3) Consider the motion of a satellite around earth :- m Jo 0,0 M Where Tr and To are the radial and lateral thrusts. The equations of motion can be written m (r-ro) = Tv - GMm m n (r + 2 8) = To 22 Express the above nonlinear system in state space form x = f (x, u) with the following States x = r 0 and the following inputs U = Tr Next, consider the nominal operating condition of the satellite to be a orbit. This means :- o = 2 geosynchronous circular W = angular speed of earth. Further, the circular orbit has the radius. % = GMT 13 W2 Determine the nominal thrusts Tr. & To, & linearize the above nonlinear system about the operating point described above.