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Phenomenology of the Lense-Thirring effect in the solar system

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Abstract

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.

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References

  • Abshire, J.B., Sun, X., Neumann, G., McGarry, J., Zagwodzki, T., Jester, P., Riris, H., Zuber, M.T., Smith, D.E.: Laser pulses from Earth detected at Mars. In: Conference on Lasers and Electro-Optics (CLEO-06), Long Beach, California, May 2006

  • Allen, B.: In: Marck, J.-A., Lasota, J.-P. (eds.) Relativistic Gravitation and Gravitational Radiation: The Stochastic Gravity-Wave Background: Sources and Detection, p. 373. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  • Anderson, J.D.: In: Gehrels, T., Matthews, M.S. (eds.) Jupiter: Studies of the Interior, Atmosphere, Magnetosphere, and Satellites: The gravity field of Jupiter, p. 113. University of Arizona Press, Tucson (1976)

    Google Scholar 

  • Anderson, J.D., Lau, E.L., Schubert, G., Palguta, J.L.: Gravity inversion considerations for radio Doppler data from the JUNO Jupiter polar orbiter. In: DPS Meeting #36, #14.09 (2004), American Astronomical Society. http://aas.org/archives/BAAS/v36n4/dps2004/158.htm. Cited 20 Mar 2010

  • Andrés, J.I.: Enhanced modelling of LAGEOS non-gravitational perturbations. Ph.D. thesis, Sieca Repro Turbineweg, Delft (2007)

  • Appourchaux, T., Burston, R., Chen, Y., Cruise, M., Dittus, H., Foulon, B., Gill, P., Gizon, L., Klein, H., Klioner, S.A., Kopeikin, S.M., Krüger, H., Lämmerzahl, C., Lobo, A., Luo, X., Margolis, H., Ni, W.-T., Pulido Patón, A., Peng, Q., Peters, A., Rasel, E., Rüdiger, A., Samain, É., Selig, H., Shaul, D., Sumner, T., Thei, S., Touboul, P., Turyshev, S.G., Wang, H., Wang, L., Wen, L., Wicht, A., Wu, J., Zhang, X., Zhao, C.: Astrodynamical Space Test of Relativity Using Optical Devices I (ASTROD I)—A class-M fundamental physics mission proposal for Cosmic Vision 2015–2025. Exp. Astron. 23, 491 (2009)

    Article  ADS  Google Scholar 

  • Arvanitaki, A., Dubovsky, S.: Exploring the string axiverse with precision black hole physics. Phys. Rev. D. 81, 123530 (2010)

    ADS  Google Scholar 

  • Ashby, N., Allison, T.: Canonical planetary equations for velocity-dependent forces, and the Lense-Thirring precession. Celest. Mech. Dyn. Astron. 57, 537 (1993)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Ashby, N., Bender, P., Wahr, J.M.: Future gravitational physics tests from ranging to the BepiColombo Mercury planetary orbiter. Phys. Rev. D 75, 022001 (2007)

    ADS  Google Scholar 

  • Balogh, A., Grard, R., Solomon, S.C., Schulz, R., Langevin, Y., Kasaba, Y., Fujimoto, M.: Missions to Mercury. Space Sci. Rev. 132, 611 (2007)

    Article  ADS  Google Scholar 

  • Barker, B.M., O’Connell, R.F.: Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation. Phys. Rev. D 2, 1428 (1970)

    Article  ADS  Google Scholar 

  • Barker, B.M., O’Connell, R.F.: Relativity gyroscope experiment at arbitrary orbit inclinations. Phys. Rev. D 6, 956 (1972)

    Article  ADS  Google Scholar 

  • Barker, B.M., O’Connell, R.F.: Effect of the rotation of the central body on the orbit of a satellite. Phys. Rev. D 10, 1340 (1974)

    Article  ADS  Google Scholar 

  • Baskaran, D., Grishchuk, L.P.: Components of the gravitational force in the field of a gravitational wave. Class. Quantum. Gravity 21, 4041 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Beck, J.G., Giles, P.: Helioseismic determination of the solar rotation axis. Astrophys. J. Lett. 621, L153 (2005)

    Article  ADS  Google Scholar 

  • Bedford, D., Krumm, P.: On relativistic gravitation. Am. J. Phys. 53, 889 (1985)

    Article  ADS  Google Scholar 

  • Bini, D., Cherubini, C., Chicone, C., Mashhoon, B.: Gravitational induction. Class. Quantum Gravity 25, 225014 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  • Biswas, A., Mani, K.R.S.: Relativistic perihelion precession of orbits of Venus and the Earth. Cent. Eur. J. Phys. 6, 754 (2008)

    Article  Google Scholar 

  • Bogorodskii, A.F.: Relativistic effects in the motion of an artificial Earth satellite. Sov. Astron. 3, 857 (1959)

    MathSciNet  ADS  Google Scholar 

  • Borderies, N., Yoder, C.F.: Phobos’ gravity field and its influence on its orbit and physical librations. Astron. Astrophys. 233, 235 (1990)

    ADS  Google Scholar 

  • Braginsky, V.B., Polnarev, A.G.: Relativistic spin quadrupole gravitational effect. J. Exp. Theor. Phys. Lett. 31, 415 (1980)

    Google Scholar 

  • Braginsky, V.B., Caves, C.M., Thorne, K.S.: Laboratory experiments to test relativistic gravity. Phys. Rev. D 15, 2047 (1977)

    Article  ADS  Google Scholar 

  • Braginsky, V.B., Polnarev, A.G., Thorne, K.S.: Foucault pendulum at the south pole: proposal for an experiment to detect the Earth’s general relativistic gravitomagnetic field. Phys. Rev. Lett. 53, 863 (1984)

    Article  ADS  Google Scholar 

  • Camacho, A., Ahluwalia, D.W.: Quantum zeno effect and the detection of gravitomagnetism. Int. J. Mod. Phys. D 10, 9 (2001)

    ADS  Google Scholar 

  • Capozziello, S., De Laurentis, M., Garufi, F., Milano, L.: Relativistic orbits with gravitomagnetic corrections. Phys. Scr. 79, 025901 (2009)

    Article  ADS  Google Scholar 

  • Capozziello, S., De Laurentis, M., Forte, L., Garufi, F., Milano, L.: Gravitomagnetic corrections on gravitational waves. Phys. Scr. 81, 035008 (2010)

    Article  ADS  Google Scholar 

  • Cavendish, H.: Experiments to determine the density of the Earth. By Henry Cavendish, Esq. F.R.S. and A.S. Philos. Trans. R. Soc. London 88, 469 (1798)

    Article  Google Scholar 

  • Cerdonio, M., Prodi, G.A., Vitale, S.: Dragging of inertial frames by the rotating Earth: proposal and feasibility for a ground-based detection. Gen. Relativ. Gravit. 20, 83 (1988)

    Article  ADS  Google Scholar 

  • Chandler, J.F., Pearlman, M.R., Reasenberg, R.D., Degnan, J.J.: Solar-system dynamics and tests of general relativity with planetary laser ranging. In: Noomen, R., Davila, J.M., Garate, J., Noll, C., Pearlman, M. (eds.) Proc. 14-th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11 2004. http://cddis.nasa.gov/lw14/docs/papers/_sci7b_jcm.pdf

  • Chashchina, O., Iorio, L., Silagadze, Z.: Elementary derivation of the Lense-Thirring precession. Acta Phys. Pol. B 40, 2363 (2009)

    ADS  Google Scholar 

  • Chauvenet, W.: A manual of spherical and practical astronomy. Vol. 2: Theory and use of astronomical instruments. Method of least squares, 1st edn. Lippincott, Philadelphia (1863); Unabridged and unaltered republication of the fifth revised and corrected edition 1891. Dover, New York, (1960)

