Low-Thrust Control of a Lunar Mapping Orbit

A method is presented for establishing and maintaining a lunar mapping orbit using continuous-low-thrust propulsion. Optimal control theory is used to maintain a lunar orbit that is low-altitude, near-polar, and sun-synchronous, which are three typical requirements for a successful lunar mapping mission. The analysis of the optimal control problem leads to the commonly seen two-point boundary-value problem, which is solved using a simple indirect shooting algorithm. Simulations are presented for a one-year mapping duration, in which it is shown that an average control force of 0.5 N for a 1000-kg-class spacecraft is required to rotate the orbit plane at the sun-synchronous rate. Because this amounts to a total A V of roughly 15 km/s, a fairly large propellant mass of 416 kg would be required from a typical ion thruster for a one-year mission. However, if the science requirements can be fulfilled in a shorter 1―2-month mission, the required propellant mass could be drastically reduced. Also, it is shown that if the desired control accuracy of the sun-synchronous ascending node is relaxed, the required thrust levels can be decreased by roughly 0.2 N.