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Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission

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Abstract

We study the impact of relativistic gravitational deflection of light on the accuracy of future Space Interferometry Mission (SIM). We estimate the deflection angles caused by the monopole, quadrupole and octupole components of gravitational fields for a number of celestial bodies in the solar system. We observe that, in many cases, the magnitude of the corresponding effects is significantly larger than the 1 µas accuracy expected from SIM. This fact argues for the development of a relativistic observational model for the mission that would account for the influence of both static and time-varying effects of gravity on light propagation. Results presented here are different from the ones obtained elsewhere by the fact that we specifically account for the differential nature of the future SIM astrometric measurements. We also obtain an estimate for the accuracy of possible determination of the Eddington’s parameter γ via SIM global astrometric campaign; we conclude that accuracy of ∼7 × 10−6 is achievable via measurements of deflection of light by solar gravity.

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References

  1. S. G. Turyshev, U. E. Israelsson, M. Shao, Yu. N. Kusenko, E. L. Wright, C. W. F. Everitt, M. Kasevich, J. A. Lipa, J. C. Mester, R. D. Reasenberg, R. L. Walsworth, N. Ashby, H. Gould, and H. J. Paik, “Space-based research in fundamental physics and quantum technologies,” Inter. J. Modern. Phys. D 16(12a), 1879–1925 (2007), arXiv:0711.0150 [gr-qc].

    Article  ADS  Google Scholar 

  2. S. G. Turyshev, “Experimental Tests of General Relativity,” Ann. Rev. Nucl. Part. Sci. 58, 207–248 (2008), arXiv:0806.1731 [gr-qc].

    Article  ADS  Google Scholar 

  3. 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. Vokrouhlický, C. M. Will, and C. Xu, “The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement,” Astron. J. 126(6), 2687–2706 (2003).

    Article  ADS  Google Scholar 

  4. S. M. Kopeikin and V. V. Makarov, “Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers,” Phys. Rev D. 75,6, 062002 (2007).

    Google Scholar 

  5. S. M. Kopeikin, “Propagation of light in the stationary field of multipole gravitational lens,” J. Math. Phys. 38, 2587–2601 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. S. C. Unwin, M. Shao, A. M. Tanner, R. J. Allen, C. A. Beichman, D. Boboltz, J. H. Catanzarite, B.C. Chaboyer, D. R. Ciardi, S. J. Edberg, A. L. Fey, D. A. Fischer, C. R. Gelino, A. P. Gould, C. Grillmair, T. J. Henry, K. V. Johnston, K. J. Johnston, D. L. Jones, S. R. Kulkarni, N. M. Law, S. R. Majewski, V. V. Makarov, G. W. Marcy, D. L. Meier, R. P. Olling, X. Pan, R. J. Patterson, J. E. Pitesky, A. Quirrenbach, S. B. Shaklan, E. J. Shaya, L. E. Strigari, J. A. Tomsick, A. E. Wehrle, and G. Worthey, “Taking the Measure of the Universe: Precision Astrometry with SIM PlanetQuest,” Publ. Astron. Soc. Pacific 120, 38–88 (2008), arXiv:0708.3953 [astro-ph].

    Article  ADS  Google Scholar 

  7. M. A. C. Perryman, K. S. de Boer, G. Gilmore, E. Høg., M. G. Lattanzi, L. Lindegren, X. Luri, F. Mignard, O. Pace, and P. T. de Zeeuw, “Gaia: Composition, Formation and Evolution of the Galaxy,” Astron. Astrophys. 369, 339–363 (2001).

    Article  ADS  Google Scholar 

  8. M. A. C. Perryman, “GAIA: An Astrometric and Photometric Survey of our Galaxy,” Astrophys. J. Suppl. Ser. 280, 1 (2002).

    Google Scholar 

  9. K. J. Johnston, A. L. Fey, N. Zacharias, J. L. Russell, C. Ma, C. de Vegt, J. E. Reynolds, D. L. Jauncey, B. A. Archinal, M. S. Carter, T. E. Corbin, T. M. Eubanks, D. R. Florkowski, D. M. Hall, D. D. McCarthy, P. M. McCulloch, E. A. King, G. Nicolson, and D. B. Shaffer, “A Radio Reference Frame,” Astron. J. 110, 880 (1995).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. M. A.C. Perryman, E. Hög, J. Kovalevsky, L. Lindegren, C. Turon, P. L. Bernacca, M. Creze, F. Donati, M. Grenon, and M. Grewing, “In-orbit performance of the HIPPARCOS astrometry satellite,” Astron. Astrophys. 258, 1 (1992).

