Comparison study of relative dynamic models for satellite formation flying

A simulation method with a modeling error index are introduced for comparing and evaluating various theories of relative motion of satellite formation dynamics. The index captures error components of relative position and velocity between a selected satellite relative model and a precise propagator. It is applicable to evaluate the accuracy performance of any valid relative dynamic model including both linear and nonlinear models. In this paper, we study the evaluation of satellite relative dynamic models described by differential equations in LVLH coordinate. Five widely used models are analyzed in different orbits in perturbed Earth environment. The results show that, when the Earth aspherical gravity and the air drag are present, the accuracy of some models is affected tremendously by eccentricity, semi-major axis, inclination, and formation size. The numerical results provide valuable information for formation design.