# Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space

## TL;DR

This paper investigates how a deformed space with a minimal length affects the dynamics of the Sun-Earth-Moon system, deriving bounds on the minimal length from lunar laser ranging data.

## Contribution

It introduces conditions on deformation parameters ensuring classical physics principles are preserved and analyzes the impact of minimal length on celestial motion.

## Key findings

- Deformation leads to non-zero Eotvos-parameter, indicating potential violations of equivalence principle.
- Upper bounds on minimal length are estimated from lunar laser ranging data.
- Conditions are proposed to maintain classical relations in deformed space.

## Abstract

A space with deformed Poisson brackets for coordinates and momenta leading to the minimal length is considered. Features of description of motion of a body in the space are examined. We propose conditions on the parameters of deformation on which Poisson brackets for coordinates and momenta of the center-of-mass reproduce relations of deformed algebra, kinetic energy of a body is independent of its composition, and the weak equivalence principle is preserved in the deformed space. Influence of minimal length on the motion of the Sun-Earth-Moon system is studied. We find that deformation of the Poisson brackets leads to corrections to the accelerations of the Earth and the Moon toward the Sun, as a result the Eotvos-parameter does not vanish even if we consider equality of gravitational and inertial masses. The upper bound for the minimal length is estimated using results of the Lunar laser ranging experiment.