Formation Design of for Space Gravitational Wave Detection Based on Second Order CW Equation

To solve the problem of arm length divergence of space gravitational wave detection formation based on CW equation in two-body nonlinear gravitational field, a formation configuration design method based on second-order CW equation was proposed. Firstly, the differential form of the second-order CW equation was derived, and the approximate analytical solution of the second-order CW equation was obtained by perturbation method. Then, the non-existence of circular flying orbit was proved, and the divergence reason of the nominal configuration based on CW equation was analyzed. Secondly, based on second-order CW equation and the energy matching period condition, the formation configuration optimization model was constructed with the phase angles of the spacecraft as optimization variables, and the multi-constraint configuration optimization method based on the global optimization algorithm and the pattern search algorithm was established. Finally, the optimization results were verified by simulation based on the Taiji mission. Simulation results show that the proposed optimization method can reduce the average error of formation arm length to 0.32% and the maximum error to 0.44 %.