The Kepler problem in the Snyder space

TL;DR

This paper investigates the Kepler problem within Snyder noncommutative space, deriving deformed potentials and analyzing their effects on Mercury's orbit precession to estimate the noncommutative deformation parameter.

Contribution

It introduces a method to incorporate Snyder noncommutativity into the Kepler problem and calculates the resulting orbital precession effects.

Findings

Deformed potential expression derived

Precession of Mercury's orbit calculated

Estimated value for noncommutative parameter obtained

Abstract

In this paper we study the Kepler problem in the non commutative Snyder scenario. We characterize the deformations in the Poisson bracket algebra under a mimic procedure from quantum standard formulations and taking into account a general recipe to build the noncommutative phase space coordinates (in the sense of Poisson brackets). We obtain an expression to the deformed potential, and then the consequences in the precession of the orbit of Mercury are calculated. This result allows us to find an estimated value for the non commutative deformation parameter introduced.