In an effort to open up the far side of the Moon to exploration, studies have been

Chapter 0, Problem CP11.6

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In an effort to open up the far side of the Moon to exploration, studies have been conducted to determine the feasibility of operating a communication satellite around the translunar equilibrium point in the Earth-Sun-Moon system. The desired satellite orbit, known as a halo orbit, is shown in Figure CP11.6.The objective of the controller is to keep the satellite on a halo orbit trajectory that can be seen from the Earth so that the lines of communication are accessible at all times. The communication link is from the Earth to the satellite and then to the far side of the Moon. The linearized (and normalized) equations of motion of the satellite around the translunar equilibrium point are [25] 0 0 0 7.3809 0 0 0 0 0 u -2.1904 0 0 0 0 0 (J -3.1904 1 0 0 0 -2 0 0 1 0 2 0 0 0 0 1 0 0 0