Skip to main content
SpringerLink
Log in

Influence of Noncommutativity on the Motion of Sun-Earth-Moon System and the Weak Equivalence Principle

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Features of motion of macroscopic body in gravitational field in a space with noncommutativity of coordinates and noncommutativity of momenta are considered in general case when coordinates and momenta of different particles satisfy noncommutative algebra with different parameters of noncommutativity. Influence of noncommutativity on the motion of three-body Sun-Earth-Moon system is examined. We show that because of noncommutativity the free fall accelerations of the Moon and the Earth toward the Sun in the case when the Moon and the Earth are at the same distance to the source of gravity are not the same even if gravitational and inertial masses of the bodies are equal. Therefore, the Eotvos-parameter is not equal to zero and the weak equivalence principle is violated in noncommutative phase space. We estimate the corrections to the Eotvos-parameter caused by noncommutativity on the basis of Lunar laser ranging experiment results. We obtain that with high precision the ratio of parameter of momentum noncommutativity to mass is the same for different particles.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Snyder, H.: Phys. Rev. 71, 38 (1947)

    Article  ADS  Google Scholar 

  2. Seiberg, N., Witten, E.: J. High Energy Phys. 9909, 032 (1999)

    Article  ADS  Google Scholar 

  3. Doplicher, S., Fredenhagen, K., Roberts, J.E.: Phys. Lett. B 331, 39 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  4. Hatzinikitas, A., Smyrnakis, I.: J. Math. Phys. 43, 113 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  5. Kijanka, A., Kosinski, P.: Phys. Rev. D 70, 127702 (2004)

    Article  ADS  Google Scholar 

  6. Jian, J., Chen, J.-F.: Eur. Phys. J. C 60, 669 (2009)

    Article  ADS  Google Scholar 

  7. Smailagic, A., Spallucci, E.: Phys. Rev. D 65, 107701 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  8. Smailagic, A., Spallucci, E.: J. Phys. A 35, 363 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  9. Giri, P.R., Roy, P.: Eur. Phys. J. C 57, 835 (2008)

    Article  ADS  Google Scholar 

  10. Ben Geloun, J., Gangopadhyay, S., Scholtz, F.G.: EPL 86, 51001 (2009)

    Article  ADS  Google Scholar 

  11. Yakup, R, Dulat, S., Li, K., Hekim, M.: Int. J. Theor. Phys. 53, 1404 (2014)

    Article  Google Scholar 

  12. Nath, D., Roy, P.: Ann. Phys 377, 115 (2017)

    Article  ADS  Google Scholar 

  13. Gamboa, J., Loewe, M., Mendez, F., Rojas, J.C.: Mod. Phys. Lett. A 16, 2075 (2001)

    Article  ADS  Google Scholar 

  14. Horvathy, P.A.: Ann. Phys. 299, 128 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  15. Dayi, O.F., Kelleyane, L.T.: Mod. Phys. Lett. A 17, 1937 (2002)

    Article  ADS  Google Scholar 

  16. Daszkiewicz, M.: Acta Phys. Polon B 44, 59 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  17. Ho, P.-M., Kao, H.-C.: Phys. Rev. Lett. 88, 151602 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  18. Djemai, A.E.F., Smail, H.: Commun. Theor. Phys. 41, 837 (2004)

    Article  ADS  Google Scholar 

  19. Bertolami, O., Queiroz, R.: Phys. Lett. A 375, 4116 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  20. Chaichian, M., Sheikh-Jabbari, M.M., Tureanu, A.: Phys. Rev. Lett. 86, 2716 (2001)

    Article  ADS  Google Scholar 

  21. Chaichian, M., Sheikh-Jabbari, M.M., Tureanu, A.: Eur. Phys. J. C 36, 251 (2004)

    Article  ADS  Google Scholar 

  22. Chair, N., Dalabeeh, M.A., Phys, J.: A: Math. Gen. 38, 1553 (2005)

    ADS  Google Scholar 

  23. Stern, A.: Phys. Rev. Lett. 100, 061601 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  24. Zaim, S., Khodja, L., Delenda, Y.: Int. J. Mod. Phys. A 26, 4133 (2011)

