Proposed new determination of the gravitational constantGand tests of Newtonian gravitation

The first "constant of nature" to be identified, Newton's constant of universal gravitation $G$, is presently the least accurately known. The currently accepted value (6.672 59±0.000 85) × ${10}^{-11\mathrm{}}$ ${\mathrm{m}}^3$ ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{s}}^{-2\mathrm{}}$ has an uncertainty of 128 parts per million (ppm), whereas most other fundamental constants are known to less than 1 ppm. Moreover, the inverse-square law and the equivalence principle are not well validated at distances of the order of meters. We propose measurements within an orbiting satellite which would improve the accuracy of $G$ by two orders of magnitude and also place new upper limits on the field-strength parameter $\alpha$ of any Yukawa-type force, assuming a null result. Preliminary analysis indicates that a test of the time variation of $G$ may also be possible. Our proposed tests would place new limits on $\alpha ={\alpha }_5{\left(\frac{q_5}{\mu }\right)}_1{\left(\frac{q_5}{\mu }\right)}_2$ for characteristic lengths $\Lambda$ between 30 cm and 30 m and for $\Lambda >1000\mathrm{}$ km. In terms of the mass $m_b$ of a vector boson presumed to mediate such a Yukawa-type force, the proposed experiment would place new limits on $\alpha$ for $7\times {10}^{-9\mathrm{}} \mathrm{eV}<m_b{c}^2<7\mathrm{}\times {10}^{-7\mathrm{}} \mathrm{eV}$ and for $m_b{c}^2<2\mathrm{}\times {10}^{-13\mathrm{}}$ eV. Two distinct tests of the inverse-square law, one employing interactions at intermediate distances and having a peak sensitivity if $\Lambda$ is a few meters (i.e., $m_b{c}^2\sim {10}^{-7\mathrm{}}$ eV), and the other employing interactions at longer distances and having a peak sensitivity for $\Lambda \sim R_{\mathrm{Earth}} (m_b{c}^2\sim 3\times {10}^{-14\mathrm{}}\mathrm{eV})$, would both place limits of ${10}^{-5\mathrm{}}$ to ${10}^{-6\mathrm{}}$ on $\alpha$. These interactions also provide tests of the equivalence principle (Eötvös' experiment). The intermediate-distance interaction would test the equivalence principle to 5 parts in