https://doi.org/10.1140/epjc/s10052-024-12943-y
Regular Article – Theoretical Physics
Towards a realistic setup for a dynamical measurement of deviations from Newton’s 
law: the impact of air viscosity
1
Instituto de Física Corpuscular, CSIC-Universitat de València, Calle Catedrático José Beltrán Martínez 2, 46980, Paterna, Spain
2
Departamento de Física Teórica, Falcultad de Física, Universitat de València, Calle Doctor Moliner 50, 46100, Burjassot, Spain
3
Donostia International Physics Center (DIPC), Paseo Manuel Lardizabal 4, 20018, Donostia-San Sebastián, Spain
4
Ikerbasque, Basque Foundation for Science, Calle María Díaz de Haro 3, 48013, Bilbao, Spain
5
Centro de Física de Materiales, CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, 20018, Donostia-San Sebastián, Spain
6
Enrico Fermi Institute, University of Chicago, 5640 S Ellis Ave, 60637, Chicago, IL, USA
Received:
11
January
2024
Accepted:
22
May
2024
Published online:
10
June
2024
A novel experimental setup to measure deviations from the distance dependence of Newtonian gravity was proposed in Donini and Marimón (Eur Phys J C 76:696, 2016). The underlying theoretical idea was to study the orbits of a microscopically-sized planetary system composed of a “Satellite”, with mass 
g, and a “Planet”, with mass 
g at an initial distance of hundreds of microns. The detection of precession of the orbit in this system would be an unambiguous indication of a central potential with terms that scale with the distance differently from 1/r. This is a huge advantage with respect to the measurement of the absolute strength of the attraction between two bodies, as most electrically-induced background potentials do indeed scale as 1/r. Detection of orbit precession is unaffected by these effects, allowing for better sensitivities. In Baeza-Ballesteros et al. (Eur Phys J C 82:154, 2022), the impact of other subleading backgrounds that may induce orbit precession, such as, e.g., the electrical Casimir force or general relativity, was studied in detail. It was found that the proposed setup could test Yukawa-like corrections, 
to the 1/r potential with couplings as low as 
for distances as small as 
m, improving by roughly an order of magnitude present bounds. In this paper, we start to move from a theoretical study of the proposal to a more realistic implementation of the experimental setup. As a first step, we study the impact of air viscosity on the proposed setup and see how the setup should be modified in order to preserve the theoretical sensitivity achieved in Donini and Marimón (2016) and Baeza-Ballesteros et al. (2022).
© The Author(s) 2024
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