    Google Scholar 

  • Christodoulidis, D.C., Smith, D.E., Williams, R.G., Klosko, S.M.: Observed tidal braking in the Earth/Moon/Sun system. J. Geophys. Res. 93, 6216 (1988)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • 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 (1989)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Ciufolini, I.: LARES/WEBER-SAT, frame-dragging and fundamental physics (2004, unpublished). gr-qc/0412001

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

  • Ciufolini, I.: Dragging of inertial frames. Nature 449, 41 (2007)

    Article  ADS  Google Scholar 

  • Ciufolini, I.: Frame-dragging, gravitomagnetism and Lunar Laser Ranging. New Astron. 15, 332 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Ciufolini, I., 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 Iorio, L. New Astron. 10, 636 (2005)

    Article  ADS  Google Scholar 

  • Ciufolini, I., Lucchesi, D.M., Vespe, F., Mandiello, A.: Measurement of dragging of inertial frames and gravitomagnetic field using laser-ranged satellites. Nuovo Cim. A 109, 575 (1996)

    Article  ADS  Google Scholar 

  • Ciufolini, I., Lucchesi, D.M., Vespe, F., Chieppa, F.: Measurement of gravitomagnetism. Europhys. Lett. 39, 359 (1997a)

    Article  ADS  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Ciufolini, I., Pavlis, E.C., Chieppa, F., Fernandes-Vieira, E., Pérez-Mercader, J.: Test of general relativity and measurement of the Lense-Thirring effect with two earth satellites. Science 279, 2100 (1998a)

    Article  ADS  Google Scholar 

  • Ciufolini, I., et al.: LARES Phase A. University La Sapienza, Rome (1998b)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  • Ciufolini, I., Paolozzi, A., Pavlis, E.C., Ries, J.C., Koenig, R., Matzner, R.A., Sindoni, G., 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 (2009)

    Article  ADS  Google Scholar 

  • Clark, S.J., Tucker, R.W.: Gauge symmetry and gravito-electromagnetism. Class. Quantum Gravity 17, 4125 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Cohen, S.C., Smith, D.E. (eds.): LAGEOS (Laser Geodynamic Satellite). Special issue. J. Geophys. Res. 90, 9215 (1985)

  • Cohen, J.M., Mashhoon, B.: Standard clocks, interferometry, and gravitomagnetism. Phys. Lett. A 181, 353 (1993)

    Article  ADS  Google Scholar 

  • Combrinck, L.: Evaluation of PPN parameter gamma as a test of general relativity using SLR data. In: Schillak, S. (ed.) Proc. 16th Int. Laser Ranging Workshop (Poznań (PL) 13–17 October 2008) (2008). http://cddis.gsfc.nasa.gov/lw16/docs/papers/sci_6_Combrinck_p.pdf. Cited 20 Mar 2010

  • Conklin, J.W.: The Gravity Probe B Collaboration: The Gravity Probe B experiment and early results. J. Phys. Conf. Ser. 140, 012001 (2008)

    Article  ADS  Google Scholar 

  • Corda, C.: The Virgo-MiniGRAIL cross correlation for the detection of scalar gravitational waves. Mod. Phys. Lett. A 22, 1727 (2007a)

    Article  MathSciNet  ADS  Google Scholar 

  • Corda, C.: The importance of the “magnetic” components of gravitational waves in the response functions of interferometers. Int. J. Mod. Phys. D 16, 1497 (2007b)

    MATH  MathSciNet  ADS  Google Scholar 

  • Corda, C.: Interferometric detection of gravitational waves: the definitive test for general relativity. Int. J. Mod. Phys. D 18, 2275 (2009)

    MATH  ADS  Google Scholar 

  • Corda, C.: A review of the stochastic background of gravitational waves in f(R) gravity with WMAP constrains. Open Astron. J. ArXiv:0901.1193 (2010, in press)

  • Corda, C., Ali, S.A., Cafaro, C.: Interferometer response to scalar gravitational waves. Int. J. Mod. Phys. D. ArXiv:0902.0093 (2010, in press)

  • Costa, L.F.O., Herdeiro, C.A.R.: Gravitoelectromagnetic analogy based on tidal tensors. Phys. Rev. D 78, 024021 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  • Costa, L.F.O., Herdeiro, C.A.R.: In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in fundamental astronomy: dynamics, reference frames, and data analysis. Proceedings IAU Symposium No. 261: EPM ephemerides and relativity, p. 31. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  • Crosta, M.T., Mignard, F.: Microarcsecond light bending by Jupiter. Class. Quantum Gravity 23, 4853 (2006)

    Article  MATH  ADS  Google Scholar 

  • Cugusi, L., Proverbio, E.: Relativistic effects on the motion of the Earth’s. satellites. J. Geodyn. 51, 249 (1977)

    Google Scholar 

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

    ADS  Google Scholar 

  • Degnan, J.J.: Satellite laser ranging: current status and future prospects. IEEE Trans. Geosci. Remote Sens. GE-23, 398 (1985)

    Article  ADS  Google Scholar 

  • Degnan, J.J.: Simulating interplanetary transponder and laser communications experiments via dual station ranging to SLR satellites. In: Proc. 15-th International Workshop on Laser Ranging, Canberra, Australia, October 15–20, 2006: http://cddis.gsfc.nasa.gov/ lw15/docs/papers/Simulating Interplanetary Transponder and Laser Communications Experiments via Dual Station Ranging to SLR Satellites.pdf. Cited 20 Mar 2010

  • Degnan, J.J.: Laser transponders for high-accuracy interplanetary laser ranging and time transfer. In: Dittus, H., Lämmerzahl, C., Turyshev, S.G. (eds.) Lasers, Clocks and Drag-Free Control Exploration of Relativistic Gravity in Space, p. 231. Springer, Berlin (2008)

    Chapter  Google Scholar 

  • de Boer, H.: Experiments relating to the Newtonian gravitational constant. In: Taylor, B.N., Philips, W.D. (eds.) Precision Measurement and Fundamental Constants. Natl. Bur. Stand. US. Spec. Publ. 617, p. 561. Washington, Natl. Bur. Stand. US (1984)

    Google Scholar 

  • de Sitter, W.: Einstein’s theory of gravitation and its astronomical consequences. Mon. Not. R. Astron. Soc. 76, 699 (1916)

    ADS  Google Scholar 

  • Dickey, J.O., Bender, P.L., Faller, J.E., Newhall, X.X., Ricklefs, R.L., Ries, J.G., Shelus, P.J., Veillet, C., Whipple, A.L., Wiant, J.R., Williams, J.G., Yoder, C.F.: Lunar laser ranging: a continuing legacy of the Apollo program. Science 265, 482 (1994)

    Article  ADS  Google Scholar 

  • Dymnikova, I.G.: Motion of particles and photons in the gravitational field of a rotating body (In memory of Vladimir Afanas’evich Ruban). Sov. Phys. Usp. 29, 215 (1986)

    Article  ADS  Google Scholar 

  • Eddington, A.S.: The Mathematical Theory of Relativity. Cambridge University Press, Cambridge (1922)

    Google Scholar 

  • Einstein, A.: Zum gegenwärtigen Stande des Gravitationsproblem. Phys. Z. 14, 1249 (1913)

    Google Scholar 

  • Einstein, A.: Zur allgemeinen Relativitätstheorie. Sitz.-ber. K. Preuß. Akad. Wiss. XLIV, 778 (1915)

    Google Scholar 

  • Einstein, A.: Näherungsweise Integration der Feldgleichungen der Gravitation. Sitz.-ber. K. Preuß. Akad. Wiss., 688 (1916)

