Astrophysics and Space Science

, Volume 336, Issue 2, pp 369–377 | Cite as

Gravitational analysis of V541 Cygni, DI Herculis, and the Pioneer anomaly

Original Paper

Abstract

Detailed analyses by independent research groups over several decades reveal a significant discrepancy between the observed rate of periastron advance in the detached eclipsing binary star systems DI Herculis and V541 Cygni and the values theoretically predicted from the combined classical and general relativistic effects. A modification to Newton’s gravitational theory is proposed in this investigation to account for these discrepancies, and is represented by
$$\mathbf{F} = - \frac{Gm_{1}m_{2}}{r^{3}}\boldsymbol{r} - \frac{G_{o}m_{1}m_{2}}{r^{2}}\boldsymbol{r}$$
where G o is a second gravitational constant. The two body problem is solved analytically in closed form, resulting in a retrograde contribution to the advance of periastron. Numerical values of G o were calculated from an analysis of the available data for each of these binary star systems, resulting in a value of G o =(1.5±0.3)×10−27 m2 kg−1 s−2 from the analysis of V541 Cygni, and \(G_{o} = (1.5_{ - 1.5}^{ + 0.3}) \times 10^{-27}~\mbox{m}^{2}\,\mbox{kg}^{-1}\,\mbox{s}^{-2}\) from an analysis of DI Herculis. The level of agreement between these values supports the assumption that the rotational axes of the stars in V541 Cygni are oriented perpendicular to the orbital plane, as opposed to the highly inclined orbits of the stars observed in DI Herculis. An independently determined value of G o was calculated through an analysis of the Pioneer anomaly data, resulting in G o =(3.00±0.37)×10−27 m2 kg−1 s−2. Within a factor of two, this value of G o agrees with the results obtained from DI Herculis and V541 Cygni. The proposed theory predicts the “turn on” of the Pioneer anomaly to occur at a heliocentric distance of 10.0 AU, in good agreement with observation.

Keywords

Binary stars Gravitational constant Pioneer anomaly DI Herculis V541 Cygni Galaxy rotation curves Modified gravity Gravity Astrophysics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albrecht, S., et al.: Nat. Lett. 461, 373 (2009) ADSCrossRefGoogle Scholar
  2. Anderson, J.D., et al.: Phys. Rev. D 65, 082004 (2002) ADSCrossRefGoogle Scholar
  3. Claret, A.: Astron. Astrophys. 330, 533–540 (1998) ADSGoogle Scholar
  4. Dariush, A., Riazi, N.: Astrophys. Space Sci. 283, 253 (2003) ADSCrossRefGoogle Scholar
  5. Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik 49 (1916) Google Scholar
  6. Fabris, J.C., Campos, J.P.: Gen. Relativ. Gravit. 41(1), 93–104 (2008). doi: 10.1007/s10714-008-0654-0 ADSCrossRefGoogle Scholar
  7. Guinan, E.F., Maloney, F.P.: Astron. J. 90, 1519 (1985) ADSCrossRefGoogle Scholar
  8. Guinan, E.F., et al.: I.B.V.S., No. 4362 (1996) Google Scholar
  9. Hoffmeister, C.: Astron. Nachr. 240, 195 (1930) ADSCrossRefGoogle Scholar
  10. Hsuan, K., Mardling, R.A.: Astrophys. Space Sci. 304, 243 (2006) ADSCrossRefGoogle Scholar
  11. Kirillov, A.A.: Phys. Lett. B 632, 453 (2006) MathSciNetADSCrossRefGoogle Scholar
  12. Kozyreva, V.S., Bagaev, L.A.: Astron. Lett. 35, 483 (2009) ADSCrossRefGoogle Scholar
  13. Lammerzahl, C., et al.: Astrophys. Space Sci. Libr. 349, 75 (2008) ADSCrossRefGoogle Scholar
  14. Milgrom, M.: Astrophys. J. 270, 365 (1983a) ADSCrossRefGoogle Scholar
  15. Milgrom, M.: Astrophys. J. 270, 371 (1983b) ADSCrossRefGoogle Scholar
  16. Moffat, J.W.: Astrophys. J. 615, 506 (2004) CrossRefGoogle Scholar
  17. Newton, I.: Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), London (1687) Google Scholar
  18. Nieto, M.M., Anderson, J.D.: Class. Quantum Gravity 22, 5343 (2005) ADSMATHCrossRefGoogle Scholar
  19. Popper, D.M.: Astrophys. J. 254, 203 (1982) ADSCrossRefGoogle Scholar
  20. Reisenberger, M.P., Guinan, E.F.: Astron. J. 97, 216 (1989) ADSCrossRefGoogle Scholar
  21. Sanberg Lacy, C.H.: Astron. J. 115, 801 (1998) CrossRefGoogle Scholar
  22. Scheffer, L.K.: Phys. Rev. D 67, 084021 (2003) ADSCrossRefGoogle Scholar
  23. Shakura, N.I.: Sov. Astron. Lett. 11, 225 (1985) ADSGoogle Scholar
  24. Sobouti, Y.: Astron. Astrophys. 464, 921 (2007) ADSMATHCrossRefGoogle Scholar
  25. Sofue, Y., Rubin, V.: Annu. Rev. Astron. Astrophys. 39, 137 (2001) ADSCrossRefGoogle Scholar
  26. Turyshev, S., Toth, V.: Space Sci. Rev. 148, 149 (2009) ADSCrossRefGoogle Scholar
  27. Turyshev, S., Toth, V.: Living Rev. Relativ. 13, 4 (2010) ADSGoogle Scholar
  28. Wolf, M., Kotkova, L.: JAAVSO 35, 185 (2006) ADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.East LongmeadowUSA

Personalised recommendations