, Volume 336, Issue 2, pp 369-377
Date: 20 Jul 2011

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

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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.