SMALL SATELLITE FORMATIONS IN RESONANT ORBITS

摘要

A novel analytical description is presented of near-circular satellite motion in resonance with a single, dominant tesseral harmonic of a gravitational field. The model has been designed to be 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 applications. The model derivation, accurate to first order in J_2, is outlined and the analogy between the motion of the resonant variable and that of a simple pendulum is highlighted. The model output is shown to compare favourably to numerical integrations and its intuitive nature is then exploited in two ways. Firstly, the absolute resonant orbit solutions are used to develop an existing curvilinear relative orbit model to characterize the motion of satellite formations in resonance. From this it is established that resonant effects on formations can be of significant magnitudes. Secondly the analogous motion of a one degree of freedom pendulum is used to develop strategies for controlling these relative resonant effects for specific applications.