  • Einstein, A.: Über Gravitationswellen. Sitz.-ber. K. Preuß. Akad. Wiss. 8, 154 (1918)

    Google Scholar 

  • Everitt, C.W.F.: The gyroscope experiment. I. General description and analysis of gyroscope performance. In: Bertotti, B. (ed.) Proc. Int. School Phys. “Enrico Fermi” Course LVI, p. 331. Academic Press, New York (1974)

    Google Scholar 

  • Everitt, C.W.F., et al.: Testing relativistic gravity in space: gravity probe B: countdown to launch. In: Lämmerzahl, C., Everitt, C.W.F., Hehl, F.W. (eds.) Gyros, Clocks, Interferometers, p. 52. Springer, Berlin (2001)

    Chapter  Google Scholar 

  • Everitt, C.W.F., et al.: Gravity probe B data analysis. Space Sci. Rev. 148, 53 (2009)

    Article  ADS  Google Scholar 

  • Fairbank, W.M., Schiff, L.I.: Proposed experimental test of general relativity. Proposal to NASA. Springer, Berlin (1961)

    Google Scholar 

  • Fienga, A., Manche, H., Laskar, J., Gastineau, M.: INPOP06: a new numerical planetary ephemeris. Astron. Astrophys. 477, 315 (2008)

    Article  ADS  Google Scholar 

  • Fienga, A., Laskar, J., Morley, T., Manche, H., Kuchynka, P., Le Poncin-Lafitte, C., Budnik, F., Gastineau, M., Somenzi, L.: INPOP08, a 4-D planetary ephemeris: from asteroid and time-scale computations to ESA Mars Express and Venus Express contributions. Astron. Astrophys. 507, 1675 (2009)

    Article  ADS  Google Scholar 

  • Fienga, A., Laskar, J., Kuchynka, P., Le Poncin-Lafitte, C., Manche, H., Gastineau, M.: Gravity tests with INPOP planetary ephemerides. In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, Proceedings IAU Symposium No. 261, p. 159. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  • Folkner, W.M., Williams, J.G., Boggs, D.H.: The planetary and lunar ephemeris DE 421. Memorandum IOM 343R-08-003. California Institute of Technology, Jet Propulsion Laboratory (2008)

  • Fomalont, E.B., Kopeikin, S.M.: Radio interferometric tests of general relativity. In: Jin, W.J., Platais, I., Perryman, M.A.C. (eds.) A Giant Step: from Milli- to Micro-arcsecond Astrometry Proceedings IAU Symposium No. 248, 2007, p. 383. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  • Forbes, J.M., Bruinsma, S., Lemoine, F.G., Bowman, B.R., Konopliv, A.S.: Variability of the satellite drag environments of Earth, Mars and Venus due to rotation of the Sun. In: Fall Meeting 2006, American Geophysical Union, Abstract #SA22A-04 (2006)

  • Förste, Ch., Flechtner, F., Schmidt, R., König, R., Meyer, U., Stubenvoll, R., Rothacher, M., Barthelmes, F., Neumayer, H., Biancale, R., Bruinsma, S., Lemoine, J.-M., Loyer, S.: A mean global gravity field model from the combination of satellite mission and altimetry/gravimetry surface data—EIGEN-GL04C. Geophys. Res. Abstr. 8, 03462 (2006)

    Google Scholar 

  • Förste, Ch., Flechtner, F., Schmidt, R., Stubenvoll, R., Rothacher, M., Kusche, J., Neumayer, H., Biancale, R., Lemoine, J.-M., Barthelmes, F., Bruinsma, S., König, R., Meyer, U.: EIGEN-GL05C—a new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. Geophys. Res. Abstr. 10, 03426 (2008)

    Google Scholar 

  • Giazotto, A.: Status of gravitational wave detection. J. Phys. Conf. Ser. 120, 032002 (2008)

    Article  ADS  Google Scholar 

  • Ginzburg, V.L.: The use of artificial earth satellites for verifying the general theory of relativity. Usp. Fiz. Nauk (Adv. Phys. Sci.) 63, 119 (1957)

    MathSciNet  Google Scholar 

  • Ginzburg, V.L.: Artificial satellites and the theory of relativity. Sci. Am. 200, 149 (1959)

    Article  ADS  Google Scholar 

  • Ginzburg, V.L.: In: Recent developments in general relativity: experimental verifications of the general theory of relativity, p. 57. Pergamon, London (1962)

    Google Scholar 

  • Gronwald, F., Gruber, E., Lichtenegger, H.I.M., Puntigam, R.A.: Gravity Probe C(lock)—probing the gravitomagnetic field of the Earth by means of a clock experiment. ESA SP-420, 29 (1997)

  • Guillot, T.: The interiors of giant planets: models and outstanding questions. Ann. Rev. Earth Planet. Sci. 33, 493 (2005)

    Article  ADS  Google Scholar 

  • Haas, M.R., Ross, D.K.: Measurement of the angular momentum of Jupiter and the Sun by use of the Lense-Thirring effect. Astrophys. Space Sci. 32, 3 (1975)

    Article  ADS  Google Scholar 

  • Heaviside, O.: Electromagnetic Theory, Vol. I. The Electrician Printing and Publishing Co., London (1894)

    Google Scholar 

  • Hiscock, W.A., Lindblom, L.: Post-Newtonian effects on satellite orbits near Jupiter and Saturn. Astrophys. J. 231, 224 (1979)

    Article  ADS  Google Scholar 

  • Holzmüller, G.: Über die Anwendung der Jacobi-Hamilton’schen Methode auf den Fall der Anziehung nach dem elektrodynamischen Gesetze von Weber. Z. Math. Phys. 15, 69 (1870)

    Google Scholar 

  • Hori, Y., Sano, T., Ikoma, M., Ida, S.: On uncertainty of Jupiter’s core mass due to observational errors. In: Sun, Y.-S., Ferraz-Mello, S., Zhou, J.-L. (eds.) Exoplanets: Detection, Formation and Dynamics, Proceedings IAU Symposium, No. 249, p. 163. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  • Hulse, R.A., Taylor, J.H.: Discovery of a pulsar in a binary system. Astrophys. J. Lett. 195, L51 (1975)

    Article  ADS  Google Scholar 

  • Inversi, P., Vespe, F.: Direct and indirect solar radiation effects acting on LAGEOS satellite: Some refinements. Adv. Space Res. 14, 73 (1994)

    Article  ADS  Google Scholar 

  • Iorio, L.: An alternative derivation of the Lense-Thirring drag on the orbit of a test body. Nuovo Cim. B 116, 777 (2001a)

    ADS  Google Scholar 

  • Iorio, L.: Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect. Class. Quantum Gravity 18, 4303 (2001b)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L.: Satellite gravitational orbital perturbations and the gravitomagnetic clock effect. Int. J. Mod. Phys. D 11, 599 (2001c)

    Google Scholar 

  • Iorio, L.: Letter to the editor: a critical approach to the concept of a polar, low-altitude LARES satellite. Class. Quantum Gravity 19, L175 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Iorio, L.: Letter to the editor: on the possibility of measuring the Earth’s gravitomagnetic force in a new laboratory experiment. Class. Quantum Gravity 20, L5 (2003a)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L.: A new proposal for measuring the Lense-Thirring effect with a pair of supplementary satellites in the gravitational field of the Earth. Phys. Lett. A 308, 81 (2003b)

    Article  MathSciNet  ADS  Google Scholar 

  • Iorio, L.: 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, 277 (2003c)

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Iorio, L.: 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 (2005c)

