Single impulsive transfer to the Earth–Moon triangular point L₄ in a bicircular model

This paper investigates a single impulsive strategy of transferring a spacecraft from the Earth to the Earth–Moon triangular point L₄ in the Sun–Earth–Moon bicircular model (BCM). The motion of the spacecraft at L₄ is influenced by the Sun's perturbation and different Sun's initial phase angles can cause different motion. The motion that can easily escape the vicinity of L₄ in a backward propagation is utilized to design the single impulsive transfer to L₄ and then the window of easily approach (WOEA) to L₄ is defined by analyzing the change in the Jacobi energy of the motion. Accordingly, the perigee of the motion can be obtained by propagating initial state of the spacecraft at L₄ backwards. The transfer whose perigee height is approximated to that of the parking low Earth orbit (LEO) can be utilized as an initial guess, and therefore the single impulsive transfer can be calculated by correcting the Sun's initial phase angle and the flight time. Meanwhile, by comparing the changes in the Jacobi energy and the energy of the spacecraft, it can be found that the lunar flyby enables the single impulsive transfer to be accomplished. Since only one maneuver is required during an entire transfer, this transfer strategy may be more suitable for the small spacecraft that has a limited propulsion capability.