Skip to main content
Log in

Test of the law of gravitation at small accelerations

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Newton’s Law of Gravitation has been tested at small values a of the acceleration, down to a ≈ 10−10 ms−2, the approximate value of MOND’s constant a 0. Within experimental errors no deviations from Newton’s Law were found. A comparison with six versions of the MOND interpolation function is given. Under the assumptions made in this paper one of the versions can be excluded.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kroupa P., Famaey B., de Boer K.S., Dabringhausen J., Pawlowski M.S., Boily C.M., Jerjen H., Forbes D. et al.: Local-group tests of dark-matter concordance cosmology: towards a new paradigm for structure formation? Astron. Astrophys. 523, A32 (2012) [arXiv:1006.1647 [astro-ph.CO]]

    Google Scholar 

  2. Milgrom M.: A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365 (1983)

    Article  ADS  Google Scholar 

  3. Scarpa, R.: Modified newtonian dynamics, an introductory review. In: AIP Conference Proceedings, vol. 822, p. 253 (2006). [astro-ph/0601478]

  4. Bekenstein, J.D.: Relativistic gravitation theory for the MOND paradigm. Phys. Rev. D 70 (2004) 083509. [Erratum-ibid. D 71 (2005) 069901] [astro-ph/0403694]

    Google Scholar 

  5. Milgrom M.: A modification of the Newtonian dynamics: implications for galaxies. Astrophys. J. 270, 371 (1983)

    Article  ADS  Google Scholar 

  6. Abramovici A., Vager Z.: Test of Newton’s Second Law at small accelerations. Phys. Rev. D 34, 3240 (1986)

    Article  ADS  Google Scholar 

  7. Gundlach J.H., Schlamminger S., Spitzer C.D., Choi K.-Y., Woodahl B.A., Coy J.J., Fischbach E.: Laboratory test of Newton’s Second Law for small accelerations. Phys. Rev. Lett. 98, 150801 (2007)

    Article  ADS  Google Scholar 

  8. Parks H.V., Faller J.E.: A simple pendulum determination of the gravitational constant. Phys. Rev. Lett. 105, 110801 (2010) [arXiv:1008.3203 [physics.class-ph]]

    Article  ADS  Google Scholar 

  9. Ignatiev A.Y.: Is violation of the second Newton’s law possible? Phys. Rev. Lett. 98, 101101 (2007) [gr-qc/0612159]

    Article  MathSciNet  ADS  Google Scholar 

  10. Ignatiev A.Y.: Newton’s second law versus modified-inertia MOND: a test using the high-latitude effect”. Phys. Rev. D 77, 102001 (2008) [arXiv:0802.1599 [gr-qc]]

    Article  MathSciNet  ADS  Google Scholar 

  11. Magueijo J., Mozaffari A.: The case for testing MOND using LISA pathfinder. Phys. Rev. D 85, 043527 (2012) [arXiv:1107.1075[astro-ph.CO]]

    Article  ADS  Google Scholar 

  12. Exirifard, Q.: Micrometer gravity in sky. [arXiv:1206.0173 [gr-qc]]

  13. Schurr, J.: Eine neue Methode zum Test des Newtonschen Gravitationsgesetzes, Ph.D. thesis, University of Wuppertal, Wuppertal (1992)

  14. Walesch, H.: Test des Newtonschen Gravitationsgesetzes und Die Präzise Bestimmung von G, Ph.D. thesis, University of Wuppertal, Wuppertal (1995)

  15. Schumacher, A.: Systematische Untersuchungen zur Messung der Newtonschen Gravitationskonstanten mit einem Pendelresonator, Ph.D. thesis, University of Wuppertal, Wuppertal (1999)

  16. Kleinevoß U., Meyer H., Schumacher A., Hartmann S.: Absolute measurement of the Newtonian force and a determination of G. Meas. Sci. Technol. 10, 492 (1999)

    Article  ADS  Google Scholar 

  17. Kleinevoß, U., Meyer, H., Piel, H., Hartmann, S.: Conference on Precision Electromagnetic Measurements. 2002, Conference Digest 2002 (2002), p. 148

  18. Kleinevoß, U.: Bestimmung der Newtonschen Gravitationskonstanten G, Ph.D. thesis, University of Wuppertal, Wuppertal (2002)

  19. Schubert, S.: Überprüfung des Newtonschen Gravitationsgesetzes bei kleinen Werten der Beschleunigung, Diplomarbeit, University of Hamburg, Hamburg (2008). DESY-THESIS-2008-025

  20. Schubert, S.: An experimental Test of Newton’s Law of Gravitation for Small Accelerations, Ph.D. thesis, University of Hamburg, Hamburg (2011). DESY-THESIS-2011-035

  21. Nakamura, K. et al. (Particle Data Group).: Review of particle physics. J. Phys. G 37, 075021 (2010)

    Google Scholar 

  22. National Institute of Standards and Technology (NIST): The NIST Reference on Constants, Units and Uncertainty (2011). http://physics.nist.gov/cuu/Constants/index.html

  23. Famaey B., Binney J.: Modified Newtonian dynamics in the Milky Way. Mon. Not. R. Astron. Soc. 363, 603 (2005) [astro-ph/0506723]

    ADS  Google Scholar 

  24. Mendoza S., Hernandez X., Hidalgo J.C., Bernal T.: A natural approach to extended Newtonian gravity: tests and predictions across astrophysical scales. Mon. Not. R. Astron. Soc. 411, 226 (2011) [arXiv:1006.5037 [astro-ph.GA]]

    Article  ADS  Google Scholar 

  25. Hernandez, X., Jimenez, M.A.: The outskirts of globular clusters as modified gravity probes. [arXiv:1108.4021 [astro-ph.CO]]

  26. Li X., Chang Z.: Debye entropic force and modified Newtonian dynamics. Commun. Theor. Phys. 55, 733 (2011) [arXiv:1005.1169 [hep-th]]

    Article  ADS  Google Scholar 

  27. Klinkhamer, F.R.: Entropic-gravity derivation of MOND. [arXiv:1201.4160 [gr-qc]]

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Lohrmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meyer, H., Lohrmann, E., Schubert, S. et al. Test of the law of gravitation at small accelerations. Gen Relativ Gravit 44, 2537–2545 (2012). https://doi.org/10.1007/s10714-012-1411-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-012-1411-y

Keywords

Navigation