Astrophysics and Space Science

, 361:365 | Cite as

Yukawa effects on the mean motion of an orbiting body

  • Ioannis Haranas
  • Ilias Kotsireas
  • Guillem Gómez
  • Màrius J. Fullana
  • Ioannis Gkigkitzis
Original Article

Abstract

In today’s gravity research there exist few modified gravitational theories which among other things predict the existence of a Yukawa-type correction to the classical gravitational potential. In this paper we study the Yukawa effect on the mean motion if any in a two-body scenario, assuming the influence of the existence of a possible Yukawa correction in the gravitational force of a primary. For that, we derive an equation in order to approximate the mean motion for secondary time rate of change of the orbiting body and its total variation over one revolution, under the influence of the non-Newtonian radial acceleration. Numerical results for Mercury and the companion star of the pulsar PSR \(1913+16\) are calculated. For specific values of the parameters \(\alpha\) and \(\lambda\), as given in the bibliography we have found that there is no corresponding Yukawa effect affecting the mean motion of the planet Mercury. On the other hand it appears that there is a periodic Yukawa effect that affects the mean motion of \(\mbox{PSR}+16\) whose maximum numerical value occurs when the eccentric anomaly is equal to \(180^{\circ}\).

Keywords

Yukawa potential Celestial mechanics orbital and rotational dynamics Classical field theories 

