  TianQin is a proposed space-based gravitational-wave observatory mission that
critically relies on the stability of an equilateral-triangle constellation.
Comprising three satellites in high Earth orbits of a $ 10^5 $ km radius, this
constellation's geometric configuration is significantly affected by
gravitational perturbations, primarily originating from the Moon and the Sun.
In this paper, we present an analytical model to quantify the effects of
lunisolar perturbations on the TianQin constellation, derived using Lagrange's
planetary equations. The model provides expressions for three kinematic
indicators of the constellation: arm-lengths, relative line-of-sight
velocities, and breathing angles. Analysis of these indicators reveals that
lunisolar perturbations can distort the constellation triangle, resulting in
three distinct variations: linear drift, bias, and fluctuation. Furthermore, it
is shown that these distortions can be optimized to display solely fluctuating
behavior, under certain predefined conditions. These results can serve as the
theoretical foundation for numerical simulations and offer insights for
engineering a stable constellation in the future.
