Space Science Reviews

, Volume 148, Issue 1–4, pp 363–381

An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging

Article

Abstract

We deal with the attempts to measure the Lense-Thirring effect with the Satellite Laser Ranging (SLR) technique applied to the existing LAGEOS and LAGEOS II terrestrial satellites and to the recently approved LARES spacecraft. According to general relativity, a central spinning body of mass M and angular momentum S like the Earth generates a gravitomagnetic field which induces small secular precessions of the orbit of a test particle geodesically moving around it. Extracting this signature from the data is a demanding task because of many classical orbital perturbations having the same pattern as the gravitomagnetic one, like those due to the centrifugal oblateness of the Earth which represents a major source of systematic bias. The first issue addressed here is: are the so far published evaluations of the systematic uncertainty induced by the bad knowledge of the even zonal harmonic coefficients J of the multipolar expansion of the Earth’s geopotential reliable and realistic? Our answer is negative. Indeed, if the differences ΔJ among the even zonals estimated in different Earth’s gravity field global solutions from the dedicated GRACE mission are assumed for the uncertainties δJ instead of using their covariance sigmas \(\sigma_{J_{\ell}}\) , it turns out that the systematic uncertainty δμ in the Lense-Thirring test with the nodes Ω of LAGEOS and LAGEOS II may be up to 3 to 4 times larger than in the evaluations so far published (5–10%) based on the use of the sigmas of one model at a time separately. The second issue consists of the possibility of using a different approach in extracting the relativistic signature of interest from the LAGEOS-type data. The third issue is the possibility of reaching a realistic total accuracy of 1% with LAGEOS, LAGEOS II and LARES, which should be launched in November 2009 with a VEGA rocket. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be likely placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact has been evaluated with the standard Kaula’s approach up to degree =60 by using ΔJ and \(\sigma_{J_{\ell }}\) ; it turns out that it may be as large as some tens percent. The different orbit of LARES may also have some consequences on the non-gravitational orbital perturbations affecting it which might further degrade the obtainable accuracy in the Lense-Thirring test.

Keywords

Experimental tests of gravitational theories Satellite orbits Harmonics of the gravity potential field 

