Exploring more solutions for low-energy transfers to lunar distant retrograde orbits

Abstract

This study aims to explore more solutions for low-energy transfers to lunar distant retrograde orbits (DROs) from the vicinity of the Earth. Millions of transfer trajectories from a lunar free-return orbit (LFO) to a prescribed DRO were computed using multiple powered lunar flybys (PLFs) and weak-stability-boundary (WSB)-like ballistic transfer. We proposed a two-step design method, consisting of a database creation and trajectory patching, to construct low-energy LFO–DRO transfers in planar bicircular restricted four-body dynamics with the Sun, Earth, and Moon as primary bodies. The parallel computation technique allows the computation of millions of solutions with times of flight (TOFs) up to 135 days and a total velocity impulse ($\Delta$V) of no more than 350 m/s, although this design method requires substantial computational load. These solutions help us identify key flight information, such as the $\Delta$V–TOF Pareto fronts and launch windows for rendezvous with a station in a DRO. Low-energy transfers to a DRO can be achieved by exploiting single or multiple PLFs and WSB-like ballistic arcs at the expense of elongated TOFs. Moreover, triple PLFs render many more options for the spacecraft to accomplish the rendezvous of DROs. The WSB-like ballistic arcs to a DRO in this study exhibit new features compared with conventional and traditional WSB concepts.

Appendices: Representative LFO−DRO transfer trajectories

Fig. 21

Transfer trajectories of the Pareto optimal solutions in Fig. 8 in the Earth–Moon rotating frame (the first blue are computed in PCRTBP, while the green and second blue arcs were computed in PBRFBP)

Fig. 22

Transfer trajectories of the Pareto optimal solutions presented in Fig. 8 in the Sun–Earth rotating frame (the first blue arc was computed in PCRTBP, while the green and second blue arcs were computed in PBRFBP)

The transfer trajectories of I−VI shown in Fig. 8 plotted in the EMR and SER frames are shown in Figs. 21 and 22, respectively.

Table 8 Orbital states in the Earth–Moon rotating frame of the representative solutions presented in Fig. 8

Fig. 23

Transfer trajectories of the Pareto optimal solutions presented in Fig. 9 in the Earth–Moon rotating frame (the first blue and green arcs were computed in PCRTBP, while the second blue arc was computed in PBRFBP)

Fig. 24

Transfer trajectories of the Pareto optimal solutions presented in Fig. 9 in the Sun–Earth rotating frame (the first blue and green arcs were computed in PCRTBP, while the second blue arc was computed in PBRFBP)

Table 9 Orbital states in the Earth–Moon rotating frame of the representative solutions presented in Fig. 9

The spacecraft reaches the perilune twice and conducts double PLFs when it moves along the trajectory (blue–green–blue arcs), where the first blue arc is the LFO–perilune track, the green arc is the perilune–perilune track, and the second blue arc is the perilune–DRO track. Transfer I has a short flight time, while transfer II–VI uses the WSB-like arc, where the first PLF places the spacecraft into a WSB-like trajectory arc, and the second PLF places the spacecraft into a trajectory that intersects with the target DRO. The orbital states at the maneuvers of the two transfers in the Earth–Moon rotating frame are presented in Table 8, where $\phi$ is the phase of the Sun, $\hbox {P}_i$ is the i-th perilune, and $t = 0$ when the spacecraft arrives at the second perilune.

Fig. 25

Transfer trajectories of the Pareto optimal solutions presented in Fig. 10 in the Earth–Moon rotating frame (the first blue and green arcs were computed in PCRTBP, while the other arcs were computed in PBRFBP)

Fig. 26

Transfer trajectories of the Pareto optimal solutions presented in Fig. 10 in the Sun–Earth rotating frame (the first blue and green arcs were computed in PCRTBP, while the other arcs were computed in PBRFBP)

Table 10 Orbital states in the Earth–Moon rotating frame of the representative solutions presented in Fig. 10

The transfer trajectories of I–V in Fig. 9 plotted in the EMR and SER frames are shown in Figs. 23 and 24, respectively. In the two figures, the perilune–perilune arcs (green arc) appear to have a figure-8 shape in the EMR frame and orbits the Earth twice in the SER frame. In transfers III–V, two PLFs occur before the WSB-like arc. The orbital states at the maneuvers of the five transfers in the Earth–Moon rotating frame are presented in Table 9, where $t = 0$ when the spacecraft arrives at the DRO.

Table 11 Orbital states in the Earth–Moon rotating frame of the representative solutions presented in Fig. 7

The transfer trajectories of I–V in Fig. 10 plotted in the EMR and SER frames are shown in Figs. 25 and 26, respectively. Four segments can be identified, including the LFO-to-perilune trajectory (blue lines), two perilune-to-perilune trajectories (green lines and blue lines), and the perilune-to-DRO trajectory (red lines), in which transfers III–VI used the WSB-like arc. The states at the maneuvers of the six transfers in the EMR frame are presented in Table 10, where $t = 0$ when the spacecraft arrives at the third perilune.

The states at the maneuvers of the representative solutions in Fig. 7 in the EMR frame are presented in Table 11, where $t = 0$ when the spacecraft arrives at the DRO.