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In this article we have studied the controllability of artificial satelliteunder the effect of zonal harmonic $J_2$ in cylindrical polar coordinatessystems. Seven different cases of thrusters in various directions have beenanalyzed and it is found that the system is controllable if we apply thrustersin either $r$, $\theta$ and $z$ or $\theta$ and $z$ direction. The equationsgoverning motion of satellite have been linearized and Kalman controllabilitytest is applied to check the controllability of the system. We have alsoderived controller $u$ for the linearized system. The trajectory of the systemhave been plotted to show the controllability of the system.

Controllability Analysis of Motion of Artificial Satellite Under the Effect of Oblateness of the Earth