References

  1. Adelberger, E.G., Heckel, B.R., Nelson, A.E.: Annu. Rev. Nucl. Part. Sci. 53, 77 (2003) ADSCrossRefGoogle Scholar
  2. Adkins, G.S., McDonnell, J.: Orbital precession due to central-force perturbations. Phys. Rev. D 75, 082001 (2007). arXiv:gr-qc/0702015v1 ADSMathSciNetCrossRefGoogle Scholar
  3. Amendola, L., Quercellini, C.: Phys. Rev. Lett. 92, 181102 (2004) ADSCrossRefGoogle Scholar
  4. Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. Lett. 81, 2858 (1998) ADSCrossRefGoogle Scholar
  5. Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. D 65, 082004 (2002) ADSCrossRefGoogle Scholar
  6. Anderson, J.D., Campbell, J.K., Nieto, M.M.: New Astron. Rev. 12, 383 (2007) CrossRefGoogle Scholar
  7. Anderson, J.D., Campbell, J.K., Ekelund, J.E., Ellis, J., Jordan, J.F.: Phys. Rev. Lett. 100, 091102 (2008) ADSCrossRefGoogle Scholar
  8. Bertolami, O.: Int. J. Mod. Phys. D 16, 2003 (2008) ADSCrossRefGoogle Scholar
  9. Bertolami, O., Paramos, J., Turyshev, S.G.: In: Dittus, H., Lämmerzahl, C., Turyshev, S.G. (eds.) Clocks and Drag Free Control: Exploration of Relativistic Gravity in Space, pp. 27–74. Springer, Berlin (2008) CrossRefGoogle Scholar
  10. Bosma, A.: Astron. J. 86, 1791 (1981) ADSCrossRefGoogle Scholar
  11. Brownstein, J.R., Moffat, J.W.: Class. Quantum Gravity 23, 3427 (2006) ADSCrossRefGoogle Scholar
  12. Camacho, A.: Gen. Relativ. Gravit. 36(5), 1207 (2004) ADSCrossRefGoogle Scholar
  13. Castel-Branco, N., Paramos, J., March, R.: Perturbation of the metric around a spherical body from a non minimal coupling between matter and curvature Phys. Lett. B 735, 25–32 (2014). arXiv:1403.7251v1 [astro-ph.CO] ADSMathSciNetCrossRefGoogle Scholar
  14. Chiaverini, J., Smullin, S.J., Geraci, A.A., Weld, D.M., Kapitulnik, A.: Phys. Rev. Lett. 90, 151301 (2003) ADSCrossRefGoogle Scholar
  15. Deng, X.-M., Xie, Y., Huang, T.-Y.: In: Proceedings of the International Astronomical Union, vol. 291, pp. 372–374 (2012) Google Scholar
  16. Diacu, F., Mioc, V., Stoica, C.: Nonlinear Anal. 41, 1029 (2000) MathSciNetCrossRefGoogle Scholar
  17. Fischbach, E., Talmadge, C.: The Search for Non-Newtonian Gravity, pp. 38–39. Springer, Berlin (1999) CrossRefMATHGoogle Scholar
  18. Fischbach, E., Talmadge, C., Krause, D.E.: Phys. Rev. D 43, 460 (1991) ADSCrossRefGoogle Scholar
  19. Hagihara, Y.: Celestial Mechanics, Vol. 2, Part 1. MIT Press, Cambridge (1975) MATHGoogle Scholar
  20. Haranas, I., Ragos, O.: Yukawa-type effects in satellites dynamics. Astrophys. Space Sci. (2010). 2010. doi:10.1007/s10509-010-0440-9 MATHGoogle Scholar
  21. Haranas, I., Ragos, O., Gkigkitzis, I., Kotsireas, I.: Quantum and post-Newtonian effects in the anomalistic period and the mean motion of celestial bodies. Astrophys. Space Sci. (2015). doi:10.1007/s10509-015-2408-2 Google Scholar
  22. Hoyle, C.D., Kapner, D.J., Heckel, B.R., Adelberger, B.R., Gundlach, J.H., Schmidt, U., Swanson, H.E.: Phys. Rev. D 70, 042004 (2004) ADSCrossRefGoogle Scholar
  23. Hu, Y.-P., Zhang, H., Hou, J.-P., Tang, L.-Z.: Perihelion precession and deflection of light in the general spherically symmetric spacetime. Adv. High Energy Phys. 2014, 604321, 7 pp. (2014). doi:10.1155/2014/60432 Google Scholar
  24. Iorio, L.: Phys. Lett. A 298(5–6), 315 (2002) ADSCrossRefGoogle Scholar
  25. Iorio, L.: J. High Energy Phys. 10, 041 (2007) ADSCrossRefGoogle Scholar
  26. Iorio, L.: Scholarly Research Exchange 2008 p. 238385 (2008) Google Scholar
  27. Iorio, L.: Astron. J. 137, 3615 (2009) ADSCrossRefGoogle Scholar
  28. Iorio, L.: Astron. J. 3, 1 (2010a) MathSciNetGoogle Scholar
  29. Iorio, L., Ruggiero, M.L.: Int. J. Mod. Phys. A 22, 5379 (2007) ADSCrossRefGoogle Scholar
  30. Klioner, S.A., Soffel, M.H.: Relativistic celestial mechanics with PPN parameters. Phys. Rev. D 62(2), 024019 (2000) (Particles, Fields, Gravitation, and Cosmology) ADSMathSciNetCrossRefGoogle Scholar
  31. Kolosnitsyn, N.I., Melnikov, V.N.: Test of the inverse square law through precession of orbits. Gen. Relativ. Gravit. 36(7), 1619–1624 (2004) ADSCrossRefMATHGoogle Scholar
  32. Krause, D.E., Fischbach, E., In: Lämmerzahl, C., Everitt, C.W.F., Hehl Lämmerzahl, C., Preuss, O., Dittus, H.: In: Dittus, H., Lämmerzahl, C., Turyshev, S.G. (eds.) Clocks and Drag Free Control: Exploration of Relativistic Gravity in Space, pp. 75–104. Springer, Berlin (2008) Google Scholar
  33. Lämmerzahl, C., Everitt, C.W.F., Hehl, F.W. (eds.): Gyros, Clocks, Interferometers: Testing Relativistic Gravity in Space, pp. 292–309. Springer, Berlin (2001) MATHGoogle Scholar
  34. Lucchesi, D.M.: Phys. Lett. A 318, 234 (2003) ADSCrossRefGoogle Scholar
  35. Maneff, G.: C. R. Acad. Sci. Paris 178, 2159 (1924) Google Scholar
  36. Maneff, G.: Z. Phys. 31, 786 (1925) ADSCrossRefGoogle Scholar
  37. Maneff, G.: C. R. Acad. Sci. Paris 190, 1374 (1930b) Google Scholar
  38. Maneff, G.: C. R. Acad. Sci. Paris 190, 963 (1930a) Google Scholar
  39. Matsumoto, J.: Universe 1(1), 17–23 (2015). doi:10.3390/universe1010017 ADSCrossRefGoogle Scholar
  40. Moffat, J.W.: J. Cosmol. Astropart. Phys. 03, 004 (2006) ADSMathSciNetCrossRefGoogle Scholar
  41. Moffat, J.W., Toth, V.T.: Fundamental parameter-free solutions in Modified Gravity (2009). arXiv:0712.1796v5 [gr-qc]
  42. Moffat, J.W., Toth, V.T.: Cosmological observations in a modified theory of gravity (MOG) (2012). arXiv:1104.2957v2[astro.ph.CO]
  43. Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999) MATHGoogle Scholar
  44. Peron, R., Colpi, M., Gorini, V., Moschella, U.: Gravity: Were Do We Stand? p. 61. Springer, Berlin (2016) CrossRefMATHGoogle Scholar
  45. Pitjeva, E.V.: In: Proc. IAA RAS, vol. 4, p. 22 (1999), St.-Petersburg Google Scholar
  46. Pitjeva, E.V.: Bull. Am. Astron. Soc. 41, 881 (2009) Google Scholar
  47. Reynaud, S., Jaekel, M.-T.: Int. J. Mod. Phys. A 20, 2294 (2005) ADSCrossRefGoogle Scholar
  48. Rubin, V.: Science 220, 1339 (1983) ADSCrossRefGoogle Scholar
  49. Scharer, A., Angelil, R., Bondarescu, R., Jetzer, P., Lundgren, A.: Testing scalar-tensor theories and PPN parameters in Earth orbit (2014). arXiv:1410.7914 [org/gr-qc]
  50. Sealfon, C., Verde, L., Jimenez, R.: Phys. Rev. D 71, 083004 (2005) ADSCrossRefGoogle Scholar
  51. Sereno, M., Peacock, J.A.: Mon. Not. R. Astron. Soc. 371, 719 (2006) ADSCrossRefGoogle Scholar
  52. Shirata, A., Shiromizu, T., Yoshida, N., Suto, Y.: Phys. Rev. D 71, 064030 (2005) ADSCrossRefGoogle Scholar
  53. Wang, F., Yang, J.M.: Some studies on dark energy related problems (2005). arXiv:hep-ph/0504046v1
  54. Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wyley and Sons, New York (1972) Google Scholar
  55. White, M., Kochanec, C.S.: Astrophys. J. 560, 539 (2001) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Ioannis Haranas
    • 1
  • Ilias Kotsireas
    • 1
  • Guillem Gómez
    • 3
  • Màrius J. Fullana
    • 3
  • Ioannis Gkigkitzis
    • 2
  1. 1.Dept. of Physics and Computer ScienceWilfrid Laurier University Science BuildingWaterlooCanada
  2. 2.Departments of MathematicsEast Carolina UniversityGreenvilleUSA
  3. 3.Institut de Matemàtica MultidisciplinàriaUniversitat Politècnica de ValènciaValenciaSpain

Personalised recommendations