Skip to main content

Space-based Tests of Relativistic Gravitation

  • Chapter
  • First Online:
Gravity: Where Do We Stand?
  • 1512 Accesses

Abstract

Since its initial publication, Einstein’s general theory of relativity had been tested to a very high precision and presently is considered to be the standard theory of gravitation, especially when the phenomena in astrophysics, cosmology, and fundamental physics are concerned. As such, this theory has many practically important applications including spacecraft navigation, relativistic geodesy, time transfer, etc. Here we discuss the foundations of general relativity, present its current empirical status, and highlight the need for the new generation of high-accuracy tests. We present some space-based gravitational experiments and discuss anticipated advances in our understanding of the fundamental laws of nature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The notational conventions employed here are as follows: Letters from the second half of the Latin alphabet, \(m, n,\)\(=0\)\(3\) denote space-time indices. Greek letters \(\alpha , \beta ,\)\(=1\)\(3\) denote spatial indices. The flat Minkowski space-time metic is \(\gamma_{mn}={\rm diag}(+1,-1,-1,-1)\). We rely on the Einstein summation convention with indices being lowered or raised using \(\gamma_{mn}\).

References

  1. Einstein A. Die Feldgleichungen der Gravitation (The field equations of gravitation). Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin; 1915. p. 844–7.

    Google Scholar 

  2. Einstein A. Die Grundlage der allgemeinen Relativitätstheorie. Ann Physik. 1916;49:146.

    Google Scholar 

  3. Turyshev SG. Experimental tests of general relativity: Recent progress and future directions. Usp Fiz Nauk. 2009;179:3–34.

    Google Scholar 

  4. Will CM. The confrontation between general relativity and experiment. Living Rev Relativ. 2006;9(3).

    Google Scholar 

  5. Turyshev SG, Israelsson UE, Shao M, Yu N, Kusenko A, Wright EL, Everitt CWF, Kasevich M, Lipa JA, Mester JC, et al. Space-based research in fundamental physics and quantum technologies. Int J Mod Phys D. 2007;16(12a):1879–1925.

    Google Scholar 

  6. Possenti A, Burghay B. 35 years of testing relativistic gravity: where do we go from here? In: Peron R, Gorini V, Moschella U, editors. Astrophysics, clocks and fundamental constants. Berlin: Springer; 2013.

    Google Scholar 

  7. Will CM. Theory and experiment in gravitational physics. Cambridge: Cambridge University Press; 1993.

    Google Scholar 

  8. Reasenberg RD, Shapiro II, MacNeil PE, Goldstein RB, Breidenthal JC, Brenkle JP, et al. Viking relativity experiment—verification of signal retardation by solar gravity. Astrophys J Lett. 1979;234:L219–21.

    Google Scholar 

  9. Anderson JD, Lau EL, Turyshev SG, Williams JG, Nieto MM. Recent results for solar-system tests of general relativity. BAAS. 2002;34:833.

    Google Scholar 

  10. Pitjeva EV. High-precision ephemerides of planets—EPM and determination of some astronomical constants. Sol Syst Res. 2005;39(3):176–86.

    Google Scholar 

  11. Fomalont E, Kopeikin S, Lanyi G, Benson J. Progress in measurements of the gravitational bending of radio Waves Using the VLBA. ApJ. 2009;699(2):1395–1402.

    Google Scholar 

  12. Williams JG, Turyshev SG, Boggs DH. Lunar laser ranging tests of the equivalence principle with the earth and moon. Int J Mod Phys D. 2009;18:1129–75.

    Google Scholar 

  13. Williams JG, Turyshev SG, Boggs DH. Progress in lunar laser ranging tests of relativistic gravity. Phys Rev Lett. 2004;93:261101.

    Google Scholar 

  14. Bertotti B, Iess L, Tortora P. A test of general relativity using radio links with the Cassini spacecraft. Nature. 2003;425:374.

    Google Scholar 

  15. Kramer M, Stairs IH, Manchester RN, McLaughlin MA, Lyne AG, Ferdman RD, Burgay M, Lorimer DR, et al. Tests of general relativity from timing the double pulsar. Science. 2006;314:97–102.

