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.
Similar content being viewed by others
Notes
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
S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, et al., Astrophys. J. 517, 565 (1999).
A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, et al., Astron. J. 116, 1009 (1998).
D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, et al., Astrophys. J. Suppl. 148, 175 (2003).
M. Tegmark, M. A. Strauss, M. R. Blanton, K. Abazajian, et al., Phys. Rev. D 69, 103501 (2004).
S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).
S. M. Carroll, W. H. Press, and E. L. Turner, Ann. Rev. Astron. Astrophys. 30, 499 (1992).
S. M. Carroll, Liv. Rev. Relativ. 4, 1 (2001).
W. Rindler, Relativity: Special, General, and Cosmological (Oxford Univ. Press, Oxford, UK, 2001).
C. O Raifeartaigh, M. O Keeffe, W. Nahm, and S. Mitton, Eur. Phys. J. H 43, 73 (2018).
B. Novosyadlyj, Eur. Phys. J. H 43, 267 (2018).
L. Iorio, Universe 1, 38 (2015).
I. Debono and G. F. Smoot, Universe 2, 23 (2016).
J. Islam, Phys. Lett. A 97, 239 (1983).
J. Cardona and J. Tejero, Astrophys. J. 493, 52 (1998).
L. Iorio, Int. J. Mod. Phys. D 15, 473 (2006).
L. Iorio, Adv. Astron. 2008, 268647 (2008).
H. Arakida, Int. J. Theor. Phys. 52, 1408 (2013).
S. S. Ovcherenko and Z. K. Silagadze, Ukr. J. Phys. 61, 342 (2016).
L. Iorio, Universe 4, 59 (2018).
J. M. Cohen and B. Mashhoon, Phys. Lett. A 181, 353 (1993).
E. Hackmann and C. Lammerzahl, Phys. Rev. D 90, 044059 (2014).
A. Kerr, J. Hauck, and B. Mashhoon, Class. Quantum Grav. 20, 2727 (2003).
M. Sereno and P. Jetzer, Phys. Rev. D 73, 063004 (2006).
V. Kagramanova, J. Kunz, and C. Lammerzahl, Phys. Lett. B 634, 465 (2006).
G. Adkins, J. McDonnell, and R. Fell, Phys. Rev. D 75, 064011 (2007).
G. Adkins and J. McDonnell, Phys. Rev. D 75, 082001 (2007).
M. Sereno and P. Jetzer, Phys. Rev. D 75, 064031 (2007).
O. I. Chashchina and Z. K. Silagadze, Phys. Rev. D 77, 107502 (2008).
A. D. Chernin, Phys. Usp. 44, 1099 (2001).
A. D. Chernin, Phys. Usp. 51, 253 (2008).
G. S. Bisnovatyi-Kogan and A. D. Chernin, Astrophys. Space Sci. 338, 337 (2012).
G. S. Bisnovatyi-Kogan and M. Merafina, Int. J. Theor. Phys. D 28, 1950155 (2019).
N. V. Emelyanov and M. Y. Kovalyov, Mon. Not. R. Astron. Soc. 429, 3477 (2013).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965).
L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Pergamon, Oxford, 1969).
G. N. Duboshin, Reference Manual on Celestial Mechanics and Astrodynamics (Nauka, Moscow, 1976) [in Russian].
G. E. O. Giacaglia, Perturbation Methods in Non-Linear Systems (Springer, New York, 1972).
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.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by E. Seifina
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063772920100054