Formation Flying Trajectory Optimization And Analysis For TAIJI Space-based Gravitational Waves Observatory

Gravitational waves are the most important prediction of Einstein's general theory of relativity.Gravitational-wave detection has been at the forefront of contemporary physics and is of great significance in astronomy and physics.Compared with ground gravitational waves observatory,space-based gravitational waves observatory is free from the limitations of ground experimental scale and noise.Thus,it is able to detect gravitational waves in medium and low frequency and has higher sensitivity.This paper is based on TAIJI Project and mainly focuses on heliocentric formation flying trajectory optimization and analysis.The contents are detailed as follows:In constellation optimization,the space-based gravitational waves observatory has a long lifetime and a high precision dynamical model.And they lead to low efficiency in constellation optimization.To solve this problem,a symplectic integral orbit propagation model with the solar gravity and other perturbation forces is constructed.In the constellation optimization,the arm length,breathing angle,arm length variation rate,and the distance to Earth are taken into consideration,and the efficiency is improved.The simulation results show that when the step size is 100000 s,the position error of symplectic integral is less than that of the traditional method RKF78 by 0.1271 km.Meanwhile,the computational time of constellation optimization based on symplectic integral is reduced by 45% compared with that based on RKF78.In terms of the stability analysis of the constellation for space-based gravitational waves observatory,the influence of celestial bodies in the solar system is firstly analyzed,mainly including planets,the moon,dwarf planets,and asteroids.To analyze the influence of asteroids on the stability of constellation,a double screening method is proposed,which takes the orbit distance and magnitude of asteroids into consideration comprehensively.The method avoids a large number of calculations on asteroids and is able to quickly estimate the influence of the relative acceleration of asteroids on constellation.The simulation results show that compared with the gravity of the planets,the influence of dwarf planets and asteroids on the constellation can be negligible.The dynamic model can be simplified reasonably according to the analysis results.Secondly,to analyze the effect of insertion errors on the constellation,an insertion error propagation analysis method for formation flying based on covariance analysis description equation technique is proposed,the error propagation equations of arm length,breathing angle,arm length variation rate,and distance to Earth are established.The method can analyze the influence of insertion error on the constellation stability quickly and accurately.Compared with the Monte-Carlo method,the computational time is greatly reduced.In the aspect of orbit determination,the requirement of orbit determination precision for space-based gravitational waves observatory is analyzed.To meet the injection requirement,an orbit determination method based on extended Kalman filtering is designed.The accuracy of orbit determination is improved by using intersatellite ranging and angle measurement information.In terms of global optimization of transfer trajectory and constellation,to meet the requirements of high-precision constellation and transfer trajectory,global optimization methods for transfer trajectory and constellation optimization based on pulse transfer,electric propulsion transfer,and lunar gravity assist transfer are studied.The methods take the constellation stability,transfer time,and required increment in velocity into consideration simultaneously.The simulation results show that after the separation of satellites and rocket,the three satellites transfer independently into the stable formation flying orbits directly.