Quantum gravity, minimum length and Keplerian orbits

We conjecture that the modified commutation relations suggested in the context of quantum gravity (QG) persist also in the classical limit, if the momentum of the classical object is not too large, and calculate the corresponding perihelion precession rate for Keplerian orbits. The main result obtained in this Letter is not new. However the derivation is much simpler than the one proposed by Benczik et al. in [S. Benczik, L.N. Chang, D. Minic, N. Okamura, S. Rayyan, T. Takeuchi, Phys. Rev. D 66 (2002) 026003, arXiv:hep-th/0204049] where the corresponding precession rate was calculated for the first time. Our interpretation of the result is also quite different. (C) 2009 Elsevier B.V. All rights reserved.