    Google Scholar 

  16. Fock VA. The theory of space, time and gravitation. Moscow: Fizmatgiz; 1959. (English translation (1959), Pergamon, Oxford).

    Google Scholar 

  17. Landau LD, Lifshitz EM. The classical theory of fields. 7th edn. Moscow: Nauka; 1988.

    Google Scholar 

  18. Misner CW, Thorne KS, Wheeler JA. Gravitation. W. H. Freeman and Co.; 1973.

    Google Scholar 

  19. Yao WM, et al. Review of particle physics. J Phys G. 2006;33:205–9.

    Google Scholar 

  20. Weinberg S. The cosmological constant problem. Rev Mod Phys. 1989;61(1):1–23.

    Google Scholar 

  21. Spergel DN, Bean R, Doré O, Nolta MR, Bennett CL, Hinshaw G, Jarosik N, Komatsu E, Page L, Peiris HV, Verde L, et al. Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology. Astrophys J Suppl. 2007;170:377.

    Google Scholar 

  22. Moyer TD. Formulation for observed and computed values of deep space network data types for navigation. JPL deep-space communications and navigation series. Wiley: Hoboken; 2003.

    Google Scholar 

  23. Turyshev SG. Experimental tests of general relativity. Ann Rev Nucl Part Sci. 2008;58:207.

    Google Scholar 

  24. Einstein A, Infeld L, Hoffmann B. The gravitational equations and the problem of motion. Ann Math. 1938;39:65.

    Google Scholar 

  25. Turyshev SG, Toth VT, Sazhin MV. General relativistic observables of the GRAIL mission. Phys Rev D. 2013;87:024020.

    Google Scholar 

  26. Brans C, Dicke RH. Mach’s principle and a relativistic theory of gravitation. Phys Rev. 1961;124(3):925.

    Google Scholar 

  27. Bertolami O, Paramos J, Turyshev SG. In: Dittus H, Lämmerzahl C, Turyshev S, editors. Lasers, clocks and drag-free control: exploration of relativistic gravity in space. Berlin: Springer; 2007. p. 27–67.

    Google Scholar 

  28. Liberati S, Mattingly D. Lorentz breaking effective field theory models for matter and gravity: theory and observational constraints. In: Peron R, Gorini V, Moschella U, editors. Gravity: where do we stand? Berlin: Springer; 2016, p. 367 (Chap. 11, this volume).

    Google Scholar 

  29. Braccini S, Fidecaro F. The detection of gravitational waves. In: Peron R, Gorini V, Moschella U, editors. Gravity: where do we stand? Berlin: Springer; 2016, p. 235 (Chap. 7, this volume).

    Google Scholar 

  30. Damour T, Nordtvedt K. General relativity as a cosmological attractor of tensor-scalar theories. Phys Rev Lett. 1993;70:2217.

    Google Scholar 

  31. Damour T, Polyakov AM. String theory and gravity. Gen Rel Grav. 1994;26:1171.

    Google Scholar 

  32. Damour T, Piazza F, Veneziano G. Runaway dilaton and equivalence principle violations. Phys Rev Lett. 2002;89:081601.

    Google Scholar 

  33. Adelberger E. New tests of Einstein’s equivalence principle and Newton’s inverse-square law. Class Quant Grav. 2001;18:2397–2405.

    Google Scholar 

  34. Baeßler S, Heckel BR, Adelberger EG, Gundlach JH, Schmidt U, Swanson HE. Improved test of the equivalence principle for gravitational self-energy. Phys Rev Lett. 1999;83(18):3585.

    Google Scholar 

  35. Schlamminger S, Choi KY, Wagner TA, Gundlach JH, Adelberger EG. Test of the equivalence principle using a rotating torsion balance. Phys Rev Lett. 2008;100:041101.

    Google Scholar 

  36. Gundlach JH, Schlamminger S, Spitzer CD, Choi KY, Woodahl BA, Coy JJ, Fischbach E. Laboratory test of Newton–s second law for small accelerations. Phys Rev Lett. 2007;98(15):150801.

