozzi, private communication (2005)

  • E.C. Pavlis, Geodetic contributions to gravitational experiments in space, in Recent Developments in General Relativity, ed. by R. Cianci et al., Genoa, 2000 (Springer, Berlin), pp. 217–233

  • D.E. Pavlis et al., GEODYN Operations Manuals, Contractor Report, Raytheon, ITSS, Landover, MD, 1998

  • G.E. Peterson, Estimation of the Lense-Thirring precession using laser-ranged satellites, Ph.D. Dissertation, Univ. of Texas, Austin, 1997

  • Ch. Reigber, F. Flechtner, R. Koenig, U. Meyer, K. Neumayer, R. Schmidt, P. Schwintzer, S. Zhu, GRACE orbit and gravity field recovery at GFZ Potsdam----first experiences and perspectives. Eos. Trans. AGU 83(47) (2002). Fall Meet. Suppl., Abstract G12B-03

  • C. Reigber, R. Schmidt, F. Flechtner, R. Konig, U. Meyer, K.H. Neumayer, P. Schwintzer, S.Y. Zhu, J. Geodyn. 39, 1–10 (2005)

    Article  Google Scholar 

  • J.C. Ries, private communication (2005)

  • J.C. Ries, Simulation of an experiment to measure the Lense-Thirring precession using a second LAGEOS satellite, Ph.D. dissertation, The University of Texas, Austin, 1989

  • J.C. Ries, R.J. Eanes, B.D. Tapley, 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, 2003a), pp. 201–211

    Google Scholar 

  • J.C. Ries, R.J. Eanes, B.D. Tapley, G.E. Peterson, Prospects for an improved Lense-Thirring test with SLR and the GRACE gravity mission, in Toward Millimeter Accuracy, Proc. 13th Int. Laser Ranging Workshop, Report NASA CP 2003-212248, NASA Goddard, Greenbelt, Maryland, 2003b

  • J.C. Ries, R.J. Eanes, M.M. Watkins, Confirming the frame-dragging effect with satellite laser ranging, in 16th International Workshop on Laser Ranging, Poznan, Poland, 13–17 October 2008

  • D.P. Rubincam, General relativity and satellite orbits: the motion of a test particle in the Schwarzschild metric. Celest. Mech. 15, 21–33 (1977)

    Article  ADS  Google Scholar 

  • D.P. Rubincam, Yarkovsky Thermal Drag on LAGEOS. J. Geophys. Res. 93(B11), 13805–13810 (1988)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • D.P. Rubincam, A. Mallama, J. Geophys. Res. 100(B10), 20285–20990 (1995)

    Article  ADS  Google Scholar 

  • C. Schmid, Cosmological gravitomagnetism and Mach’s principle. Phys. Rev. D 74, 044031–1-18 (2006)

    Article  ADS  Google Scholar 

  • G. Sindoni, C. Paris, P. Ialongo, On the systematic errors in the detection of the Lense-Thirring effect with a Mars orbiter (2007). arXiv:gr-qc/0701141

  • I.H. Stairs, S.E. Thorsett, Z. Arzoumanian, Measurement of gravitational spin-orbit coupling in a binary-pulsar system. Phys. Rev. Lett. 93, 141101–1-4 (2004)

    Article  ADS  Google Scholar 

  • B.D. Tapley, The GRACE mission: status and performance assessment. Eos. Trans. AGU 83(47) (2002). Fall Meet. Suppl., Abstract G12B-01

  • B.D. Tapley, J.C. Ries, R.J. Eanes, M.M. Watkins, NASA-ASI Study on LAGEOS III, CSR-UT publication n. CSR-89-3, Austin, Texas, 1989

  • B.D. Tapley, S. Bettadpur, M. Watkins, C. Reigber, The gravity recovery and climate experiment: Mission overview and early results. Geophys. Res. Lett. 31, L09607–1-4 (2004)

    Article  Google Scholar 

  • B.D. Tapley, J. Ries, S. Bettadpur, D. Chambers, M. Cheng, F. Condi, S. Poole, The GGM03 mean Earth gravity model from GRACE, Eos Trans. AGU 88(52) (2007). Fall Meet.Suppl., Abstract G42A-03

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

    Google Scholar 

  • R.A. Van Patten, C.W.F. Everitt, 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, 629–632 (1976)

    Article  ADS  Google Scholar 

  • M. Watkins, D. Yuan, W. Bertiger, G. Kruizinga, L. Romans, S. Wu, GRACE gravity field results from JPL. Eos. Trans. AGU 83(47) (2002). Fall Meet. Suppl., Abstract G12B-02

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

    Google Scholar 

  • J.M. Weisberg, J.H. Taylor, General relativistic geodetic spin precession in binary pulsar B1913+16: mapping the emission beam in two dimensions. Astrophys. J. 576, 942–949 (2002)

    Article  ADS  Google Scholar 

  • J.G. Williams, X.X. Newhall, J.O. Dickey, Relativity parameters determined from lunar laser ranging. Phys. Rev. D 53, 6730–6739 (1996)

    Article  ADS  Google Scholar 

  • J.G. Williams, S.G. Turyshev, D.H. Boggs, Progress in lunar laser ranging tests of relativistic gravity. Phys. Rev. Lett. 93, 261101–1-4 (2004a)

    ADS  Google Scholar 

  • J.G. Williams, S.G. Turyshev, T.W. Jr. Murphy, Improving LLR tests of gravitational theory. Int. J. Mod. Phys. D 13, 567–582 (2004b)

    Article  ADS  MATH  Google Scholar 

  • H. Yilmaz, Proposed test of the nature of gravitational interaction. Bull. Am. Phys. Soc. 4, 65 (1959)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Salento and INFN Sezione di Lecce, via Monteroni, 73100, Lecce, Italy

    Ignazio Ciufolini

  2. Sapienza University of Rome, Scuola di Ingegneria Aerospaziale, via Salaria 851/881, 00138, Roma, Italy

    Antonio Paolozzi & Giampiero Sindoni

  3. University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA

    Erricos C. Pavlis

  4. Center for Space Research, University of Texas at Austin, Austin, TX, 78759, USA

    John C. Ries

  5. GFZ German Research Centre for Geosciences, Potsdam, Germany

    Rolf Koenig & Hans Neumayer

  6. Center for Relativity, University of Texas at Austin, Austin, TX, 78712, USA

    Richard A. Matzner

Authors
  1. Ignazio Ciufolini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Paolozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erricos C. Pavlis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. John C. Ries
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Rolf Koenig
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Richard A. Matzner
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Giampiero Sindoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hans Neumayer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ignazio Ciufolini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ciufolini, I., Paolozzi, A., Pavlis, E.C. et al. 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). https://doi.org/10.1007/s11214-009-9585-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11214-009-9585-7

Search

Navigation