How to Maneuver Around in Eccentricity Vector Space

The GRAIL mission to the Moon will be the first time that two separate robotic orbiters will be placed into formation in orbit around a body other than Earth. The need to design an efficient series of maneuvers to shape the orbits and phasing of the two orbiters after arrival presents a significant challenge to mission designers. This paper presents a simple geometric method for relating in-plane impulsive maneuvers to changes in the eccentricity vector, which determines the shape and orientation of an orbit in the orbit plane. Examples then show how such maneuvers can accommodate desired changes to other orbital elements such as period, incination, and longitude of the ascending node.