    Google Scholar 

  37. Mota DF, Barrow JD. Local and global variations of the fine-structure constant. Mon Not Roy Astron Soc. 2004;349:291.

    Google Scholar 

  38. Touboul P, Rodrigues M. The MICROSCOPE space mission. Class Quant Grav. 2001;18:2487–98.

    Google Scholar 

  39. Nobili A, Shao M, Pegna R, Zavattini G, Turyshev S, et al. ‘Galileo Galilei’ (GG): space test of the weak equivalence principle to 10−17 and laboratory demonstrations. Class Quant Grav. 2012;29:184011.

    Google Scholar 

  40. Mester J, Torii R, Worden P, Lockerbie N, Vitale S, Everitt CWF. The STEP mission: principles and baseline design. Class Quant Grav. 2001;18:2475–86.

    Google Scholar 

  41. Nordtvedt K. Equivalence principle for massive bodies. I. Phenomenology. Phys Rev. 1968;169:1014–6.

    Google Scholar 

  42. Ulrich RK. The influence of partial ionization and scattering states on the solar interior structure. Astrophys J. 1982;258:404.

    Google Scholar 

  43. Williams JG, Turyshev SG, Boggs D. Lunar laser ranging tests of the equivalence principle. Class Quant Grav. 2012;29:184004.

    Google Scholar 

  44. Murphy TW, Michelson EL, Orin AE, Adelberger EG, Hoyle CD, Swanson HE, Stubbs CW, Battat JE. APOLLO: next-generation lunar laser ranging. Int J Mod Phys D. 2007;16:2127.

    Google Scholar 

  45. Williams JG, Turyshev SG, Murphy TW. Improving LLR tests of gravitational theory. Int J Mod Phys D. 2004;13:567–82.

    Google Scholar 

  46. Turyshev SG, Williams JG, Folkner WM, Gutt GM, et al. Corner-cube retro-reflector instrument for advanced lunar laser ranging. Exp Astron. 2012. doi:10.1007/s10686-012-9324-z, arXiv:1210.7857 [physics.ins-det].

    Google Scholar 

  47. Turyshev SG, Williams JG. Space-based tests of gravity with laser ranging. Int J Mod Phys D. 2007;16:2165–79.

    Google Scholar 

  48. Turyshev SG, Farr W, Folkner WM, Girerd AR, et al. Advancing tests of relativistic gravity via laser ranging to phobos. Exp Astron. 2010;28:209–49.

    Google Scholar 

  49. Uzan JP. The fundamental constants and their variation: observational status and theoretical motivations. Rev Mod Phys. 2003;75:403.

    Google Scholar 

  50. Williams JG, Turyshev SG, Boggs DH. Williams et al. Reply (to the comment by Dumin on Progress in Lunar Laser Ranging Tests of Relativistic Gravity). Phys Rev Lett. 2007;98:059002.

    Google Scholar 

  51. Nordtvedt K. Space-time variation of physical constants and the equivalence principle. Int J Mod Phys A. 2002;17:2711–5.

    Google Scholar 

  52. Adelberger EG, Heckel BR, Nelson AE. Tests of the gravitational inverse-square law. Ann Rev Nucl Part Sci. 2003;53:77–121.

    Google Scholar 

  53. Antoniadis I, Dimopoulos S, Dvali GR. Millimeter range forces in superstring theories with weak-scale compactification. Nucl Phys B. 1998;516:70–82.

    Google Scholar 

  54. Dimopoulos S, Giudice GF. Macroscopic forces from supersymmetry. Phys Lett B. 1996;379:105–14.

    Google Scholar 

  55. Sundrum R. Towards an effective particle-string resolution of the cosmological constant problem. JHEP. 1999;07:001.

    Google Scholar 

  56. Dvali G, Gabadadze G, Kolanovic M, Nitti F. Scales of gravity. Phys Rev D. 2002;65:024031.

    Google Scholar 

  57. Dvali G, Gruzinov A, Zaldarriaga M. The accelerated universe and the Moon. Phys Rev D. 2003;68:024012.

    Google Scholar 

  58. Peron R. Fundamental physics with the LAGEOS satellites. In: Peron R, Gorini V, Moschella U, editors. Gravity: where do we stand? Berlin: Springer; 2016, p.167 (Chap. 4, this volume).

