Newton's equation on the κ-spacetime and the kepler problem

Abstract

We study the modification of Newton's second law, upto first order in the deformation parameter a, in the κ-spacetime. We derive the deformed Hamiltonian, expressed in terms of the commutative phase space variables, describing the particle moving in a central potential in the κ-spacetime. Using this, we find the modified equations of motion and show that there is an additional force along the radial direction. Using Pioneer anomaly data, we set a bound for a. We also analyze the violation of equivalence principle predicted by the modified Newton's equation, valid up to first order in a and use this also to set an upper bound on a. © 2010 World Scientific Publishing Company.