Configuration Stability Analysis for Geocentric Space Gravitational-Wave Observatories

Long-term configuration stability is essential for a space-based gravitational-wave observatory, which can be affected by orbit insertion errors. This paper investigated the stability of a geocentric gravitational-wave observatory from the view of the configuration uncertainty propagation. The effects of the orbit insertion errors on the configuration stability are propagated using the Unscented Transformation (UT). The best UT tuning factor is selected based on the accuracy analysis of different UT tuning factors. The effects of the position and velocity insertion errors in different directions are firstly discussed. Compared with the Monte Carlo simulations, the UT method has relative errors of no more than 2.7%, while the time cost is only 3.6%. It is found that the radial position and tangential velocity insertion errors have the largest influence on the configuration stability. Finally, based on the proposed method, the stability domain of the geocentric space gravitational-wave detection constellation is investigated by considering two kinds of insertion errors, i.e., independent and identically distributed insertion errors and insertion errors in spatial directions. The analysis results in this paper can be potentially useful for the configuration design of a geocentric gravitational-wave observatory.