PACS

04.80.Cc 91.10.Sp 91.10.Qm 

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References

  1. J.I. Andrés, Enhanced Modelling of LAGEOS Non-Gravitational Perturbations. PhD Thesis Book (Ed. Sieca Repro Turbineweg, Delft, 2007) Google Scholar
  2. D.C. Christodoulidis, D.E. Smith, R.G. Williams, S.M. Klosko, Observed tidal braking in the Earth/Moon/Sun system. J. Geophys. Res. 93(B6), 6216–6236 (1988) CrossRefADSGoogle Scholar
  3. I. Ciufolini, Measurement of the Lense-Thirring drag on high-altitude, laser-ranged artificial satellites. Phys. Rev. Lett. 56(4), 278–281 (1986) CrossRefADSGoogle Scholar
  4. I. Ciufolini, On a new method to measure the gravitomagnetic field using two orbiting satellites. Nuovo Cim. A 109(12), 1709–1720 (1996) CrossRefADSGoogle Scholar
  5. I. Ciufolini, LARES/WEBER-SAT, frame-dragging and fundamental physics. http://arxiv.org/abs/gr-qc/0412001. Accessed 3 January 2005
  6. I. Ciufolini, On the orbit of the LARES satellite. http://arxiv.org/abs/gr-qc/0609081. Accessed 20 September 2006
  7. I. Ciufolini, http://www.infn.it/indexen.php. Astroparticle Physics. Calendario riunioni. Roma, 30 gennaio 2008. 14:30 Aggiornamento LARES (20’). lares_dellagnello.pdf (2008a), p. 17
  8. I. Ciufolini, http://www.infn.it/indexen.php. Astroparticle Physics. Calendario riunioni. Villa Mondragone, 30 sett.–4 ott. Friday 03 October 2008. 10:20 LARES (20’) (2008b)
  9. I. Ciufolini, E.C. Pavlis, A confirmation of the general relativistic prediction of the Lense–Thirring effect. Nature 431, 958–960 (2004) CrossRefADSGoogle Scholar
  10. 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) CrossRefADSGoogle Scholar
  11. I. Ciufolini, D.M. Lucchesi, F. Vespe, A. Mandiello, Measurement of dragging of inertial frames and gravitomagnetic field using laser-ranged satellites. Nuovo Cim. A 109(5), 575–590 (1996) CrossRefADSGoogle Scholar
  12. I. Ciufolini, E.C. Pavlis, F. Chieppa, E. Fernandes-Vieira, J. Pérez-Mercader, Test of general relativity and measurement of the Lense-Thirring effect with two Earth satellites. Science 279(5359), 2100–2103 (1998a) CrossRefADSGoogle Scholar
  13. I. Ciufolini et al., LARES Phase A (University La Sapienza, Rome, 1998b) Google Scholar
  14. I. Ciufolini, E.C. Pavlis, R. Peron, Determination of frame-dragging using Earth gravity models from CHAMP and GRACE. New Astron. 11(8), 527–550 (2006) CrossRefADSGoogle Scholar
  15. L. Combrinck, Evaluation of PPN parameter Gamma as a test of General Relativity using SLR data, in 16th Int. Laser Ranging Workshop, Poznań (PL), 13–17 October 2008 Google Scholar
  16. L. Cugusi, E. Proverbio, Relativistic effects on the motion of Earth’s artificial satellites. Astron. Astrophys. 69, 321–325 (1978) ADSGoogle Scholar
  17. J.J. Degnan, Satellite laser ranging: current status and future prospects. IEEE Trans. Geosci. Remote Sens. GE-23(4), 398–413 (1985) CrossRefADSGoogle Scholar
  18. C.W.F. Everitt, The gyroscope experiment I. General description and analysis of gyroscope performance, in Proc. Int. School Phys. “Enrico Fermi” Course LVI, ed. by B. Bertotti (New Academic Press, New York, 1974), pp. 331–360 Google Scholar
  19. C.W.F. Everitt et al., Gravity Probe B: Countdown to launch, in Gyros, Clocks, Interferometers… : Testing Relativistic Gravity in Space, ed. by C. Lämmerzahl, C.W.F. Everitt, F.W. Hehl (Springer, Berlin, 2001), pp. 52–82 CrossRefGoogle Scholar
  20. P. Inversi, F. Vespe, Direct and indirect solar radiation effects acting on LAGEOS satellite: Some refinements. Adv. Space Res. 14(5), 73–77 (1994) CrossRefADSGoogle Scholar
  21. L. Iorio, Letter to the editor: A critical approach to the concept of a polar, low-altitude LARES satellite. Class. Quantum Gravity 19(17), L175–L183 (2002) MATHCrossRefMathSciNetADSGoogle Scholar
  22. L. Iorio, The impact of the static part of the Earth’s gravity field on some tests of General Relativity with satellite laser ranging. Celest. Mech. Dyn. Astron. 86(3), 277–294 (2003) MATHCrossRefMathSciNetADSGoogle Scholar
  23. 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(8), 616–635 (2005a) CrossRefADSGoogle Scholar
  24. L. Iorio, On the possibility of testing the Dvali Gabadadze Porrati brane-world scenario with orbital motions in the Solar system. J. Cosmol. Astropart. Phys. 7, 8 (2005b) CrossRefMathSciNetADSGoogle Scholar
  25. L. Iorio, Comments, replies and notes: A note on the evidence of the gravitomagnetic field of Mars. Class. Quantum Gravity 23(17), 5451–5454 (2006a) MATHCrossRefADSGoogle Scholar
