Effect of Earth-Moon’s gravity on TianQin’s range acceleration noise. III. An analytical model

TianQin is a proposed space-based gravitational-wave detector designed to operate in circular high Earth orbits. As sequel [Zhang et al. Phys. Rev. D 103, 062001 (2021)], this work provides an analytical model account for the perturbing effect of Earth's gravity field on range acceleration noise between two satellites. For such ``orbital noise,'' contribution dominates above $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{Hz}$ frequency spectrum, and calibration mitigation, if needed, can benefit from in-depth modeling. Our derivation based Kaula's theory satellite gravimetry with Fourier-style decomposition uses reference orbits as approximation. To validate model, we compare numerical results main scenarios. First, case static field, both spectra are shown agree well each other at various orbital inclinations radii, confirming our previous while providing more insight. Second, extended incorporate time-variable gravity. Particularly relevant TianQin, augment formulas capture disturbance free oscillations triggered by earthquakes, which mode frequencies enter TianQin's measurement band 0.1 mHz. The may find applications environment monitoring noise-reduction pipelines TianQin.