Analytical analysis on the orbits of Taiji spacecrafts to infinite order of the orbital eccentricity

The dual configuration of the original one is proposed for the orbit design of Taiji spacecrafts. In terms of these two configurations of Taiji, an algorithm is devised to expand the unperturbed Keplerian orbits of spacecrafts to infinite order of $e$, the orbital eccentricity, in the heliocentric coordinate system. Further, based on the algorithm, all the kinematic indicators of Taiji triangles, say three arm-lengths and their corresponding rates of change, and three vertex angles, in both configurations are also be expanded to infinite order of $e$, and it is proved that both configurations of Taiji possess the same symmetry: At every order, three components of every kinematic indicator of Taiji triangle are identical to each other up to a phase shift of $2\pi/3$, which is independent on the tilt angle of Taiji plane relative to the ecliptic plane. Finally, the above algorithm is slightly modified, and with it, by adjusting the tilt angle around $\pi/3$ to any order of $e$, the orbits of Taiji spacecrafts in each configuration can be optimized.