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Motion of a Pair of Gravitating Bodies in Dark Energy Presence: Small Deviations from Keplerian Motion

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Abstract

The problem of the motion of two gravitating bodies in the presence of dark energy (DE), considered as a perturbing factor, is investigated. In addition to the orbit precession frequency obtained in previous studies, the correction to the orbital motion frequency was calculated, and the oscillations of the semi-major axis and the eccentricity of the orbit caused by the influence of DE were studied.

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Notes

  1. This procedure was proposed for non-integrable problems, but it is also useful in constructing approximate solutions in simpler cases when the problem is integrable and has an exact solution. The use of the Hori–Depri procedure [37], which is more suitable for computer implementation, would lead to the same theoretical results. In the first approximation, the Delaunay–Zeipel and Hori–Depri procedures are equivalent.

REFERENCES

  1. S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, et al., Astrophys. J. 517, 565 (1999).

    ADS  Google Scholar 

  2. A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, et al., Astron. J. 116, 1009 (1998).

    ADS  Google Scholar 

  3. D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, et al., Astrophys. J. Suppl. 148, 175 (2003).

    Google Scholar 

  4. M. Tegmark, M. A. Strauss, M. R. Blanton, K. Abazajian, et al., Phys. Rev. D 69, 103501 (2004).

    ADS  Google Scholar 

  5. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).

    ADS  Google Scholar 

  6. S. M. Carroll, W. H. Press, and E. L. Turner, Ann. Rev. Astron. Astrophys. 30, 499 (1992).

    ADS  Google Scholar 

  7. S. M. Carroll, Liv. Rev. Relativ. 4, 1 (2001).

    ADS  MathSciNet  Google Scholar 

  8. W. Rindler, Relativity: Special, General, and Cosmological (Oxford Univ. Press, Oxford, UK, 2001).

    MATH  Google Scholar 

  9. C. O Raifeartaigh, M. O Keeffe, W. Nahm, and S. Mitton, Eur. Phys. J. H 43, 73 (2018).

    Google Scholar 

  10. B. Novosyadlyj, Eur. Phys. J. H 43, 267 (2018).

    Google Scholar 

  11. L. Iorio, Universe 1, 38 (2015).

    ADS  Google Scholar 

  12. I. Debono and G. F. Smoot, Universe 2, 23 (2016).

    ADS  Google Scholar 

  13. J. Islam, Phys. Lett. A 97, 239 (1983).

    ADS  MathSciNet  Google Scholar 

  14. J. Cardona and J. Tejero, Astrophys. J. 493, 52 (1998).

    ADS  Google Scholar 

  15. L. Iorio, Int. J. Mod. Phys. D 15, 473 (2006).

    ADS  Google Scholar 

  16. L. Iorio, Adv. Astron. 2008, 268647 (2008).

    ADS  Google Scholar 

  17. H. Arakida, Int. J. Theor. Phys. 52, 1408 (2013).

    MathSciNet  Google Scholar 

  18. S. S. Ovcherenko and Z. K. Silagadze, Ukr. J. Phys. 61, 342 (2016).

    Google Scholar 

  19. L. Iorio, Universe 4, 59 (2018).

    ADS  Google Scholar 

  20. J. M. Cohen and B. Mashhoon, Phys. Lett. A 181, 353 (1993).

    ADS  Google Scholar 

  21. E. Hackmann and C. Lammerzahl, Phys. Rev. D 90, 044059 (2014).

    ADS  Google Scholar 

  22. A. Kerr, J. Hauck, and B. Mashhoon, Class. Quantum Grav. 20, 2727 (2003).

    ADS  Google Scholar 

  23. M. Sereno and P. Jetzer, Phys. Rev. D 73, 063004 (2006).

    ADS  Google Scholar 

  24. V. Kagramanova, J. Kunz, and C. Lammerzahl, Phys. Lett. B 634, 465 (2006).

    ADS  Google Scholar 

  25. G. Adkins, J. McDonnell, and R. Fell, Phys. Rev. D 75, 064011 (2007).

    ADS  MathSciNet  Google Scholar 

  26. G. Adkins and J. McDonnell, Phys. Rev. D 75, 082001 (2007).

    ADS  Google Scholar 

  27. M. Sereno and P. Jetzer, Phys. Rev. D 75, 064031 (2007).

    ADS  MathSciNet  Google Scholar 

  28. O. I. Chashchina and Z. K. Silagadze, Phys. Rev. D 77, 107502 (2008).

    ADS  Google Scholar 

  29. A. D. Chernin, Phys. Usp. 44, 1099 (2001).

    ADS  Google Scholar 

  30. A. D. Chernin, Phys. Usp. 51, 253 (2008).

    ADS  Google Scholar 

  31. G. S. Bisnovatyi-Kogan and A. D. Chernin, Astrophys. Space Sci. 338, 337 (2012).

    ADS  Google Scholar 

  32. G. S. Bisnovatyi-Kogan and M. Merafina, Int. J. Theor. Phys. D 28, 1950155 (2019).

    ADS  Google Scholar 

  33. N. V. Emelyanov and M. Y. Kovalyov, Mon. Not. R. Astron. Soc. 429, 3477 (2013).

    ADS  Google Scholar 

  34. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965).

    MATH  Google Scholar 

  35. L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Pergamon, Oxford, 1969).

  36. G. N. Duboshin, Reference Manual on Celestial Mechanics and Astrodynamics (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  37. G. E. O. Giacaglia, Perturbation Methods in Non-Linear Systems (Springer, New York, 1972).

    MATH  Google Scholar 

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Funding

The work of G.S. B.-K. was partially supported by the Russian Foundation for Basic Research, project nos. 18-02-00619, 20-02-000455, and 20-52-12053. The work of A.I.N. was partially supported by the Leverhulme Trust, project no. RPG-2018-143.

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Authors and Affiliations

  1. Space Research Institute, Russian Academy of Sciences, 117997, Moscow, Russia

    A. I. Neishtadt & G. S. Bisnovatyi-Kogan

  2. Loughborough University, Loughborough, UK

    A. I. Neishtadt

Authors
  1. A. I. Neishtadt
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  2. G. S. Bisnovatyi-Kogan
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Corresponding authors

Correspondence to A. I. Neishtadt or G. S. Bisnovatyi-Kogan.

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Translated by E. Seifina

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Neishtadt, A.I., Bisnovatyi-Kogan, G.S. Motion of a Pair of Gravitating Bodies in Dark Energy Presence: Small Deviations from Keplerian Motion. Astron. Rep. 64, 731–737 (2020). https://doi.org/10.1134/S1063772920100054

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