    Article  MathSciNet  ADS  Google Scholar 

  • Iorio, L.: Is it possible to measure the Lense-Thirring effect on the orbits of the planets in the gravitational field of the Sun? Astron. Astrophys. 431, 385 (2005d)

    Article  ADS  Google Scholar 

  • Iorio, L.: On the impossibility of measuring the general relativistic part of the terrestrial acceleration of gravity with superconducting gravimeters. J. Geophys. Res. 167, 567 (2006a)

    Google Scholar 

  • Iorio, L.: A critical analysis of a recent test of the Lense-Thirring effect with the LAGEOS satellites. J. Geodyn. 80, 128 (2006b)

    MATH  ADS  Google Scholar 

  • Iorio, L.: Comments, replies and notes: a note on the evidence of the gravitomagnetic field of Mars. Class. Quantum Gravity 23, 5451 (2006c)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L. (ed.): The Measurement of Gravitomagnetism: A Challenging Enterprise. NOVA, Hauppauge (2007a)

    Google Scholar 

  • Iorio, L.: A comment on the paper “On the orbit of the LARES satellite”, by Ciufolini, I. Planet. Space Sci. 55, 1198 (2007b)

    Article  ADS  Google Scholar 

  • Iorio, L.: LARES/WEBER-SAT and the equivalence principle. Europhys. Lett. 80, 40007 (2007c)

    Article  ADS  Google Scholar 

  • Iorio, L.: 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 Iorio, L.: ”, by Ciufolini, I., and E. Pavlis. Planet. Space Sci. 55, 503 (2007d)

    Article  ADS  Google Scholar 

  • Iorio, L.: First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data. Planet. Space Sci. 55, 1290 (2007e)

    Article  ADS  Google Scholar 

  • Iorio, L.: Dynamical determination of the mass of the Kuiper Belt from motions of the inner planets of the Solar system. Mon. Not. R. Astron. Soc. 375, 1311 (2007f)

    Article  ADS  Google Scholar 

  • Iorio, L.: Is it possible to measure the Lense-Thirring effect in the gravitational fields of the Sun and of Mars? In: Iorio, L. (ed.) The Measurement of Gravitomagnetism: A Challenging Enterprise, p. 177. NOVA, Hauppauge (2007g)

    Google Scholar 

  • Iorio, L.: Advances in the measurement of the Lense-Thirring effect with planetary motions in the field of the Sun. Schol. Res. Exch. 2008, 105235 (2008)

    ADS  Google Scholar 

  • Iorio, L.: Will it be possible to measure intrinsic gravitomagnetism with lunar laser ranging? Int. J. Mod. Phys. D 18, 1319 (2009a)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L.: Mars and frame-dragging: study for a dedicated mission. Gen. Relativ. Gravit. 41, 1273 (2009b)

    Article  MATH  ADS  Google Scholar 

  • 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 (2009c)

    Article  ADS  Google Scholar 

  • Iorio, L.: A conservative approach to the evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test. Centr. Eur. J. Phys. 8, 25 (2010a)

    Article  ADS  Google Scholar 

  • Iorio, L.: On possible a-priori “imprinting” of general relativity itself on the performed Lense-Thirring tests with LAGEOS satellites. Commun. Netw. 2, 26 (2010b)

    Article  Google Scholar 

  • Iorio, L.: On the impact of the atmospheric drag on the LARES mission. Acta Phys. Pol. B 4, 753 (2010c)

    Google Scholar 

  • Iorio, L.: Effects of standard and modified gravity on interplanetary ranges. http://arxiv.org/abs/1002.4585 (2010d)

  • Iorio, L.: On the Lense-Thirring test with the Mars Global Surveyor in the gravitational field of Mars. Centr. Eur. J. Phys. 8, 509 (2010e)

    Article  ADS  Google Scholar 

  • Iorio, L.: Juno, the angular momentum of Jupiter and the Lense-Thirring effect. New Astron. 15, 554 (2010f)

    Article  ADS  Google Scholar 

  • Iorio, L., Corda, C.: Gravitomagnetic effect in gravitational waves. AIP Conf. Proc. 1168, 1072 (2009)

    Article  ADS  Google Scholar 

  • Iorio, L., Corda, C.: Gravitomagnetism and gravitational waves. Open Astron. J. ArXiv:1001.3951 (2010, in press)

  • Iorio, L., Lainey, V.: The Lense-Thirring effect in the Jovian system of the Galilean satellites and its measurability. Int. J. Mod. Phys. D 14, 2039 (2005)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L., Lichtenegger, H.I.M.: On the possibility of measuring the gravitomagnetic clock effect in an Earth space-based experiment. Class. Quantum Gravity 22, 119 (2005)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L., Morea, A.: The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect. Gen. Relativ. Gravit. 36, 1321 (2004)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L., Lucchesi, D.M., Ciufolini, I.: The LARES mission revisited: an alternative scenario. Class. Quantum Gravity 19, 4311 (2002a)

    Article  MATH  ADS  Google Scholar 

  • Iorio, L., Lichtenegger, H.I.M., Mashhoon, B.: An alternative derivation of the gravitomagnetic clock effect. Class. Quantum Gravity 19, 39 (2002b)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Irwin, P.: Giant Planets of Our Solar System. Springer, Berlin (2003)

    Google Scholar 

  • Jacobson, R.A.: JUP230 orbit solution (2003)

  • Jacobson, R.A., Rush, B.: Ephemerides of the martian satellites—MAR063, JPL IOM 343R-06-004 (2006)

  • Jäggi, A., Beutler, G., Mervart, L.: GRACE gravity field determination using the celestial mechanics approach—first results. In: IAG Symposium on “Gravity, Geoid, and Earth Observation 2008”, Chania, GR, 23–27 June 2008

  • Jäggi, A., Beutler, G., Meyer, U., Prange, L., Dach, R., Mervart, L.: AIUB-GRACE02S—Status of GRACE gravity field recovery using the celestial mechanics approach. In: IAG Scientific Assembly 2009, Buenos Aires, Argentina, August 31–September 4 (2009)

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

    Google Scholar 

  • Keiser, G.M., Kolodziejczak, J., Silbergleit, A.S.: Misalignment and resonance torques and their treatment in the GP-B data analysis. Space Sci. Rev. 148, 383 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Klein, M.J., Kox, A.J., Schulmann, R. (eds.): The Collected Papers of Albert Einstein. Vol. 4. The Swiss Years: Writings, 1912–1914, p. 344. Princeton University Press, Princeton (1995)

    Google Scholar 

  • Kolbenstvedt, H.: Gravomagnetism in special relativity. Am. J. Phys. 56, 523 (1988)

    Article  ADS  Google Scholar 

  • Konopliv, A.S., Yoder, C.F., Standish, E.M., Yuan, D.-N., Sjogren, W.L.: A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris. Icarus 182, 23 (2006)

    Article  ADS  Google Scholar 

  • Kopeikin, S.M., Fomalont, E.B.: Aberration and the fundamental speed of gravity in the jovian deflection experiment. Found. Phys. 36, 1244 (2006)

    Article  MATH  ADS  Google Scholar 

  • Kopeikin, S.M.: Comment on “Gravitomagnetic influence on gyroscopes and on the lunar orbit”. Phys. Rev. Lett. 98, 229001 (2007)

    Article  ADS  Google Scholar 

  • Kramer, M., Stairs, I.H., Manchester, R.N., McLaughlin, M.A., Lyne, A.G., Ferdman, R.D., Burgay, M., Lorimer, D.R., Possenti, A., D’Amico, N., Sarkissian, J.M., Hobbs, G.B., Reynolds, J.E., Freire, P.C.C., Camilo, F.: Tests of general relativity from timing the double pulsar. Science 314, 97 (2006)

