Dynamical measurements of deviations from Newton's $1/r^2$ law

Abstract

In a previous work (arXiv:1609.05654v2), an experimental setup aiming at the measurement of deviations from the Newtonian $1/r^2$ distance dependence of gravitational interactions was proposed. The theoretical idea behind this setup was to study the trajectories of a "Satellite" with a mass $m_{\mathrm{S}}\sim \mathcal{O}(10^{-9})$ $\mathrm{g}$ around a "Planet" with mass $m_{\mathrm{P}}\in [10^{-7},10^{-5}]$ $\mathrm{g}$, looking for precession of the orbit. The observation of such feature induced by gravitational interactions would be an unambiguous indication of a gravitational potential with terms different from $1/r$ and, thus, a powerful tool to detect deviations from Newton's $1/r^2$ law. In this paper we optimize the proposed setup in order to achieve maximal sensitivity to look for {\em Beyond-Newtonian} corrections. We study in detail possible background sources that could induce precession and quantify their impact on the achievable sensitivity. We conclude that a dynamical measurement of deviations from newtonianity can test Yukawa-like corrections to the $1/r$ potential with strength as low as $\alpha \sim 10^{-2}$ for distances as small as $\lambda \sim 10\mu \mathrm{m}$.

Two-column format (26 pages), 18 figures. Matches published version. References added, new appendix and minor corrections

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