Abstract: With the maturation and application of global satellite constellation flying technology, solving relative motion through the fundamental equations of satellite motion and designing various formation configurations have become a development trend. This paper establishes a relative motion model based on deviations in relative orbital elements, first theoretically derives the relative motion equations suitable for high eccentricity elliptical orbits under second order approximation conditions, and further analyzes the accuracy of the second order terms. Additionally, under the two body assumption, the true anomaly difference at perigee is used instead of the mean anomaly difference as the input for formation configuration design. Various typical formation configurations are designed and analyzed under different initial orbital element difference conditions. Finally, simulations are conducted to verify the correctness of the formation configuration design and analyze its applicability from the two body assumption to scenarios involving perturbations，the results show that the formation configuration design and the relative motion equations suitable for high eccentricity elliptical orbits are correct and effective.

Key words: elliptical orbits, the true anomaly difference, second order relative error, formation configuration design