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This paper presents the trajectory design for EQUilibriUm Lunar-Earth point 6U Spacecraft (EQUULEUS), which aims to demonstrate orbit control capability of CubeSats in the cislunar space. The mission plans to observe the far side of the Moon from an Earth-Moon L2 (EML2) libration point orbit. The EQUULEUS trajectory design needs to react to uncertainties of mission design parameters such as the launch conditions, errors, and thrust levels. The main challenge is to quickly design science orbits at EML2 and low-energy transfers from the post-deployment trajectory to the science orbits within the CubeSat’s limited propulsion capabilities. To overcome this challenge, we develop a systematic trajectory design approach that 1) designs over 13,000 EML2 quasi-halo orbits in a full-ephemeris model with a statistical stationkeeping cost evaluation, and 2) identifies families of low-energy transfers to the science orbits using lunar flybys and solar perturbations. The approach is successfully applied for the trajectory design of EQUULEUS.

The beta angle, an angle formed by the sunlight and a spacecraft orbital plane, is an important parameter for science orbit design of orbiter missions. This angle defines lighting conditions and eclipse occurrences, and is used for science observation planning. Not only is this parameter perturbed by the irregular gravity field of the primary body, it varies with the body’s motion around the Sun. Investigating the evolution of the beta angle is therefore critical for science orbit design. This paper analyzes the J2-perturbed beta angle evolution via orbit averaging and year averaging, and derives conditions to constrain the short- and long-term evolutions of the beta angle. The orbit averaging analysis is further extended to provide a relaxed orbit condition that allows flexible science orbit design while naturally maintaining the beta angle evolution within science requirements. These analyses are carried out for an arbitrary rotation pole direction as it defines the orientation of the irregular gravity field seen in an inertial frame. The analytical work is numerically demonstrated with science orbit design for the Psyche mission, a recently selected mission of the NASA’s Discovery Program.