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Measurements of Space Curvature by Solar Mass

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General Relativity and John Archibald Wheeler

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 367))

Abstract

Unlike Newtonian mechanics, Einstein’s General Theory of Relativity predicts that the Sun causes the space around it to curve. As a result, a light ray passing near the solar limb will be deflected by twice the amount predicted by Newtonian theory. As John Archibald Wheeler put it, “space-time geometry tells mass-energy how to move and mass-energy tells space-time geometry how to curve.” This chapter reviews the experimental verification of light deflection, from an early eclipse expedition in 1919 to more recent measurements using interplanetary spacecraft and very long baseline interferometry (VLBI). It turns out that the Einstein prediction is correct to within a realistic standard error of about 26 parts per million.

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References

  1. Z. Altamimi, P. Sillard, C. Boucher, “ITRF2000: A New Release of the International Terrestrial Reference Frame for Earth Science Applications,” Jour. Geophys. Res., 107 B10 (2002).

    Article  Google Scholar 

  2. J. D. Anderson, P. B. Esposito, W. Martin, C. L. Thornton, D. O. Muhleman, “Experimental Test of General Relativity Using Time-Delay Data from Mariner 6 and Mariner 7,” Astrophys. Jour. 200, 221 (1975).

    Article  ADS  Google Scholar 

  3. J. D. Anderson, E. L. Lau, G. Giampieri, “Measurement of the PPN Parameter γ with Radio Signals from the Cassini Spacecraft at X- and Ka-Bands,” in Proceedings of the 22nd Texas Symposium on Relativistic Astrophysics, Stanford University, December 13-17 2004, ed. by P.Chen, E. Bloom, G. Madejski, V. Petrosian, SLAC-R-752, (Stanford Linear Accelerator Center Technical Publications, Menlo Park, CA 2004).

    Google Scholar 

  4. B. Bertotti, G. Giampieri, “Relativistic Effects for Doppler Measurements Near Solar Conjunction,” Class. Quant. Grav. 9, 777 (1992).

    Article  MathSciNet  ADS  Google Scholar 

  5. B. Bertotti, G. Giampieri, “Solar Corona Plasma in Doppler Measurements,” Solar Phys. 178, 85–107 (1998).

    Article  ADS  Google Scholar 

  6. B. Bertotti, L. Iess, P. Tortora, “A Test of General Relativity Using Radio Links with the Cassini Spacecraft,” Nature 425, 374–376 (2003).

    Article  ADS  Google Scholar 

  7. C. Brans, R. H. Dicke, “Mach’s Principle and a Relativistic Theory of Gravitation,” Phys. Rev. Lett. 124, 925–935 (1961).

    MathSciNet  ADS  MATH  Google Scholar 

  8. I. Ciufolini, J. A. Wheeler, Gravitation and Inertia, (Princeton University Press, Princeton 1995).

    MATH  Google Scholar 

  9. T. A. Clark et al., “Precision geodesy using the Mark-III very-long-baseline interferometer system,” IEEE Trans. Geosci. Remote Sens. 23 438 (1985).

    Article  ADS  Google Scholar 

  10. A. N. Cox, Allen’s Astrophysical Quantities Fourth Edition, Chapter 2, (AIP Press, New York 1999).

    Google Scholar 

  11. T. Damour, K. Nordtvedt, “General relativity as a cosmological attractor of tensor-scalar theories,” Phys. Rev. Lett. 70, 2217 (1993a).

    Article  ADS  Google Scholar 

  12. T. Damour, K. Nordtvedt, “Tensor-scalar cosmological models and their relaxation toward general relativity,” Phys. Rev. D48, 3436 (1993b).

    MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  14. C. W. F. Everitt, in J. D. Fairbank, B. S. Deaver, Jr., C. W. F. Everitt and P. F. Michelson, Near Zero: New Frontiers of Physics, (Freeman, San Francisco, 1988).

    Google Scholar 

  15. E. B. Fomalont, R. A. Sramek, “Measurements of the Solar Gravitational Deflection of Radio Waves in Agreement with General Relativity,” Phys. Rev. Lett. 36, 1475–1478 (1976).

    Article  ADS  Google Scholar 

  16. E. B. Fomalont, R. A. Sramek, “A Confirmation of Einstein’s General Theory of Relativity by Measuring the Bending of Microwave Radiation in the Gravitational Field of the Sun,” Astrophys. Jour. 199, 749 (1975).

    Article  ADS  Google Scholar 

  17. B. F. Jones, “Gravitational Deflection of Light: Solar Eclipse of 30 June 1973 II. Plate Reductions,” Astron. Jour. 81, 455–463 (1976).

