Abstract
A concise, novel description is presented of near-circular satellite motion at arbitrary inclination in resonance with a single dominant tesseral harmonic of a gravitational potential. A practical method is then given for determining the validity of the ideal resonance assumption in specific regions of phase space. The model has been designed to be potentially sufficiently accurate for use in orbit determination yet computationally concise enough for implementation on-board small satellites. Unlike more traditional, mathematically rigorous approaches the orbit description has a relatively simple geometric interpretation making it ideal for use in mission analysis and design. It also facilitates a summary of the factors determining and affecting the nature of resonant motion experienced by satellites. This resonance model is incorporated into a curvilinear relative orbit framework to characterize the effects of tesseral resonance on the relative motion of formations of satellites. The results show that these effects can be the same magnitude as that due to short periodic J2 motion, or secular motion due to small inclination differences for close LEO satellite formations. The analytical relative resonant orbit model also allows the key factors determining the relative resonant motion to be isolated. Finally, the intuitive nature of the resonant orbit model is exploited in two ways. Firstly, the analogy between the non-linear motion of a satellite in resonance to that of a simple pendulum is exploited to develop control strategies for maintaining both spatial and temporal separations between satellites in a resonant formation. Secondly, a simple mission analysis tool is developed to allow orbit analysts to determine whether a given satellite mission could encounter a resonance of significant strength. The output of this software tool is also used to identify the limitations of the resonance model for describing motion about other celestial bodies such as the Moon, Venus and Mars.