Science orbit design with a quasi-frozen beta angle: effects of body obliquity on J2-perturbed dynamics

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.