    Article  ADS  Google Scholar 

  • Krasinsky, G.A., Pitjeva, E.V., Vasilyev, M.V., Yagudina, E.I.: Hidden mass in the asteroid belt. Icarus 158, 98 (2002)

    Article  ADS  Google Scholar 

  • Krogh, K.: Comments, replies and notes: Comment on ‘Evidence of the gravitomagnetic field of Mars’. Class. Quantum Gravity 24, 5709 (2007)

    Article  ADS  Google Scholar 

  • Lainey, V., Dehant, V., Pätzold, M.: First numerical ephemerides of the martian moons. Astron. Astrophys. 465, 1075 (2007)

    Article  ADS  Google Scholar 

  • Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields, 4th edn. Pergamon, New York (1975)

    Google Scholar 

  • Lämmerzahl, C., Neugebauer, G.: The Lense-Thirring effect: from the basic notions to the observed effects. In: Lämmerzahl, C., Everitt, C.W.F., Hehl, F.W. (eds.) Gyros, Clocks, Interferometers…: Testing Relativistic Gravity in Space, p. 31. Springer, Berlin (2001a)

    Chapter  Google Scholar 

  • 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., Olson, T.R.: The development of the joint NASA GSFC and the National Imagery Mapping Agency (NIMA) geopotential model EGM96. NASA/TP-1998-206861 (1998)

  • Lense, J., Thirring, H.: Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z. 19, 156 (1918)

    Google Scholar 

  • Lerch, F.J., Nerem, R.S., Putney, B.H., Felsentreger, T.L., Sanchez, B.V., Marshall, J.A., Klosko, S.M., Patel, G.B., Williamson, R.G., Chinn, D.S.: A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM-T3. J. Geophys. Res. 99, 2815 (1994)

    Article  ADS  Google Scholar 

  • Lichtenegger, H.I.M., Gronwald, F., Mashhoon, B.: On detecting the gravitomagnetic field of the Earth by means of orbiting clocks. Adv. Space Res. 25, 1255 (2000)

    Article  ADS  Google Scholar 

  • Lichtenegger, H.I.M., Iorio, L., Mashhoon, B.: The gravitomagnetic clock effect and its possible observation. Ann. Phys. 15, 868 (2006)

    Article  MATH  Google Scholar 

  • Lichtenegger, H.I.M., Iorio, L.: Post-Newtonian orbital perturbations. In: Iorio, L. (ed.) The Measurement of Gravitomagnetism: A Challenging Enterprise, p. 87. NOVA, Hauppauge (2007)

    Google Scholar 

  • Ljubičić, A., Logan, B.A.: A proposed test of the general validity of Mach’s principle. Phys. Lett. A 172, 3 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  • Lucchesi, D.M.: 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, 447 (2001)

    Article  ADS  Google Scholar 

  • Lucchesi, D.M.: 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 (2002)

    Article  ADS  Google Scholar 

  • Lucchesi, D.M.: The asymmetric reflectivity effect on the LAGEOS satellites and the germanium retroreflectors. Geophys. Res. Lett. 30, 1957 (2003)

    Article  ADS  Google Scholar 

  • Lucchesi, D.M.: LAGEOS satellites germanium cube-corner-retroreflectors and the asymmetric reflectivity effect. Celest. Mech. Dyn. Astron. 88, 269 (2004)

    Article  MATH  ADS  Google Scholar 

  • 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. Mod. Phys. D 14, 2005 (1989)

    Google Scholar 

  • Lucchesi, D.M.: The Lense Thirring effect measurement and LAGEOS satellites orbit analysis with the new gravity field model from the CHAMP mission. Adv. Space Res. 39, 324 (2007a)

    Article  ADS  Google Scholar 

  • Lucchesi, D.M.: The LAGEOS satellites orbital residuals determination and the way to extract gravitational and non-gravitational unmodeled perturbing effects. Adv. Space Res. 39, 1559 (2007b)

    Article  ADS  Google Scholar 

  • Lucchesi, D.M., Paolozzi, A.: A cost effective approach for LARES satellite. In: XVI Congresso Nazionale AIDAA, Palermo, IT, 24–28 September 2001

  • Lucchesi, D.M., Ciufolini, I., Andrés, J.I., Pavlis, E.C., Peron, R., Noomen, R., Currie, D.G.: LAGEOS II perigee rate and eccentricity vector excitations residuals and the Yarkovsky–Schach effect. Planet. Space Sci. 52, 699 (2004)

    Article  ADS  Google Scholar 

  • Lucchesi, D.M., Balmino, G.: The LAGEOS satellites orbital residuals determination and the Lense Thirring effect measurement. Planet. Space Sci. 54, 581 (2006)

    ADS  Google Scholar 

  • Lyth, D.H., Liddle, A.R.: Primordial Density Perturbation. Cambridge University Press, Cambridge (2009)

    MATH  Google Scholar 

  • Machida, M.N., Kokubo, E., Inutsuka, S., Matsumoto, T.: Angular momentum accretion onto a gas giant planet. Astrophys. J. 685, 1220 (2008)

    Article  ADS  Google Scholar 

  • Marov, M.Ya., Avduevsky, V.S., Akim, E.L., Eneev, T.M., Kremnev, R.S., Kulikov, S.D., Pichkhadze, K.M., Popov, G.A., Rogovsky, G.N.: Phobos-Grunt: Russian sample return mission. Adv. Space Res. 33, 2276 (2004)

    Article  ADS  Google Scholar 

  • Mashhoon, B.: Gravitoelectromagnetism: a brief review. In: Iorio, L. (ed.) The Measurement of Gravitomagnetism: A Challenging Enterprise, p. 29. NOVA, Hauppauge (2007)

    Google Scholar 

  • Mashhoon, B., Theiss, D.S.: Relativistic tidal forces and the possibility of measuring them. Phys. Rev. Lett. 49, 1542 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  • Mashhoon, B., Paik, H.J., Will, C.M.: Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer, theoretical principles. Phys. Rev. D 39, 2825 (1989)

    Article  ADS  Google Scholar 

  • Mashhoon, B., Gronwald, F., Theiss, D.S.: On measuring gravitomagnetism via spaceborne clocks: a gravitomagnetic clock effect. Ann. Phys. 8, 135 (1999)

    Article  MATH  Google Scholar 

  • Mashhoon, B., Gronwald, F., Lichtenegger, H.I.M.: Testing relativistic gravity in space: gravitomagnetism and the clock effect. In: Lämmerzahl, C., Everitt, C.W.F., Hehl, F.W. (eds.) Gyros, Clocks, Interferometers…, p. 83. Springer, Berlin (2001a)

    Chapter  Google Scholar 

  • Mashhoon, B., Iorio, L., Lichtenegger, H.I.M.: On the gravitomagnetic clock effect. Phys. Lett. A 292, 49 (2001b)

    Article  MATH  ADS  Google Scholar 

  • Mathisson, M.: Neue Mechanik materieller Systemes. Acta Phys. Pol. 6, 163 (1937)

    MATH  Google Scholar 

  • Matousek, S.: The Juno New Frontiers mission. Acta Astronaut. 61, 932 (2007)

    Article  ADS  Google Scholar 

  • Mayer-Gürr, T., Eicker, A., Ilk, K.-H.: 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

  • Mayer-Gürr, T.: ITG-Grace03s: The latest GRACE gravity field solution computed in Bonn Joint Int. GSTM and DFG SPP Symp., Potsdam, D, 15–17 October 2007. http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace03. Cited 20 Mar 2010

  • Mayer-Gürr, T., Kurtenbach, E., Eicker, A.: The satellite-only gravity field model ITG-Grace2010s. http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010. Cited 20 Mar 2010

