Measurement of the PPN parameter \(\gamma \) by testing the geometry of near-Earth space

  • Jie Luo
  • Yuan Tian
  • Dian-Hong Wang
  • Cheng-Gang Qin
  • Cheng-Gang Shao
Research Article

Abstract

The Beyond Einstein Advanced Coherent Optical Network (BEACON) mission was designed to achieve an accuracy of \(10^{-9}\) in measuring the Eddington parameter \(\gamma \), which is perhaps the most fundamental Parameterized Post-Newtonian parameter. However, this ideal accuracy was just estimated as a ratio of the measurement accuracy of the inter-spacecraft distances to the magnitude of the departure from Euclidean geometry. Based on the BEACON concept, we construct a measurement model to estimate the parameter \(\gamma \) with the least squares method. Influences of the measurement noise and the out-of-plane error on the estimation accuracy are evaluated based on the white noise model. Though the BEACON mission does not require expensive drag-free systems and avoids physical dynamical models of spacecraft, the relatively low accuracy of initial inter-spacecraft distances poses a great challenge, which reduces the estimation accuracy in about two orders of magnitude. Thus the noise requirements may need to be more stringent in the design in order to achieve the target accuracy, which is demonstrated in the work. Considering that, we have given the limits on the power spectral density of both noise sources for the accuracy of \(10^{-9}\).

Keywords

BEACON mission The Eddington parameter The measurement noise The out-of-plane error 

References

  1. 1.
    Will, C.M.: Theory and Experiment in Gravitational Physics, 2nd edn. Cambridge University Press, Cambridge (1993)CrossRefMATHGoogle Scholar
  2. 2.
    Will, C.M.: Living Rev. Relativ. 9, 3 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    Turyshev, S.G., Shao, M., Girerd, A., et al.: Int. J. Mod. Phys. D 18, 1025 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    Turyshev, S.G.: Usp. Fiz. Nauk. 179, 3 (2009)CrossRefGoogle Scholar
  5. 5.
    Turyshev, S.G.: Phys. Usp. 52, 1 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    Reasenberg, R.D., Shapiro, I.I., MacNeil, P.E., et al.: Astrophys. J. Lett. 234, L219 (1979)ADSCrossRefGoogle Scholar
  7. 7.
    Fomalont, E., Kopeikin, S., Lanyi, G., Benson, J.: Astrophys. J. 699, 1395–1402 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Bertotti, B., Iess, L., Tortora, P.: Nature 425, 374 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    Turyshev, S.G., et al.: Exp. Astron. 27, 27 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    Braxmaier, C., Dittus, H., Foulon, B., et al.: Exp. Astron. 34, 181 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    Pierce, R., Leitch, J., Stephens, M., et al.: Appl. Opt. 47, 5007 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Coddington, I., Swann, W.C., Nenadovic, L., et al.: Nat. Photonics 3, 351 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Mechanical Engineering and Electronic InformationChina University of GeosciencesWuhanPeople’s Republic of China
  2. 2.MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of PhysicsHuazhong University of Science and TechnologyWuhanPeople’s Republic of China

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