  We study presence of an additional symmetry of a generic central potential in
the $\kappa$-space-time. An explicit construction of Fradkin and Bacry, Ruegg,
Souriau (FBRS) for a central potential is carried out and the piece-wise
conserved nature of the vector is established. We also extend the study to
Kepler systems with a drag term, particularly Gorringe-Leach equation is
generalized to the $\kappa$-deformed space. The possibility of mapping
Gorringe-Leach equation to an equation with out drag term is exploited in
associating a similar conserved vector to system with a drag term. An extension
of duality between two class of central potential is introduced in the
$\kappa$-deformed space and is used to investigate the duality existing between
two class of Gorringe-Leach equations. All the results obtained can be retraced
to the correct commutative limit as we let $a \rightarrow 0$.