  26. L. Iorio, A critical analysis of a recent test of the Lense-Thirring effect with the LAGEOS satellites. J. Geod. 80(3), 128–136 (2006b) MATHCrossRefADSGoogle Scholar
  27. L. Iorio, The impact of the new Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some existing Earth satellites. Gen. Relativ. Gravit. 38(3), 523–527 (2006c) MATHCrossRefADSGoogle Scholar
  28. L. Iorio, Reply to “Comment on ‘Evidence of the gravitomagnetic field of Mars’ ”, by Kris Krogh. J. Gravit. Phys. (2007a, in press). http://arxiv.org/abs/gr-qc/0701146
  29. L. Iorio (ed.), The Measurement of Gravitomagnetism: A Challenging Enterprise (NOVA, Hauppauge, 2007b) Google Scholar
  30. L. Iorio, A comment on the paper “On the orbit of the LARES satellite”, by I. Ciufolini. Planet. Space Sci. 55(10), 1198–1200 (2007c) CrossRefADSGoogle Scholar
  31. L. Iorio, LARES/WEBER-SAT and the equivalence principle. Europhys. Lett. 80(4), 40007 (2007d) CrossRefADSGoogle Scholar
  32. L. Iorio, An assessment of the measurement of the Lense-Thirring effect in the Earth gravity field, in reply to: “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”, by I. Ciufolini and E. Pavlis. Planet. Space Sci. 55(4), 503–511 (2007e) CrossRefADSGoogle Scholar
  33. L. Iorio, Advances in the measurement of the Lense-Thirring effect with planetary motions in the field of the Sun. Sch. Res. Exch. 2008, 105235 (2008a) Google Scholar
  34. L. Iorio, On the impact of the atmospheric drag on the LARES mission (2008b). http://arxiv.org/abs/gr-qc/0809.3564. Accessed 8 October 2008
  35. L. Iorio, A. Morea, The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect. Gen. Relativ. Gravit. 36(6), 1321–1333 (2004) MATHCrossRefADSGoogle Scholar
  36. L. Iorio, D.M. Lucchesi, I. Ciufolini, The LARES mission revisited: an alternative scenario. Class. Quantum Gravity 19(16), 4311–4325 (2002) MATHCrossRefADSGoogle Scholar
  37. A. Jäggi, G. Beutler, L. Mervart, GRACE gravity field determination using the celestial mechanics approach—first results. Presented at the IAG Symposium on “Gravity, Geoid, and Earth Observation 2008”, Chania, GR, 23–27 June 2008 Google Scholar
  38. W.M. Kaula, Theory of Satellite Geodesy (Blaisdell, Waltham, 1966) Google Scholar
  39. K. Krogh, Comments, replies and notes: Comment on ‘Evidence of the gravitomagnetic field of Mars’. Class. Quantum Gravity 24(22), 5709–5715 (2007) CrossRefADSGoogle Scholar
  40. F.G. Lemoine, S.C. Kenyon, J.K. Factor, R.G. Trimmer, N.K. Pavlis, D.S. Chinn, C.M. Cox, S.M. Klosko, S.B. Luthcke, M.H. Torrence, Y.M. Wang, R.G. Williamson, E.C. Pavlis, R.H. Rapp, T.R. Olson, The Development of the Joint NASA GSFC and the National Imagery Mapping Agency (NIMA) Geopotential Model EGM96. NASA/TP-1998-206861, 1998 Google Scholar
  41. J. Lense, H. Thirring, Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z. 19, 156–163 (1918) Google Scholar
  42. F.J. Lerch, R.S. Nerem, B.H. Putney, T.L. Felsentreger, B.V. Sanchez, J.A. Marshall, S.M. Klosko, G.B. Patel, R.G. Williamson, D.S. Chinn, A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM-T3. J. Geophys. Res. 99(B2), 2815–2839 (1994) CrossRefADSGoogle Scholar
  43. D.M. Lucchesi, Reassessment of the error modelling of non-gravitational perturbations on LAGEOS II and their impact in the Lense-Thirring determination. Part I. Planet. Space Sci. 49(5), 447–463 (2001) CrossRefADSGoogle Scholar
  44. 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(10–11), 1067–1100 (2002) CrossRefADSGoogle Scholar
  45. D.M. Lucchesi, The asymmetric reflectivity effect on the LAGEOS satellites and the germanium retroreflectors. Geophys. Res. Lett. 30(18), 1957 (2003) CrossRefADSGoogle Scholar
  46. D.M. Lucchesi, LAGEOS satellites germanium cube-corner-retroreflectors and the asymmetric reflectivity effect. Celest. Mech. Dyn. Astron. 88(3), 269–291 (2004) MATHCrossRefMathSciNetADSGoogle Scholar
  47. 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(12), 1989–2023 (2005) MATHCrossRefADSGoogle Scholar
  48. D.M. Lucchesi, The LAGEOS satellites orbital residuals determination and the way to extract gravitational and non-gravitational unmodeled perturbing effects. Adv. Space Res. 39(10), 1559–1575 (2007) CrossRefADSGoogle Scholar
  49. D.M. Lucchesi, G. Balmino, The LAGEOS satellites orbital residuals determination and the Lense Thirring effect measurement. Planet. Space Sci. 54(6), 581–593 (2006) ADSGoogle Scholar
  50. D.M. Lucchesi, A. Paolozzi, A cost effective approach for LARES satellite, in XVI Congresso Nazionale AIDAA, Palermo, IT, 24–28 September 2001 Google Scholar
