Dynamics Modeling of Spacecraft Formation Flying and Evaluating the Models Accuracy under the Effects of Relative Distance, Eccentricity and Earth Gravitational Perturbation

Relative motion of satellites in a formation can be studied in several forms of dynamics models. In this paper, some of the most applicable models each implying particular assumptions, constraints and specifications are described in Cartesian and orbital element spaces. Despite the significant applications of models based on linear equations of motion in modeling orbital rendezvous and ducking maneuvers, it is shown that the modeling errors of these simplified models limits their application in long term missions such as formation flying. Nonlinear equations of relative motion are derived in addition to 6 other dynamical models to simulate a low earth two satellite formation with projected circular relative orbit. Models are evaluated under the effects of non-spherical earth perturbation, relative distance between the satellites, and the eccentricity of the chief orbit. Analyzing the results of simulations emphasizes the importance of accuracy of the system.