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 ${10}^7$ for $\Lambda >5\mathrm{} m (m_b{c}^2<4\mathrm{}\times {10}^{-8\mathrm{}} \mathrm{eV})$, while the longer-distance interaction would test the equivalence principle to 4 parts in ${10}^{13}$ for $\Lambda >R_{\mathrm{Earth}} (m_b{c}^2<3\mathrm{}\times {10}^{-14\mathrm{}}\mathrm{eV})$. Specifically, we propose to observe the motion of a small mass during the encounter phase of a "horseshoe" orbit—that is, in the vicinity of its closest approach to a large mass in a nearly identical orbit. The essential aspect of the interaction of the two bodies during the encounter is an exchange of energy, and we call the proposed method the "satellite energy exchange" (SEE) method. Successful application of the SEE method to gravity measurements will depend on the particular experimental design, including the configurations of the test bodies, the characteristics of the systems for maneuvering the test bodies and the satellite, and the choice of orbital parameters, which are described below. We are not aware of any existing or proposed method which approaches the accuracy of the SEE method.

Close

PrevNext

View figure in article