  • McCarthy, D.D., Petit, G.: IERS Conventions (2003), p. 106. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main (2004)

    Google Scholar 

  • Merkowitz, S.M., Dabney, P.W., Livas, J.C., McGarry, J.F., Neumann, G.A., Zagwodzki, T.W.: Laser ranging for gravitational, lunar and planetary science. Int. J. Mod. Phys. D 16, 2151 (2007)

    Article  ADS  Google Scholar 

  • Milani, A., Nobili, A.M., Farinella, P.: Non-gravitational Perturbations and Satellite Geodesy. Adam Hilger, Bristol (1987)

    MATH  Google Scholar 

  • Milani, A., Vokrouhlický, D., Villani, D., Bonanno, C., Rossi, A.: Testing general relativity with the BepiColombo radio science experiment. Phys. Rev. D 66, 082001 (2002)

    Article  ADS  Google Scholar 

  • Milani, A., Tommei, G., Vokrouhlický, D., Latorre, E., Cicalò, S.: Relativistic models for the BepiColombo radioscience experiment. In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Proceedings of the International Astronomical Union, IAU Symposium, Vol. 261. Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, p. 356. Cambridge University Press, Cambridge (2008)

    Google Scholar 

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

    Google Scholar 

  • Mohr, P.J., Taylor, B.N.: CODATA recommended values of the fundamental physical constants: 1998. J. Phys. Chem. Ref. Data 28, 1713 (1999)

    Article  ADS  Google Scholar 

  • Muhlfelder, B., Adams, M., Clarke, B., Keiser, G.M., Kolodziejczak, J., Li, J., Lockhart, J.M., Worden, P.: GP-B systematic error determination. Space Sci. Rev. 148, 429 (2009)

    Article  ADS  Google Scholar 

  • Murphy, T.W., Nordtvedt, K., Turyshev, S.G.: Gravitomagnetic influence on gyroscopes and on the lunar orbit. Phys. Rev. Lett. 98, 071102 (2007a)

    Article  ADS  Google Scholar 

  • Murphy, T.W., Nordtvedt, K., Turyshev, S.G.: Murphy, Nordtvedt, and Turyshev reply. Phys. Rev. Lett. 98, 229002 (2007b)

    Article  ADS  Google Scholar 

  • Murphy, T.W., Adelberger, E.G., Battat, J.B.R., Carey, L.N., Hoyle, C.D., Leblanc, P., Michelsen, E.L., Nordtvedt, K. Jr., Orin, A.E., Strasburg, J.D., Stubbs, C.W., Swanson, H.E., Williams, E.: The Apache point observatory lunar laser-ranging operation: instrument description and first detections. Publ. Astron. Soc. Pacif. 120, 20 (2008)

    Article  ADS  Google Scholar 

  • Neumann, G., Cavanaugh, J., Coyle, B., McGarry, J., Smith, D., Sun, X., Zagwodzki, T., Zuber, M.: Laser ranging at interplanetary distances. In: Proc. 15-th International Workshop on Laser Ranging, Canberra, Australia, October 15–20, 2006. http://cddis.gsfc.nasa. gov/lw15/docs/papers/Laser Ranging at Interplanetary Distances.pdf. Cited 20 Mar 2010

  • Newhall, X.X., Standish, E.M., Williams, J.G.: DE 102—a numerically integrated ephemeris of the moon and planets spanning forty-four centuries. Astron. Astrophys. 125, 150 (1983)

    MATH  ADS  Google Scholar 

  • Ni, W.-T.: Theoretic frameworks for testing relativistic gravity IV. Astrophys. J. 176, 769 (1972)

    Article  ADS  Google Scholar 

  • Ni, W.-T.: ASTROD and ASTROD I—overview and progress. Int. J. Mod. Phys. D 17, 921 (2008)

    Article  MATH  ADS  Google Scholar 

  • Nordtvedt, K. Jr.: Equivalence principle for massive bodies II. Theory. Phys. Rev. 169, 1017 (1968)

    Article  ADS  Google Scholar 

  • Nordtvedt, K. Jr.: Equivalence principle for massive bodies including rotational energy and radiation pressure. Phys. Rev. 180, 1293 (1969)

    Article  ADS  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Nordtvedt, K. Jr.: Slr contributions to fundamental physics. Surv. Geophys. 22, 597 (2001)

    Article  ADS  Google Scholar 

  • Nordtvedt, K. Jr.: Some considerations on the varieties of frame dragging. In: Ruffini, R.J., Sigismondi, C. (eds.): Nonlinear Gravitodynamics. The Lense-Thirring Effect, p. 35. World Scientific, Singapore (2003)

    Chapter  Google Scholar 

  • North, J.D.: The Measure of the Universe. Dover, New York (1989)

    Google Scholar 

  • Ohanian, H.C., Ruffini, R.J.: Gravitation and Spacetime, 2nd edn. Norton, New York (1994)

    MATH  Google Scholar 

  • Paik, H.-J.: Tests of general relativity in earth orbit using a superconducting gravity gradiometer. Adv. Space Res. 9, 41 (1989)

    Article  ADS  Google Scholar 

  • Paik, H.-J.: Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer: principle and experimental considerations. Gen. Relativ. Gravit. 40, 907 (2008)

    Article  MATH  ADS  Google Scholar 

  • Papapetrou, A.: Spinning test-particles in general relativity. I. Proc. R. Soc. Lond. Series A, Math. Phys. Sci. 209, 248 (1951)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Pavlis, E.C.: Geodetic contributions to gravitational experiments in space. In: Cianci, R., Collina, R., Francaviglia, M., Fré, P. (eds.) Recent Developments in General Relativity, Proc. 14th SIGRAV Conf. on General Relativity and Gravitational Physics, Genova, IT, 18–22 September 2000, p. 217. Springer, Berlin (2002)

    Google Scholar 

  • Peirce, B.: Criterion for the rejection of doubtful observations. Astron. J. 2, 161 (1852); Errata. Astron. J. 2, 176 (1852)

    Article  ADS  Google Scholar 

  • Pfister, H.: On the history of the so-called Lense-Thirring effect. Gen. Relativ. Gravit. 39, 1735 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Pijpers, F.P.: Helioseismic determination of the solar gravitational quadrupole moment. Mon. Not. R. Astron. Soc. 297, L76 (1998)

    Article  ADS  Google Scholar 

  • Pijpers, F.P.: Asteroseismic determination of stellar angular momentum. Astron. Astrophys. 402, 683 (2003)

    Article  ADS  Google Scholar 

  • Pirani, F.A.E.: On the physical significance of the Riemann tensor. Acta Phys. Pol. 15, 389 (1956)

    MathSciNet  Google Scholar 

  • Pirani, F.A.E.: Invariant formulation of gravitational radiation theory. Phys. Rev. 105, 1089 (1957)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Pireaux, S., Rozelot, J.-P.: Solar quadrupole moment and purely relativistic gravitation contributions to Mercury’s perihelion advance. Astrophys. Space Sci. 284, 1159 (2003)

    Article  ADS  Google Scholar 

  • Pitjeva, E.V.: Relativistic effects and solar oblateness from radar observations of planets and spacecraft. Astron. Lett. 31, 340 (2005a)

    Article  ADS  Google Scholar 

  • Pitjeva, E.V.: High-precision ephemerides of planets-EPM and determination of some astronomical constants. Sol. Syst. Res. 39, 176 (2005b)

