The impact of possible a-priori “imprinting” effects of general relativity itself on recent attempts to measure the general relativistic Lense-Thirring effect with the LAGEOS satellites orbiting the Earth and the terrestrial geopotential models from the dedicated mission GRACE is investigated. It is analytically shown that general relativity, not explicitly solved for in the GRACE-based models, may “imprint” their even zonal harmonic coeffi-cients of low degrees at a non-negligible level, given the present-day accuracy in recovering them. This trans-lates into a bias of the LAGEOS-based relativistic tests as large as the Lense-Thirring effect itself. Further analyses should include general relativity itself in the GRACE data processing by explicitly solving for it.
Keywordsexperimental studies of gravitysatellite orbitsharmonics of the gravity potential field
K. S. Thorne, “Gravitomagnetism, jets in quasars, and the stanford gyroscope experiment,” in Near Zero: New Frontiers of Physics, J. D. Fairbank, B. S. Deaver, C. W. F. Everitt, and P. F. Michelson, Eds., W. H. Freeman and Company, New York, pp. 573–586, 1988.
W. Rindler, Relativity. Special, General and Cosmo- logical, Oxford University Press, Oxford, pp. 195–198, 2001.
B. Mashhoon, “Gravitoelectromagnetism: a brief review”, in The Measurement of Gravitomagnetism: A Challenging Enterprise, L. Iorio, Ed., Nova, Hauppauge, pp. 29–39, 2007.
M. L. Ruggiero and A. Tartaglia, “Gravitomagnetic effects,” II Nuovo Cimento B, Vol. 117, No. 7, pp. 743– 768, July 2002.
G. Sch?fer, “Gravitomagnetic effects,” General Relativity and Gravitation, Vol. 36, No. 10, pp. 2223–2235, October 2004.
H. C. Ohanian and R. J. Ruffini, Gravitation and Spacetime, 2nd Edition, W. W. Norton and Company, New York, pp. 130–240, 1994.
B. Mashhoon, L. Iorio, and H. I. M. Lichtenegger, “On the gravitomagnetic clock effect,” Physics Letters A, Vol. 292, No. 1–2, pp. 49–57, December 2001.
H. Pfister, “On the history of the socalled Lense-Thirring effect,” General Relativity and Gravitation, Vol. 39, No. 11, pp. 1735–1748, November 2007.
J. Lense and H. Thirring, “über den Einflu? der Eigenro- tation der Zentralk?rper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie,” Physikalische Zeitschrift, Vol. 19, pp. 156–163, 1918.
G. E. Pugh, Proposal for a satellite test of the Coriolis prediction of general relativity WSEG Research Memo- randum, The Pentagon, Washington DC, No. 11, Novem- ber 1959.
L. I. Schiff, “Possible new experimental test of general relativity theory,” Physical Review Letters, Vol. 4, No. 5, pp. 215–217, March 1960.
C. W. F. Everitt, S. Buchman, D. B. DeBra, G. M. Keiser, J. M. Lockhart, B. Muhlfelder, B. W. Parkinson, J. P. Turneaure and other members of the Gravity Probe B team, “Gravity Probe B: Countdown to Launch,” in Gyros, Clocks, Interferometers: Testing Relativistic Gravity in Space, C. L?mmerzahl, C. W. F. Everitt and F. W. Hehl, Eds., Springer, Berlin, pp. 52–82, 2001.
C. W. F. Everitt, M. Adams, W. Bencze, S. Buchman, B. Clarke, J. W. Conklin, D. B. DeBra, M. Dolphin, M. Heifetz, D. Hipkins, T. Holmes, G. M. Keiser, J. Kolod- ziejczak, J. Li, J. Lipa, J. M. Lockhart, J. C. Mester, B. Muhlfelder, Y. Ohshima, B. W. Parkinson, M. Salomon, A. Silbergleit, V. Solomonik, K. Stahl, M. Taber, J. P. Tur- neaure, S. Wang, and P. W. Worden, “Gravity Probe B data analysis,” Space Science Reviews, Vol. 148, No. 1–4, pp. 53–69, December 2009.
V. L. Ginzburg, “The use of artificial earth satellites for verifying the general theory of relativity,” Advances in Physical Science (Uspekhi Fizicheskikh Nauk), Vol. 63, No. 1, pp. 119–122, 1957.
V. L. Ginzburg, “Artificial satellites and the theory of relativity,” Scientific American, Vol. 200, No. 5, pp. 149– 160, May 1959.
V. L. Ginzburg, “Experimental verifications of the general theory of relativity,” in Recent Developments in General Relativity, Pergamon press, London, pp. 57–71, 1962.
A. F. Bogorodskii, “Relativistic effects in the motion of an artificial earth satellite,” Soviet Astronomy, Vol. 3, No. 5, pp. 857–862, October 1959.
L. Cugusi and E. Proverbio, “Relativistic effects on the motion of the earth’s satellites,” Journal of Geodesy, Vol. 51, pp. 249–252, 1977.
L. Cugusi and E. Proverbio, “Relativistic effects on the motion of earth’s artificial satellites,” Astronomy and Astrophysics, Vol. 69, pp. 321–325, October 1978.
W. M. Kaula, Theory of Satellite Geodesy, Blaisdell, Waltham, 1966.
L. Iorio, “The impact of the static part of the Earth’s gravity field on some tests of General Relativity with sat- ellite laser ranging,” Celestial Mechanics and Dynamical Astronomy, Vol. 86, No. 3, pp. 277–294, July 2003.
I. Ciufolini, D. M. Lucchesi, F. Vespe, and A. Mandiello, “Measurement of dragging of inertial frames and gravi- tomagnetic field using laser-ranged satellites,” II Nuovo Cimento A, Vol. 109, No. 5, pp. 575–590, May 1996.
