  In this article we have studied the controllability of artificial satellite
under the effect of zonal harmonic $J_2$ in cylindrical polar coordinates
systems. Seven different cases of thrusters in various directions have been
analyzed and it is found that the system is controllable if we apply thrusters
in either $r$, $\theta$ and $z$ or $\theta$ and $z$ direction. The equations
governing motion of satellite have been linearized and Kalman controllability
test is applied to check the controllability of the system. We have also
derived controller $u$ for the linearized system. The trajectory of the system
have been plotted to show the controllability of the system.