    Article  ADS  Google Scholar 

  • Pitjeva, E.V.: Use of optical and radio astrometric observations of planets, satellites and spacecraft for ephemeris astronomy. In: Jin, W.J., Platais, I., Perryman, M.A.C. (eds.) A Giant Step: From Milli- to Micro-arcsecond Astrometry, p. 20. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  • Pitjeva, E.V.: EPM ephemerides and relativity. In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, Proceedings IAU Symposium No. 261, p. 170. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  • Polnarev, A.G.: Proposals for an experiment to detect the Earth’s gravitomagnetic field. In: Kovalevsky, J., Brumberg, V.H. (eds.) Relativity in Celestial Mechanics and Astrometry. High Precision Dynamical Theories and Observational Verifications. Proceedings IAU Symposium No. 114, p. 401. Reidel, Dordrecht (1986)

    Google Scholar 

  • Pugh, G.E.: WSEG research memorandum No. 11 (1959)

  • Reigber, Ch., Schmidt, R., Flechtner, F., König, 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 (2005)

    Article  Google Scholar 

  • Ries, J.C.: Relativity in satellite laser ranging. Bull. Am. Astron. Soc. 41, 889 (2009)

    Google Scholar 

  • Ries, J.C., Eanes, R.J., Watkins, M.M., Tapley, B.D.: 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 

  • Ries, J.C., Eanes, R.J., Tapley, B.D.: In: Ruffini, R.J., Sigismondi, C. (eds.) Nonlinear Gravitodynamics. The Lense–Thirring Effect: Lense-Thirring Precession Determination from Laser Ranging to Artificial Satellites, p. 201. World Scientific, Singapore (2003a)

    Google Scholar 

  • Ries, J.C., Eanes, R.J., Tapley, B.D., Peterson, G.E.: Prospects for an improved Lense-Thirring test with SLR and the GRACE Gravity Mission, Greenbelt: NASA Goddard. In: Noomen, R., Klosko, S., Noll, C., Pearlman, M. (eds.) Proc. 13th Int. Laser Ranging Workshop, NASA CP (2003-212248). (2003b). http://cddis.gsfc.nasa.gov/lw13/docs/papers/sci_ries_1m.pdf. Cited 20 Mar 2010

  • Ries, J.C., Eanes, R.J., Watkins, M.M.: Confirming the frame-dragging effect with satellite laser ranging. In: Schillak, S. (ed.) Proc. 16th Int. Laser Ranging Workshop, Poznań (PL) 13–17 October 2008 (2008). http://cddis.gsfc.nasa.gov/lw16/docs/papers/sci_3_Ries_p.pdf. Cited 20 Mar 2010

  • Rindler, W.: Relativity. Special, General and Cosmological. Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  • Ross, S.M.: Peirce’s criterion for the elimination of suspect experimental data. J. Eng. Technol. (Fall 2003)

  • Roy, A.E.: Orbital Motion, 4th edn. Institute of Physics, Bristol (2005)

    Google Scholar 

  • Rubincam, D.P.: On the secular decrease in the semimajor axis of Lageos’s orbit. Celest. Mech. Dyn. Astron. 26, 361 (1982)

    MATH  Google Scholar 

  • Ruggiero, M.L., Tartaglia, A.: Gravitomagnetic effects. Nuovo Cim. B 117, 743 (2002)

    ADS  Google Scholar 

  • Schäfer, G.: Gravitomagnetic effects. Gen. Relativ. Gravit. 36, 2223 (2004)

    Article  MATH  ADS  Google Scholar 

  • Schäfer, G.: Gravitomagnetism in physics and astrophysics. Space Sci. Rev. 148, 37 (2009)

    Article  ADS  Google Scholar 

  • Schiff, L.I.: Possible new experimental test of general relativity theory. Phys. Rev. Lett. 4, 215 (1960a)

    Article  ADS  Google Scholar 

  • Schiff, L.I.: On experimental tests of the general theory of relativity. Am. J. Phys. 28, 340 (1960b)

    Article  MathSciNet  ADS  Google Scholar 

  • Schiff, L.I.: Motion of gyroscope according to Einsteins theory of gravitation. Proc. Natl. Acad. Sci. USA 46, 871 (1960c)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Schulmann, R., Kox, A.J., Janssen, M., Illy, J. (eds.): The Collected Papers of Albert Einstein. Vol. 8. The Berlin Years: Correspondence, 1914–1918. Princeton University Press, Princeton (1998), Documents 361, 369, 401, 405

    MATH  Google Scholar 

  • Silbergleit, A.S., Conklin, J., DeBra, D., Dolphin, M., Keiser, G.M., Kozaczuk, J., Santiago, D., Salomon, M., Worden, P.: Polhode motion, trapped flux, and the GP-B science data analysis. Space Sci. Rev. 148, 397 (2009)

    Article  ADS  Google Scholar 

  • Smith, D.E., Zuber, M.T., Sun, X., Neumann, G.A., Cavanaugh, J.F., McGarry, J.F., Zagwodzki, T.W.: Two-way laser link over interplanetary distance. Science 311, 53 (2006)

    Article  Google Scholar 

  • Smoot, G.F., Steinhardt, P.J.: Gravity’s rainbow. Gen. Relativ. Gravit. 25, 1095 (1993)

    Article  ADS  Google Scholar 

  • Soffel, M.H.: Relativity in Astrometry, Celestial Mechanics and Geodesy. Springer, Berlin (1989)

    Google Scholar 

  • Soffel, M.H., Klioner, S.A., Petit, G., Wolf, P., Kopeikin, S.M., Bretagnon, P., Brumberg, V.A., Capitaine, N., et al.: The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement. Astron. J. 126, 2687 (2003)

    Article  ADS  Google Scholar 

  • Soffel, M.H., Klioner, S.A., Müller, J., Biskupek, L.: Gravitomagnetism and lunar laser ranging. Phys. Rev. D 78, 024033 (2008)

    Article  ADS  Google Scholar 

  • Spergel, D.N., Verde, D.N., Peiris, H.V., Komatsu, E., Nolta, M.R., et al.: First Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters. Astrophys. J. Suppl. 148, 175 (2003)

    Article  ADS  Google Scholar 

  • Standish, E.M.: JPL planetary and lunar ephemerides. DE414 Interoffice Memo IOM 343R-06-002 (2006)

  • Stedman, G.E., Schreiber, K.U., Bilger, H.R.: On the detectability of the Lense Thirring field from rotating laboratory masses using ring laser gyroscope interferometers. Class. Quantum Gravity 20, 2527 (2003)

    Article  MATH  ADS  Google Scholar 

  • Stella, L., Possenti, A.: Lense-Thirring precession in the astrophysical context. Space Sci. Rev. 148, 105 (2009)

    Article  ADS  Google Scholar 

  • Tapley, B.D., Ries, J.C., Bettadpur, S., Chambers, D., Cheng, M.K., Condi, F., Gunter, B., Kang, Z., Nagel, P., Pastor, R., Pekker, T., Poole, S., Wang, F.: GGM02-An improved Earth gravity field model from GRACE. J. Geodyn. 79, 467 (2005)

    ADS  Google Scholar 

  • Tapley, B.D., Ries, J.C., Bettadpur, S., Chambers, D., Cheng, M.K., Condi, F., Poole, S.: In: Fall Meeting 2007, American Geophysical Union, Abstract #G42A-03 (2007)

  • Tartaglia, A.: Geometric treatment of the gravitomagnetic clock effect. Gen. Relativ. Gravit. 32, 1745 (2000a)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Tartaglia, A.: Detection of the gravitomagnetic clock effect. Class. Quantum Gravity 17, 783 (2000b)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Tartaglia, A., Ruggiero, M.L.: Angular momentum effects in Michelson-Morley type experiments. Gen. Relativ. Gravit. 34, 1371 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Tartaglia, A., Ruggiero, M.L.: Gravito-electromagnetism versus electromagnetism. Eur. J. Phys. 25, 203 (2004)