    ADS  Google Scholar 

  12. A. Gould, “Deflection of light by the earth,” Astrophys. J. 414, L37 (1993).

    Article  ADS  Google Scholar 

  13. S. A. Klioner, “Physically adequate reference system of a massless observer and relativistic description of the GAIA attitude,” Phys. Rev. D 69, 124001 (2004), astro-ph/0311540.

    Google Scholar 

  14. V. A. Brumberg, Relativistic Celestial Mechanics (Nauka, Moscow, 1972).

    Google Scholar 

  15. V. A. Brumberg, Essential Relativistic Celestial Mechanics (Adam Hilger, London, 1991).

    MATH  Google Scholar 

  16. O. J. Sovers and C. S. Jacobs, in Observation Model and Parameter Partials for the JPL VLBI Parameter Estimation Software “MODEST”-1996, JPL Technical Report 83-39, Rev. 6, Pasadena, CA (1996).

  17. C. M. Will, Theory and Experiment in Gravitational Physics, (Rev. Ed.), Cambridge Univ. Press, England (1993).

    MATH  Google Scholar 

  18. E. B. Fomalont and S. M. Kopeikin, “The Measurement of the Light Deflection from Jupiter: Experimental Results,” Astrophys. J. 598, 704–711 (2003).

    Article  ADS  Google Scholar 

  19. A. Dar, “Tests of general relativity and Newtonian gravity at large distances and the dark matter problem,” Nucl. Phys. B (Suppl. A) 28, 321 (1992).

    Article  ADS  Google Scholar 

  20. R. N. Treuhaft and S. T. Lowe, “A Measurement of Planetary Relativistic Deflection,” Astron. J. 102, 1879 (1991).

    Article  ADS  Google Scholar 

  21. S. G. Turyshev, “Analytical Modeling of the White Light Fringe,” Applied Optics 42,1, 71–90 (2003), physics/0301026.

    Article  ADS  Google Scholar 

  22. S. G. Turyshev, “Relativistic Effects in the SIM Astrometric Campaign,” Bull Am. Astron. Soc. 29,5, 1223 (1998); S. G. Turyshev, gr-qc/0205061; grqc/0205062; gr-qc/0205063.

    ADS  Google Scholar 

  23. O. J. Sovers, J. L. Fanselow, and C. S. Jacobs, “Astrometry and geodesy with radio interferometry: experiments, models, results”, Rev. Mod. Phys. 70,4, 1393–1454 (1998).

    Article  ADS  Google Scholar 

  24. V. A. Brumberg, S. A. Klioner, and S. M. Kopeikin, “Relativistic reduction of astrometric observations at POINTS level of accuracy”, eds. J. H. Lieske and V. K. Abalakin, IAU Symposium 141, 229–239(1990).

    Google Scholar 

  25. C. M. Will, “The Confrontation between General Relativity and Experiment,” Liv. Rev. Relativity 9 (2006), gr-qc/0510072.

  26. B. Bertotti, L. Iess, and P. Tortora, “A test of general relativity using radio links with the Cassini spacecraft,” Nature 425, 374 (2003).

    Article  ADS  Google Scholar 

  27. T. D. Moyer, Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation, JPL Deep-Space Communications and Navigation Series (John Wiley and Sons, Inc., Hoboken, New Jersey, 2003).

    Book  Google Scholar 

  28. S. M. Kopeikin and G. Schäfer, “Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies,” Phys. Rev. D 60,12, 124002 (1999).

    Google Scholar 

  29. S. A. Klioner, “A Practical Relativistic Model for Microarcsecond Astrometry in Space,” Astrophys J. 125, 1580–1597 (2003).

    ADS  Google Scholar 

  30. E. M. Standish, Jr. and R. W. Hellings, “A determination of the masses of Ceres, Pallas, and Vesta from their perturbations upon the orbit of Mars,” Icarus 80, 326–333 (1989).

    Article  ADS  Google Scholar 

  31. S. Mouret, D. Hestroffer, and F. Mignard, “Asteroid masses and improvement with Gaia,” Astron. Astrophys. 472, 1017–1027 (2007).

    Article  ADS  Google Scholar 

  32. R. Epstein and I. I. Shapiro, “Post-post-Newtonian deflection of light by the Sun,” Phys. Rev. D 22, 2947 (1980); E. Fischbach and B. S. Freeman, “Second-order contribution to the gravitational deflection of light,” Phys. Rev. D 22, 2950 (1980); G. W. Richter and R. A. Matzner, “2nd-order contributions to relativistic time delay in the parametrized post-Newtonian formalism,” Phys. Rev. D 26, 1219 (1982); “Second-order contributions to gravitational deflection of light in the parametrized post-Newtonian formalism. II. Photon orbits and deflections in three dimensions,” ibid., Phys. Rev. D 26, 2549 (1982); G. W. Richter and R. A. Matzner, ibid., Phys. Rev. D 28, 3007 (1983).

