Code in matlab the translational motion via numeric integration of the orbit (two-body orbit sufficient). Use the orbital characteristics of the Centaur V upper stage from the Atlas V launch on August 21, 2002 with the COSPAR ID 2002-038-B. You can look up the most recent orbital elements online (heavens-above.com). Make a 3D plot of the propagation over one orbital period. Combine the quaternion attitude integration with the translational motion of the orbit in a combined 6DoF integration. Assume an initial orientation of the upper stage with the long cylinder axis exactly orthogonal the orbital plane and no initial angular velocities. You can assume that the gravity gradient torque is the only torque acting on the upper stage. Plot the attitude motion in Euler angles over three periods of the orbit. 1. Assume a Centaur V upper stage with an empty mass of 2,247 kg, diameter of 3.05 meters and height of 12.68m, the wall thickness is 41mm, whereas the motor can be assumed to fill up 1/4 of the inner volume. You can assume the density of the walls and the motor to be uniform. You can assume the upper stage has been properly passivated and has no fuel remaining.