Configuration Uncertainty Propagation of Geocentric Interferometric Constellation with Respect to Orbital Element Errors

The interferometric constellations are widely applied to high-precision measurement in space, such as space gravitational waves detection. Uncertain propagation study of constellations can provide guidance for configuration design, but highly nonlinear dynamics and large evolution time make it very difficult. This paper aims at the uncertainty propagation of the geocentric interferometric constellations under the action of complex conservative forces. First, the configuration parameters of a constellation are introduced. The magnitudes of the conservative perturbations at different orbital altitudes are analyzed, including the third body perturbations from the Moon, the Sun and the Earth's non-spherical perturbation. Secondly, the initial state of the constellation is represented by the set of orbital elements of each spacecraft. The deviations of the orbital elements are separately applied to the initial configurations of different orientations and sizes to study the configuration uncertainty propagations. It is found that the accumulation of phase deviation is the major factor leading to the configuration deformation. The uncertainty magnitude of the constellation is inversely related to the configurational size. Besides, the configuration of the constellations, whose orbital period is resonated with the Moon, should be avoided in the mission design.