Abstract: In this article, a collision probability model is introduced based on the relative orbit elements. Under the two-body circular orbit conditions, its equivalence relation with the collision model based on Clohessy-Wiltshire (C-W) equation is derived and verified. Some remained problems of the C-W equations are also solved. A new method for collision analysis based on the relative elements is proposed for the configuration design of the close relative motion. Then the role of the relative orbital elements is highlighted on configuration design and collision analysis. The impact of the earth gravity harmonics perturbation (mainly J₂ perturbation) on the orbit error is analyzed. The drift equation of the relative elements in the unit time is derived, the propagation equation of the covariance matrix is given, and the collision probability model is established with the consideration of the impact of J₂ perturbation. Finally, the proposed calculation method is validated by simulation through a typical example.

Key words: relative orbit elements, relative motion, collision avoidance, perturbations, formation fly