I. Ciufolini, “On a new method to measure the gravitomagnetic field using two orbiting satellites,” II Nuovo Cimento A, Vol. 109, No. 12, pp. 1709–1720, December 1996.
I. Ciufolini and E. C. Pavlis, “A confirmation of the general relativistic prediction of the Lense-Thirring effect,” Nature, Vol. 431, No. 7011, pp. 958–960, October 2004.
I. Ciufolini, E. C. Pavlis and R. Peron, “Determination of frame-dragging using Earth gravity models from CHAMP and GRACE,” New Astronomy, Vol. 11, No. 8, pp. 527– 550, July 2006.
D. M. Lucchesi, “The lense thirring effect measurement and LAGEOS satellites orbit analysis with the new grav- ity field model from the CHAMP mission,” Advances in Space Research, Vol. 39, No. 2, pp. 324–332, 2007.
J. C. Ries, R. J. Eanes and M. M. Watkins, “Confirming the frame-dragging effect with satellite laser ranging,” in Proceedings of The 16th International Laser Ranging Workshop, “SLR-The Next Generation”, Poznań (PL), 13–17 October 2008, S. Schillak, Ed. Available from: http://cddis.gsfc.nasa.gov/lw16/.
L. Iorio, “The new Earth gravity models and the meas- urement of the lense-thirring effect,” in The Tenth Marcel Grossmann Meeting On Recent Developments in Theo- retical and Experimental General Relativity, Gravitation and Relativistic Field Theories. Proceedings of the MG10 Meeting, Rio de Janeiro, Brazil 20–26 July 2003, M. Novello, S. P. Bergliaffa, and R. J. Ruffini, Eds. Singa- pore: World Scientific, 2006, pp. 1011–1020.
E. C. Pavlis, “Geodetic contributions to gravitational experi- ments in space,” in Recent Developments in Gen- eral Relativity: Proceedings of the 14th SIGRAV Con- ference on General Relativity and Gravitational Physics (Genova, IT, 18–22 September 2000), R. Cianci, R. Col- lina, M. Francaviglia, and P. Fré P., Eds. Milan: Springer, 2002, pp. 217–233.
J. C. Ries, R. J. Eanes and B. D. Tapley, “Lense-thirring precession determination from laser ranging to artificial satellites,” in Nonlinear Gravitodynamics, The Lense- Thirring Effect, R. J. Ruffini and C. Sigismondi, Eds., World Scientific, Singapore, pp. 201–211, 2003.
J. C. Ries, R. J. Eanes, B. D. Tapley, and G. E. Peterson, “Prospects for an improved lense-thirring test with slr and the GRACE gravity mission,” in Proceedings of The 13th International Laser Ranging Workshop, NASA CP (2003-212248), R. Noomen, S. Klosko, C. Noll and M. Pearlman, Eds., NASA Goddard, Greenbelt, 2003, http://cddisa.gsfc.nasa.gov/lw13/lw_proceedings.html#science.
L. Iorio, “On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAG EOS satellites,” New Astronomy, Vol. 10, No. 8, pp. 603–615, August 2005.
I. Ciufolini and 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 Astronomy, Vol. 10, No. 8, pp. 636–651, August 2005.
D. M. Lucchesi, “The impact of the even zonal harmonics secular variations on the lense-thirring effect measure- ment with the two lageos satellites,” International Journal of Modern Physics D, Vol. 14, No. 12, pp. 1989–2023, 2005.
L. Iorio, “A critical analysis of a recent test of the lense–thirring effect with the LAGEOS satellites,” Journal of Geodesy, Vol. 80, No. 3, pp. 128–136, June 2006.
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 sofar performed tests for measuring the lense-thirring effect with the LAGEOS satellites” by L. Iorio,” by I. Ciufolini and E. Pavlis,” Planetary and Space Science, Vol. 55, No. 4, pp. 503–511, March 2007.
L. Iorio, “An assessment of the systematic uncertainty in present and future tests of the lense-thirring effect with satellite laser ranging,” Space Science Reviews, Vol. 148, No. 1–4, pp. 363–381, December 2009.
L. Iorio, “Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II lense-thirring test,” Central European Journal of Physics, Vol. 8, No. 1, pp. 25–32, February 2010.
D. M. Lucchesi and G. Balmino, “The LAGEOS satellites orbital residuals determination and the lense thirring effect measurement,” Planetary and Space Science, Vol. 54, No. 6, pp. 581–593, May 2006.
D. M. Lucchesi, “The LAGEOS satellites orbital resi- duals determination and the way to extract gravitational and non-gravitational unmodeled perturbing effects,” Ad- vances in Space Research, Vol. 39, No. 10, pp. 1559– 1575, 2007.
K. Nordtvedt jr., “Slr contributions to fundamental physics,” Surveys in Geophysics, Vol. 22, No. 5–6, pp. 597– 602, September 2001.
B. D. Tapley and Ch. Reigber, “The GRACE mission: status and future plans,” EOS Transactions AGU 2001; 82: Fall Meeting Supplement G41, C–02.
C. Reigber, R. Schmidt, F. Flechtner, R. K?nig, U. Meyer, K. H. Neumayer, P. Schwintzer and S. Y. Zhu, “An earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S,” Journal of Geody- namics, Vol. 39, No. 1, pp. 1–10, January 2005.
B. D. Tapley, J. C. Ries, S. Bettadpur, D. Chambers, M. Cheng, F. Condi and S. Poole, “The GGM03 mean earth gravity model from GRACE,” American Geophysical Union, Fall Meeting, abstract # G42A-03, 2007.