Stable Domain for Geocentric GWs Observatory Based on Deviation Boundary Analysis

The drift of in the orbital elements between spacecraft directly affects the stability of triangular constellations, which in turn leads to the apparent instability in part of the parameter design space. This paper investigates the stable domain of the geocentric gravitational waves (GWs) constellation configuration considering the stability constraints. Select breathing angle index as stability criteria through analysis. Using the univariate method, the geometric relationship between the arm length and the orbital elements of spacecraft in a triangular configuration is analyzed to determine the orbital element deviation boundaries. Furthermore, numerical integration is adopted to determine the natural evolution extremum of the omnidirectional geocentric configuration during the mission period, and the most sensitive orbital elements are determined. The deviation boundary delineates certain unstable and quasi stable domains in the omnidirectional parameter design space. The proposed method can potentially be useful for constellation design and optimization.