Study on Zero Relative Radial Acceleration Region of Formation near Sun-Earth Libration Points under Solar Radiation Pressure

Abstract

Formation interferometry near the Sun-Earth libration point is an essential direction for developing high-precision astronomical observation. Keeping the formation configuration stable for a long time is the premise of achieving high-precision measurement. However, the solar radiation pressure will disturb the satellite’s orbit, which challenges the formation configuration’s stability. This paper studies the stable region of formation motion near the libration point under the influence of solar radiation pressure. Based on the Sun-Earth three-body model considering solar radiation pressure, then linearizing the dynamic equation near the reference trajectory of the formation, the analytical expression of the zero relative radial acceleration region near the chief satellite is derived. It is found that the zero relative radial acceleration region is a quadric surface passing through the reference trajectory. The evolution characteristics of zero relative radial acceleration region are further analyzed, and the variation law of region distribution with reference trajectory type, amplitude, and phase is given. Finally, the formation configuration evaluation indexes such as shape, size, and coplanarity are defined. The formation configuration design and control method based on zero relative radial acceleration region is proposed and applied to the design of the five-satellite formation mission. The simulation results show that the formation configuration is bounded within 70 days, and the change rate of the relative distance between the chief satellite and deputy satellite is less than 2% in the first 60 days. In this paper, the study of zero relative radial acceleration region under the influence of solar radiation pressure can provide a basis for designing future Sun-Earth libration point interferometry formation orbits.

Keywords

zero relative radial acceleration region / solar radiation pressure / formation flight / libration point

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