    Article  ADS  Google Scholar 

  25. Adorno, T.C., Baldiotti, M.C., Chaichian, M., Gitman, D.M., Tureanu, A.: Phys. Lett. B 682, 235 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  26. Khodja, L., Zaim, S.: Int. J. Mod. Phys. A 27, 1250100 (2012)

    Article  ADS  Google Scholar 

  27. Alavi, S.A.: Mod. Phys. Lett. A 22, 377 (2007)

    Article  ADS  Google Scholar 

  28. Masum, H., Dulat, S., Tohti, M.: Int. J. Theor. Phys. 56, 2724 (2017)

    Article  Google Scholar 

  29. Gnatenko, K. h. P., Tkachuk, V.M.: Phys. Lett. A 378, 3509 (2014)

    Article  MathSciNet  ADS  Google Scholar 

  30. Gnatenko, Kh.P., Tkachuk, V.M.: Int. J. Mod. Phys. A 32, 1750161 (2017)

    Article  ADS  Google Scholar 

  31. Gnatenko, K. h. P.: J. Phys. Conf. Ser. 670, 012023 (2016)

    Article  Google Scholar 

  32. Bertolami, O., Rosa, J.G., de Aragao, C.M.L., Castorina, P., Zappala, D.: Phys. Rev. D 72, 025010 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  33. Bastos, C., Bertolami, O.: Phys. Lett. A 372, 5556 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  34. Gamboa, J., Loewe, M., Rojas, J.C.: Phys. Rev. D 64, 067901 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  35. Romero, J.M., Vergara, J.D.: Mod. Phys. Lett. A 18, 1673 (2003)

    Article  ADS  Google Scholar 

  36. Mirza, B., Dehghani, M.: Commun. Theor. Phys. 42, 183 (2004)

    Article  ADS  Google Scholar 

  37. Djemai, A.E.F.: Int. J. Theor. Phys. 43, 299 (2004)

    Article  Google Scholar 

  38. Daszkiewicz, M., Walczyk, C.J.: Mod. Phys. Lett. A 26, 819 (2011)

    Article  ADS  Google Scholar 

  39. Gnatenko, Kh.P.: Phys. Lett. A 377, 3061 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  40. Gnatenko, Kh.P.: J. Phys. Stud. 17, 4001 (2013)

    MathSciNet  Google Scholar 

  41. Daszkiewicz, M.: Acta Phys. Polon B 44, 699 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  42. Gnatenko, Kh.P., Tkachuk, V.M.: Ukr. J. Phys. 61, 432 (2016)

    Article  Google Scholar 

  43. Gnatenko, Kh.P., Tkachuk, V.M.: Int. J. Mod. Phys A 33, 1850037 (2018)

    Article  ADS  Google Scholar 

  44. Saha, A.: Phys. Rev. D. 89, 025010 (2014)

    Article  ADS  Google Scholar 

  45. Gnatenko, Kh.P., Tkachuk, V.M.: Mod. Phys. Lett. A 31, 1650026 (2016)

    Article  ADS  Google Scholar 

  46. Bastos, C., Bertolami, O., Dias, N.C., Prata, J.N.: Class. Quant. Grav. 28, 125007 (2011)

    Article  ADS  Google Scholar 

  47. Bertolami, O., Leal, P.: Phys. Lett. B 750, 6 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  48. Gnatenko, Kh.P., Tkachuk, V.M.: Phys. Lett. A 381, 2463 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  49. Williams, J.G., Turyshev, S.G., Boggs, D.H.: Class. Quantum Grav. 29, 184004 (2012)

    Article  ADS  Google Scholar 

  50. Gnatenko, Kh.P.: Mod. Phys. Lett. A 32, 1750166 (2017)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

This work was partly supported by the projects ΦΦ-63Hp (No. 0117U007190) and ΦΦ-30Φ (No. 0116U001539) from the Ministry of Education and Science of Ukraine.

Author information

Authors and Affiliations

  1. Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., Lviv, 79005, Ukraine

    Kh. P. Gnatenko & V. M. Tkachuk

Authors
  1. Kh. P. Gnatenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Tkachuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kh. P. Gnatenko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gnatenko, K.P., Tkachuk, V.M. Influence of Noncommutativity on the Motion of Sun-Earth-Moon System and the Weak Equivalence Principle. Int J Theor Phys 57, 3359–3368 (2018). https://doi.org/10.1007/s10773-018-3848-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3848-6

Keywords

Search

Navigation