Dynamical measurements of deviations from Newton’s $$1/r^2$$ 1 / r 2 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 $$1/r^2$$ 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 $$m_\mathrm{S} \sim \mathcal{O}(10^{-9})$$ m S ∼ O ( 10 - 9 ) g around a “Planet” with mass $$m_\mathrm{P} \in [10^{-7},10^{-5} ]$$ m P ∈ [ 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 $$1/r^2$$ 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 $$\alpha \sim 10^{-2}$$ α ∼ 10 - 2 for distances as small as $$\lambda \sim 10 \, \upmu $$ λ ∼ 10 μ m.