Optimal control of a spacecraft orbiting the Moon in a Sun-synchronous orbit that provides consistent illumination and efficient imaging for mapping is investigated in this paper. The perturbations due to the gravitational force from the Earth, Sun and the non-spherical gravity field of the Moon are utilized as a framework for deriving the equations of motion of the spacecraft. The spacecraft position is controlled to maintain a constant semimajor axis, eccentricity, inclination and argument of periapsis with the ascending node changing at a Sun-synchronous rate. A nonlinear model is developed that describes the dynamics of the system and then this model is converted into a linear-like structure. This nonlinear dynamic problem is then solved by employing an optimal nonlinear control approach, known as the State Dependent Algebraic Riccati Equation i.e. the SDRE technique. Control accelerations are found using the SDRE approach to maintain the spacecraft in the desired orbit. An interesting approximate closed form solution that makes the control implementation simple is found after tracking the change in the control gains obtained from the SDRE technique. Numerical results are presented and analyzed.