    Article  MATH  Google Scholar 

  • Taylor, J.: Error Analysis, 2nd edn., p. 166. University Sci. Books, Sausalito (1997)

    Google Scholar 

  • Theiss, D.S.: A general relativistic effect of a rotating spherical mass and the possibility of measuring it in a space experiment. Phys. Lett. A 109, 19 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  • Thirring, H.: Über die formale Analogie zwischen den elektromagnetischen Grundgleichungen und den Einsteinschen Gravitationsgleichungen erster Näherung. Phys. Z. 19, 204 (1918a)

    Google Scholar 

  • Thirring, H.: Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Phys. Z. 19, 33 (1918b)

    Google Scholar 

  • Thirring, H.: Berichtigung zu meiner Arbeit: “Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie”. Phys. Z. 22, 29 (1921)

    Google Scholar 

  • Thorne, K.S., MacDonald, D.A., Price, R.H. (eds.): Black Holes: The Membrane Paradigm. Yale University Press, Yale (1986)

    Google Scholar 

  • Thorne, K.S.: Gravitomagnetism, jets in quasars, and the Stanford gyroscope experiment. In: Fairbank, J.D., Deaver, B.S., Everitt, C.W.F., Michelson, P.F. (eds.) Near Zero: New Frontiers of Physics, p. 573. Freeman, New York (1988)

    Google Scholar 

  • Tisserand, F.F.: Sur le mouvement des planètes au tour du Soleil, d’après la loi électrodynamique de Weber. C. R. Acad. Sci. (Paris) 75, 760 (1872)

    Google Scholar 

  • Tisserand, F.F.: Sur le mouvement des planètes, en supposant l’attraction représentée par l’une des lois électrodynamiques de Gauss ou de Weber. C. R. Acad. Sci. (Paris) 100, 313 (1890)

    Google Scholar 

  • Turyshev, S.G., Williams, J.G.: Space-based tests of gravity with laser ranging. Int. J. Mod. Phys. D 16, 2165 (2007)

    Article  ADS  Google Scholar 

  • Turyshev, S.G., Shao, M., Nordtvedt, K., Dittus, H., Lämmerzahl, C., Theil, S., Salomon, C., Reynaud, S., Damour, T., Johann, U., Bouyer, P., Touboul, P., Foulon, B., Bertolami, O., Páramos, J.: Advancing fundamental physics with the laser astrometric test of relativity, the LATOR mission. Exp. Astron. 27, 27 (2009)

    Article  ADS  Google Scholar 

  • 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 (1976a)

    Article  ADS  Google Scholar 

  • Van Patten, R.A., Everitt, C.W.F.: A possible experiment with two counter-rotating drag-free satellites to obtain a new test of Einsteins general theory of relativity and improved measurements in geodesy. Celest. Mech. Dyn. Astron. 13, 429 (1976b)

    Google Scholar 

  • Vespe, F.: The perturbations of Earth penumbra on LAGEOS II perigee and the measurement of Lense-Thirring gravitomagnetic effect. Adv. Space Res. 23, 699 (1999)

    Article  ADS  Google Scholar 

  • Vladimirov, Yu., Mitskiévic, N., Horský, J.: Space Time Gravitation, p. 91. Mir, Moscow (1987)

    Google Scholar 

  • Vrbik, J.: Zonal-harmonics perturbations. Celest. Mech. Dyn. Astron. 91, 217 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Weber, J.: Gravitational waves. First Award at the 1959 Gravity Research Foundation Competion. Available from www.gravityresearchfoundation.org (1959)

  • Weber, J.: Detection and generation of gravitational waves. Phys. Rev. 117, 306 (1960)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Weber, J.: Evidence for discovery of gravitational radiation. Phys. Rev. Lett. 22, 1320 (1969)

    Article  ADS  Google Scholar 

  • Weber, W.: Elektrodynamische Massbestimmungen über ein allgemeines Grundgesetz der elektrischen Wirkung. Abh. Kön. Sächsischen Ges. Wiss., p. 211 (1846)

  • Wermuth, M., Svehla, D., Földvary, L., Gerlach, Ch., Gruber, T., Frommknecht, B., Peters, T., Rothacher, M., Rummel, R., Steigenberger, P.: A gravity field model from two years of CHAMP kinematic orbitsusing the energy balance approach. Presentation at EGU 1st General Assmbly, 25–30 April, Nice, France (2004)

  • Whittaker, E.: A History of the Theories of Aether and Electricity, Vol. I: The Classical Theories. Harper, New York (1960)

    Google Scholar 

  • Will, C.M.: Theoretical frameworks for testing relativistic gravity II: parameterized post-Newtonian hydrodynamics and the Nordtvedt effect. Astrophys. J. 163, 611 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  • Will, C.M., Nordtvedt, K. Jr.: Conservation laws and preferred frames in relativistic gravity I. Astrophys. J. 177, 757 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  • Will, C.M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge (1993). Revised edn.

    MATH  Google Scholar 

  • Will, C.M.: The confrontation between general relativity and experiment. Living Rev. Relativ. 9, 3 (2006) Cited 29 Jul 2010. http://www.livingreviews.org/lrr-2006-3

    ADS  Google Scholar 

  • Williams, R.K.: Extracting X rays, γ rays, and relativistic ee+ pairs from supermassive Kerr black holes using the Penrose mechanism. Phys. Rev. D 51, 5387 (1995)

    Article  ADS  Google Scholar 

  • Williams, R.K.: Collimated escaping vortical polar ee+ jets intrinsically produced by rotating black holes and Penrose processes. Astrophys. J. 611, 952 (2004)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  • Yoder, C.F.: Astrometric and geodetic properties of Earth and the solar system. Table 6. In: Ahrens, T.J. (ed.) Global Earth Physics a Handbook of Physical Constants. AGU Reference Shelf Series, Vol. 1 (1995)

  • You, R.J.: The gravitational Larmor precession of the Earth’s artificial satellite orbital motion. Boll. Geod. Sci. Affini 57, 453 (1998)

    Google Scholar 

  • Yuan, D.-N., Sjogren, W.L., Konopliv, A.S., Kucinskas, A.B.: Gravity field of Mars: a 75th degree and order model. J. Geophys. Res. 106, 23377 (2001)

    Article  ADS  Google Scholar 

  • Zel’dovich, Ya.B.: Analog of the Zeeman effect in the gravitational field of a rotating star. J. Exp. Theor. Phys. Lett. 1, 95 (1965)

    Google Scholar 

  • Zel’dovich, Ya.B., Novikov, I.D.: Stars and Relativity. The University of Chicago Press, Chicago (1971)

    Google Scholar 

  • Zerbini, S.: In: Mueller, I.I., Zerbini, S. (eds.) The Interdisciplinary Role of Space Geodesy. Proceedings of an International Workshop “Ettore Majorana” Center for Scientific Culture, International School of Geodesy-Director, Enzo Boschi-Erice, Sicily, Italy, July 23–29, 1988, p. 269. Springer, Berlin (1989). Appendix 5. The LAGEOS II project

    Google Scholar 

  • Zuber, M.T., Smith, D.E.: One-way ranging to the planets. In: Proc. 16-th International Workshop on Laser Ranging, Poznań, Poland, October 12–17 2008. http://cddis.gsfc.nasa.gov/lw16/docs/presentations/llr_9_Zuber.pdf. Cited 20 Mar 2010

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Iorio, L., Lichtenegger, H.I.M., Ruggiero, M.L. et al. Phenomenology of the Lense-Thirring effect in the solar system. Astrophys Space Sci 331, 351–395 (2011). https://doi.org/10.1007/s10509-010-0489-5

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