  51. D.M. Lucchesi, I. Ciufolini, J.I. Andrés, E.C. Pavlis, R. Peron, R. Noomen, D.G. Currie, LAGEOS II perigee rate and eccentricity vector excitations residuals and the Yarkovsky-Schach effect. Planet. Space Sci. 52(8), 699–710 (2004) CrossRefADSGoogle Scholar
  52. B. Mashhoon, Gravitoelectromagnetism: a brief review, in The Measurement of Gravitomagnetism: A Challenging Enterprise, ed. by L. Iorio (NOVA, Hauppauge, 2007), pp. 29–39 Google Scholar
  53. T. Mayer-Gürr, A. Eicker, K.-H. Ilk, ITG-GRACE02s: a GRACE gravity field derived from short arcs of the satellite’s orbit, in 1st Int. Symp. of the International Gravity Field Service “Gravity Field of the Earth”, Istanbul, TR, 28 August–1 September 2006 Google Scholar
  54. T. Mayer-Gürr, ITG-Grace03s: The latest GRACE gravity field solution computed in Bonn, in Joint Int. GSTM and DFG SPP Symp., Potsdam, 15–17 October 2007. http://www.geod.uni-bonn.de/itg-grace03.html
  55. A. Milani, A.M. Nobili, P. Farinella, Non-Gravitational Perturbations and Satellite Geodesy (Adam Hilger, Bristol, 1987) MATHGoogle Scholar
  56. E.C. Pavlis, Geodetic contributions to gravitational experiments in space, in Recent Developments in General Relativity: Proc. 14th SIGRAV Conf. on General Relativity and Gravitational Physics, ed. by R. Cianci, R. Collina, M. Francaviglia, P. Fré. Genova, IT, 18–22 September 2000 (Springer, Milan, 2002), pp. 217–233 Google Scholar
  57. H. Pfister, On the history of the so-called Lense-Thirring effect. Gen. Relativ. Gravit. 39(11), 1735–1748 (2007) MATHCrossRefMathSciNetADSGoogle Scholar
  58. G.E. Pugh, WSEG Research Memorandum No. 11, 1959 Google Scholar
  59. Ch. Reigber, R. Schmidt, F. Flechtner, R. König, U. Meyer, K.-H. Neumayer, P. Schwintzer, S.Y. Zhu, An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J. Geodyn. 39(1), 1–10 (2005) CrossRefGoogle Scholar
  60. J.C. Ries, R.J. Eanes, M.M. Watkins, B.D. Tapley, Joint NASA/ASI Study on Measuring the Lense-Thirring Precession Using a Second LAGEOS Satellite CSR-89-3 Center for Space Research, Austin, 1989 Google Scholar
  61. 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, ed. by R.J. Ruffini, C. Sigismondi (World Scientific, Singapore, 2003a), pp. 201–211 Google Scholar
  62. 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 Proc. 13th Int. Laser Ranging Workshop, NASA CP (2003-212248), ed. by R. Noomen, S. Klosko, C. Noll, M. Pearlman (NASA Goddard, Greenbelt, 2003b). http://cddisa.gsfc.nasa.gov/lw13/lw_proceedings.html#science Google Scholar
  63. J.C. Ries, R.J. Eanes, M.M. Watkins, Confirming the frame-dragging effect with satellite laser ranging, in 16th Int. Laser Ranging Workshop, Poznań (PL), 13–17 October 2008 Google Scholar
  64. M.L. Ruggiero, A. Tartaglia, Gravitomagnetic effects. Nuovo Cim. B 117(7), 743–768 (2002) ADSGoogle Scholar
  65. G. Schäfer, Gravitomagnetic effects. Gen. Relativ. Gravit. 36(10), 2223–2235 (2004) MATHCrossRefADSGoogle Scholar
  66. L. Schiff, Possible new experimental test of general relativity theory. Phys. Rev. Lett. 4(5), 215–217 (1960) CrossRefADSGoogle Scholar
  67. M. Soffel, Relativity in Astrometry, Celestial Mechanics and Geodesy (Springer, Berlin, 1989) Google Scholar
  68. B.D. Tapley, J.C. Ries, S. Bettadpur, D. Chambers, M. Cheng, F. Condi, B. Gunter, Z. Kang, P. Nagel, R. Pastor, T. Pekker, S. Poole, F. Wang, GGM02-An improved Earth gravity field model from GRACE. J. Geod. 79(8), 467–478 (2005) CrossRefADSGoogle Scholar
  69. B.D. Tapley, J.C. Ries, S. Bettadpur, D. Chambers, M. Cheng, F. Condi, S. Poole, American Geophysical Union, Fall Meeting 2007, Abstract #G42A-03, 2007 Google Scholar
  70. 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(12), 629–632 (1976a) CrossRefADSGoogle Scholar
  71. R.A. Van Patten, C.W.F. Everitt, A possible experiment with two counter-rotating drag-free satellites to obtain a new test of Einstein’s general theory of relativity and improved measurements in geodesy. Celest. Mech. Dyn. Astron. 13(4), 429–447 (1976b) Google Scholar
  72. F. Vespe, The perturbations of Earth penumbra on LAGEOS II perigee and the measurement of Lense-Thirring gravitomagnetic effect. Adv. Space Res. 23(4), 699–703 (1999) CrossRefADSGoogle Scholar

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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.INFN-Sezione di PisaPisaItaly
  2. 2.BariItaly

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