    Article  ADS  Google Scholar 

  33. M. T. Crosta and F. Mignard, “Microarcsecond light bending by Jupiter,” Class. Quant. Grav. 23,15, 4853 (2006).

    Article  MATH  ADS  Google Scholar 

  34. E. B. Fomalont and S.M. Kopeikin, “Radio interferometric tests of general relativity,” eds. Jin et al., Proc. IAU Symposium No. 248, 383 (2007).

  35. C. F. Yoder, Astrometric and Geodetic Properties of Earth and the Solar System. Global Earth Physics. A Handbook of Physical Constants, AGU Reference Shelf 1 (1995).

  36. E. V. Pitjeva, “High-Precision Ephemerides of Planets “—EPM and Determination of Some Astronomical Constants,” Solar System Res. 39, 176–186 (2005).

    Article  ADS  Google Scholar 

  37. W. M. Folkner, J. G. Williams, and D. H. Boggs, “The Planetary and Lunar Ephemeris DE 421,” JPL Memorandum IOM 343R-08-003, 31 March 2008, ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/de421.

  38. E. M. Standish, Jr., Astronomical and Astrophysical Objectives of Sub-Milliarcsecond Optical Astrometry. IAU-SYMP, eds. E. Hög and P. K. Seidelmann 166, 109 (1995).

  39. E. M. Standish, Jr., X. X. Newhall, J. G. Williams, and W. M. Folkner, JPL Planetary and Lunar Ephemeris, DE403/LE403, Jet Propulsion Laboratory IOM No. 314, 10–127 (1995).

  40. W. M. Folkner, P. Charlot, M. H. Finger, J. G. Williams, O. J. Sovers, X. X. Newhall, and E. M. Standish, Jr., “Determination of the extragalactic-planetary frame tie from joint analysis of radio interferometric and lunar laser ranging measurements,” Astron. Astrophys. 287, 279 (1994).

    ADS  Google Scholar 

  41. S. A. Klioner, “Influence of the Quadrupole Field and Rotation of Objects on Light Propagation,” Soviet Astron. 35, 523 (1991).

    ADS  Google Scholar 

  42. S. M. Kopeikin and E. B. Fomalont, “General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI,” in Proc. of the 6th EVN Symposium, 2002, eds.E. Ros et al., 49 (2002).

  43. I. Ciufolini, S. Kopeikin, B. Mashhoon, and F. Ricci, “On the gravitomagnetic time delay,” Phys. Lett. A 308, 101–109 (2003).

    Article  ADS  Google Scholar 

  44. S. Kopeikin and B. Mashhoon, “Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies,”Phys. Rev. D 65, 064025 (2002).

    Google Scholar 

  45. R. H. Dicke, “The Oblateness of the Sun and Relativity,” Science 184, 419–429 (1974).

    Article  ADS  Google Scholar 

  46. T. Damour and K. Nordtvedt, Phys. Rev. D 48, 3436 (1993); T. Damour and A. M. Polyakov, Nucl. Phys. B 423, 532 (1994); T. Damour, F. Piazza, and G. Veneziano, Phys. Rev. D 66, 046007 (2002) [arXiv:hep-th/0205111].

    Article  ADS  MathSciNet  Google Scholar 

  47. D. N. Spergel, R. Bean, O. Doré, M. R. Nolta, C. L. Bennett, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H.V. Peiris, L. Verde, C. Barnes, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, “Wilkinson Microwave Anisotropy Probe (WMAP) three year results: Implications for cosmology,” Astrophys. J. Suppl. 170, 377 (2007), [arXiv:astro-ph/0603449].

    Article  ADS  Google Scholar 

  48. S. M. Kopeikin and V. V. Makarov, “Astrometric Effects of secular aberration”, Astron. J. 131,3, 1471–1478 (2006).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Sternberg Astronomical Institute, 13 Universitetskii pr., Moscow, 119992, Russia

    V. G. Turyshev

  2. California Institute of Technology, Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA, 91109-0899, USA

    V. G. Turyshev

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Published in Russian in Pis’ma v Astronomicheskiĭ Zhurnal, 2009, Vol. 35, No. 4, pp. 243–264.

The article was translated by the authors.

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Turyshev, V.G. Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission. Astron. Lett. 35, 215–234 (2009). https://doi.org/10.1134/S106377370904001X

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