    Google Scholar 

  18. S. M. Kopeikin, A. G. Polnarev, G. Schaefer, I. Yu. Vlasov, “Gravimagnetic Effect of the Barycentric Motions of the Sun and Determination of the Post-Newtonian Parameter Gamma in the Cassini Experiment,” Phys. Lett. A 367 (2007).

    Google Scholar 

  19. T. P. Krisher, J. D. Anderson, A. H. Taylor, “Voyager 2 Test of the Radar Time-delay Effect,” Astrophys. Jour. 373, 665 (1999).

    Article  ADS  Google Scholar 

  20. F. van Leeuwen, Hipparcos, the New Reduction of the Raw Data, (Springer, 2007).

    Google Scholar 

  21. C. Ma, E. F. Arias, T. M. Eubanks, A. L. Fey, A.-M. Gontier, C. S. Jacobs, O. J. Sovers, B.A.Archinal, P. Charlot, “The International Celestial Reference Frame as Realized by Very Long Baseline Interferometry,” Astron. Jour. 116 516–546 (1998).

    Article  ADS  Google Scholar 

  22. C. Misner, K. Thorne, J. A. Wheeler, Gravitation, (Freeman, 1973).

    Google Scholar 

  23. T. D. Moyer, Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation, (Wiley-Interscience, 2003).

    Google Scholar 

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

    ADS  MATH  Google Scholar 

  25. R. D. Reasenberg, et al., “Viking Relativity Experiment: Verification of Signal Retardation by Solar Gravity,” Astrophys. Jour. 234, L219–L221 (1979).

    Article  ADS  Google Scholar 

  26. H. P. Robertson, In Space Age Astronomy, ed. by A. J. Deutsch and W. B. Klemperer, (Academic Press, New York 1962).

    Google Scholar 

  27. D. S. Robertson, W. E. Carter, W. H. Dillinger, “New measurement of solar gravitational deflection of radio signals using VLBI,” Nature 349 768–770 (1991).

    Article  ADS  Google Scholar 

  28. D. K. Ross, L. I. Schiff, “Analysis of the Proposed Planetary Radar Reflection Experiment,” Phys. Rev. 141, 1215 (1966).

    Article  ADS  Google Scholar 

  29. F. Schmeidler, “Observations of the light deflection during the Solar eclipse on 15th February, 1961,” Astron. Nachr. 306, 71 (1985).

    Article  ADS  Google Scholar 

  30. I. I. Shapiro, “Fourth Test of General Relativity,” Phys. Rev. Lett. 13, 789–791 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  31. I. I. Shapiro, “Ross-Schiff Analysis of a Proposed Test of General Relativity: A Critique,” Phys. Rev. 145 1005 (1966).

    Article  ADS  Google Scholar 

  32. I. I. Shapiro, “New Method for the Detection of Light Deflection by Solar Gravity,” Science 157 806 (1967).

    Article  ADS  Google Scholar 

  33. I. I. Shapiro, M. E. Ash, R. P. Ingalls, W. B. Smith, D. B. Campbell, R. B. Dyce, R. F. Jurgens, G. H. Pettengill, “Fourth Test of General Relativity: New Radar Result,” Phys. Rev. Lett. 26 1132 (1971).

    Article  ADS  Google Scholar 

  34. S. S. Shapiro, J. L. Davis, D. E. Lebach, J. S. Gregory, “Measurement of the Solar Gravitational Deflection of Radio Waves using Geodetic Very-Long Baselene Interferometry Data, 1979–1999, Phys. Rev. Lett. 92 121101 (2004).

    Article  ADS  Google Scholar 

  35. M. Soffel, S. A. Klioner, G. Petit, P. Wolf, S. M. Kopeikin, P. Bretagnon, V.A.Brumberg, N. Capitaine, T. Damour, T. Fukushima, B. Guinot, T.-Y. Huang, L. Lindegren, C. Ma, K.Nordtvedt, J. C. Ries, P. K. Seidelmann, D. Vokrouhlicky, C. M. Will, C. Xu, “The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement,” Astron. Jour. 126, 2687–2706 (2003).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  37. C. M. Will, Theory and Experiment in Gravitational Physics, Rev. ed., (Cambridge University Press, Cambridge 1993).

    Book  Google Scholar 

  38. C. M. Will, “was Einstein Right? Testing Relativity at the Centenary,” in 100 Years of Relativity, ed. by Abhay Ashtekar, (World Scientific, Singapore 2005).

    Google Scholar 

  39. O. I. Yakolev, Space Radio Science, (Taylor and Francis, New York 2002).

    Google Scholar 

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Correspondence to John D. Anderson .

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Anderson, J.D., Lau, E.L. (2010). Measurements of Space Curvature by Solar Mass. In: Ciufolini, I., Matzner, R. (eds) General Relativity and John Archibald Wheeler. Astrophysics and Space Science Library, vol 367. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3735-0_7

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