There is some indication that the force between two masses is not as described in this chapter. The deviation from the simple law \(F=\frac{G M m}{R^2}\) is being taken as an indication of the existence of a fifth interaction besides gravitational, electromagnetic, nuclear and weak. It has been reported (Phys. Rev. Lett. Jan 6, 1986) that the force between two masses may be better represented by
\(
F=\frac{G_{\infty} m_1 m_2}{r^2}\left[1+\left(1+\frac{r}{\lambda}\right) \alpha e^{-\frac{r}{\lambda}}\right]
\)
with \(\alpha \approx-0.007\) and \(\lambda \approx 200 \mathrm{~m}\). As \(\alpha\) is negative, the second term in the square bracket represents a repulsive force. For \(r \gg 200 \mathrm{~m}\)
\(
F=\frac{G_{\infty} m_1 m_2}{r^2}
\)
which is the force operative between the earth and other objects. For \(r<200 \mathrm{~m}\)
\(
F=\frac{G_{\infty} m_1 m_2(1+\alpha)}{r^2}=\frac{G^{\prime} m_1 m_2}{r^2}
\)
where \(G^{\prime}=G_{\infty}(1+\alpha)\).
This is the force we measure in a Cavendish experiment. The value of \(G\) for small distances is about \(1 \%\) less than the value of \(G\) for large distances.
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