Dynamical measurements of deviations from Newton's \(1/r^2\) law

• Published in: arXiv.org 2022-02
• Main Authors: Baeza-Ballesteros, J, Donini, A, Nadal-Gisbert, S
• Format: Article
• Language: English
• Subjects: Deviation; Precession; Sensitivity
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2106.08611

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 \(m_{\rm S} \sim {\cal O}(10^{-9})\) \(\mathrm{g}\) around a "Planet" with mass \(m_{\rm P} \in [10^{-7},10^{-5} ]\) \(\mathrm{g}\), 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 \(\lambda \sim 10 \, \mu\mathrm{m}\).