Astrophysics and Space Science

, Volume 336, Issue 2, pp 369–377

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

Original Paper

DOI: 10.1007/s10509-011-0789-4

Cite this article as:
Reardon, A.C. Astrophys Space Sci (2011) 336: 369. doi:10.1007/s10509-011-0789-4


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 Go 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 Go were calculated from an analysis of the available data for each of these binary star systems, resulting in a value of Go=(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 Go was calculated through an analysis of the Pioneer anomaly data, resulting in Go=(3.00±0.37)×10−27 m2 kg−1 s−2. Within a factor of two, this value of Go 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.


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

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.East LongmeadowUSA

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