Dynamical measurements of deviations from Newton’s 1/r2 law

Abstract

In Ref. Donini and Marimón (Eur Phys J C 76:696, arXiv:1609.05654, 2016), 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 $m_{\mathrm{S}}\sim \mathcal{O}({10}^{-9})$ g around a “Planet” with mass $m_{\mathrm{P}}\in [{10}^{-7},{10}^{-5}]$ 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 such Beyond-Newtonian corrections. We then study in detail possible background sources that could induce precession and quantify their impact on the achievable sensitivity. We finally 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 $\lambda \sim 10\mathrm{\mu }$m.