Algebraic orbit elements difference description of dynamics models for satellite formation flying

In recent years, spacecraft formation flying has turn to a feasible solution to achieve improvements in performance and capabilities of space assets. As a result, dynamics of satellite formations has become an active area of research. To take full advantage of the benefits offered by formation flying concepts, it is necessary to develop and examine its dynamics models. In this paper, four models in terms of orbital elements namely Nonlinear Orbit Element Model, Linear Orbit Element Model, Linear Small eccentricity Orbit Element Model and Linear Circular Orbit Element Model are studied. An error index is given to measure accuracy of each model compared to the nonlinear model as the reference. This is performed by investigating the effects of main error sources in LEO orbits on the accuracy of formation modeling. These error sources are Earth gravitational perturbation, formation size and eccentricity of chief orbit. Based on the simulation results, one may be able to choose the appropriate model according to the desired accuracy for a given mission.