Exercise $2[40\backslash \%$ mark$]$ A large Earth$-$observation satellite in Low$-$Earth Orbit $($LEO$)$ is required to study different areas of interest on the surface of Earth. The first area of interest is $6$ degrees to the left of the satellite's ground track, whereas the second is $14$ degrees to the right. The satellite will pass abeam the second area of interest exactly $3\mathrm{.}5$ minutes after having passed abeam the first one. The moment of inertia of the satellite around the rotation axis is I$=5000$kg$$m$2.$ When activated, the actuators which can accomplish the maneuver produce a co $2\mathrm{.}7$N$$m$.$ You are required to: a$)$ sketch the plots over time of angular acceleration, velocity and position for the fast mane b$)$ determine the maximum angular velocity which the satellite will reach during the fast maneuver; c$)$ the duration of each firing period in the case of a minimum$-$fuel maneuver.