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International Journal of Theoretical Physics

, Volume 57, Issue 11, pp 3359–3368 | Cite as

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

  • Kh. P. Gnatenko
  • V. M. Tkachuk
Article

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.

Keywords

Noncommutative phase space Weak equivalence principle Eotvos-parameter 

Notes

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.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department for Theoretical PhysicsIvan Franko National University of LvivLvivUkraine

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