    Google Scholar 

  59. Turyshev SG, Toth VT, Kinsella G, Lee SC, et al. Support for the thermal origin of the Pioneer anomaly. Phys Rev Lett. 2012;108:241101.

    Google Scholar 

  60. Turyshev SG, Toth VT. The Puzzle of the flyby anomaly. Space Sci Rev. 2010;148:169–74.

    Google Scholar 

  61. Deffayet C, Dvali GR, Gabadadze G. Accelerated universe from gravity leaking to extra dimensions. Phys Rev D. 2002;65:044023.

    Google Scholar 

  62. Dvali G. Predictive power of strong coupling in theories with large distance modified gravity. New J Phys. 2006;8:326.

    Google Scholar 

  63. Dvali G, Gabadadze G, Porrati M. 4D gravity on a brane in 5D Minkowski space. Phys Lett B. 2000;485:208–14.

    Google Scholar 

  64. Deffayet C. Cosmology on a brane in Minkowski bulk. Phys Lett B. 2001;502:199–208.

    Google Scholar 

  65. Magueijo J, Bekenstein J. Testing strong MOND behavior in the solar system. Int J Mod Phys D. 2007;16:2035–53.

    Google Scholar 

  66. Damour T, Nordtvedt K. Tensor–scalar cosmological models and their relaxation toward general relativity. Phys Rev D. 1993;48:3436–50.

    Google Scholar 

  67. Turyshev SG. Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission. Astron Lett. 2009;35:215–34.

    Google Scholar 

  68. Ashby N, Bender P. Measurement of the shapiro time delay between drag-free spacecraft. In: Dittus H, Lämmerzahl C, Turyshev SG, editors. Lasers, clocks, and drag-free: technologies for future exploration in space and tests of gravity. Berlin: Springer; 2006. p. 219.

    Google Scholar 

  69. Turyshev SG, Shao M. Laser astrometric test of relativity: science, technology, and mission design. Int J Mod Phys D. 2007;16:2191–203.

    Google Scholar 

  70. Ni WT, Shiomi S, Liao AC. ASTROD, ASTROD I and their gravitational-wave sensitivities. Class Quant Grav. 2004;21(5):S641.

    Google Scholar 

  71. Appourchaux T, Burston R, Chen Y, Cruise M, Dittus H, et al. 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. 2009;23(2):491–527.

    Google Scholar 

  72. Turyshev SG, Lane B, Shao M, Girerd AR. A search for new physics with the BEACON mission. Int J Mod Phys D. 2009;18:1025–38.

    Google Scholar 

  73. Turyshev SG, Minazzoli OL, Toth VT. Accelerating relativistic reference frames in Minkowski space-time. J Math Phys. 2012;53(1):032501.

    Google Scholar 

  74. Turyshev SG, Toth VT. New perturbative method for solving the gravitational N-body problem in general relativity. 2013. arXiv:1304.8122 [gr-qc].

    Google Scholar 

  75. Turyshev SG, Sazhin MV, Toth VT. General relativistic laser interferometric observables of the GRACE-Follow-On mission. Phys Rev D. 2014;D89:105029. doi:10.1103/PhysRevD. 89.105029.

    Google Scholar 

Download references

Acknowledgements

The work described here was carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, under a contract with the National Aeronautics and Space Administration.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vyacheslav G. Turyshev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Turyshev, V. (2016). Space-based Tests of Relativistic Gravitation. In: Peron, R., Colpi, M., Gorini, V., Moschella, U. (eds) Gravity: Where Do We Stand?. Springer, Cham. https://doi.org/10.1007/978-3-319-20224-2_6

Download citation

Publish with us

Policies and ethics