  The unperturbed Keplerian orbits of Taiji spacecrafts are expanded to $e^3$
order in the heliocentric coordinate system, where $e$ is their orbital
eccentricity. The three arm-lengths of Taiji triangle and their rates of change
are also expanded to $e^3$ order, while the three vertex angles are expanded to
$e^2$ order. These kinematic indicators of Taiji triangle are, further,
minimized, respectively, by adjusting the tilt angle of Taiji plane relative to
the ecliptic plane around $\pm\pi/3$, and thus, their corresponding optimized
expressions are presented. Then, under the case that the nominal trailing angle
of Taiji constellation following the Earth is set to be $\chi(\approx\pm\pi/9)$
from the viewpoint of the Sun, the influence of the Earth perturbation on three
spacecrafts is calculated according to the equations of motion in the problem
of three bodies, and the perturbative solutions of the leading order and the
next leading order are derived. With the perturbative solutions, the
leading-order corrections to the above kinematic indicators of Taiji triangle
and the expression of the above trailing angle to the order of $e^3$ are
provided.
