# Newton&#x27;s Equation on the kappa space-time and the Kepler problem - High Energy Physics - Theory

Abstract: We study the modification of Newton-s second law, upto first order in thedeformation parameter $a$, in the $\kappa$-space-time. We derive the deformedHamiltonian, expressed in terms of the commutative phase space variables,describing the particle moving in a central potential in the$\kappa$-space-time. Using this, we find the modified equations of motion andshow that there is an additional force along the radial direction. UsingPioneer anomaly data, we set a bond as well as fix the sign of $a$. We alsoanalyse the violation of equivalence principle predicted by the modifiedNewton-s equation, valid up to first order in $a$ and use this also to set anupper bound on $a$.

Author: E. Harikumar, A. K. Kapoor

Source: https://arxiv.org/