Navigating Interplanetary Highways: How AI and Celestial Mechanics Revolutionize Space Trajectories

Analyzing exit trajectories from the Earth-Moon system is a crucial phase in designing interplanetary missions. Unlike traditional two-body problems, spacecraft movement within the gravitational fields of multiple bodies lacks an analytical solution, requiring numerical methods to find realistic trajectories. In a new study, scientists systematically explored potential paths for leaving Earth’s vicinity, comparing a three-body model (Earth-Moon-spacecraft) and a four-body model factoring in the Sun’s gravitational influence, to understand how solar perturbations alter the structure of permissible trajectories.

Recent advancements highlight the integration of AI algorithms in space exploration missions for trajectory planning. These innovations optimize computational efficiency by incorporating multi-body gravitational dynamics, allowing real-time adjustments based on unexpected variables. The utilization of deep learning techniques further enhances spacecraft trajectory predictability and precision by considering intricate gravitational interactions, facilitating precise target location arrivals.

As a foundational approach, the planar circular restricted three-body problem for the Earth-Moon system was used. In this model, Earth and the Moon orbit a common barycenter, with equations of motion recorded in a rotating coordinate system. Compared to traditional methods, this model provides a more accurate representation of flight dynamics near the Moon and accurately accounts for gravitational maneuvers.

The transition to a planar bicircular four-body problem was utilized to analyze solar influence, where the Earth-Moon system’s barycenter orbits the Sun, and solar attraction is introduced through an additional term in the effective potential, depending on the Sun’s phase angle. Technological progress has led to hybrid models that seamlessly transition between gravitational reference frames, providing more robust solutions for missions spanning vast distances and involving multiple celestial interactions.

“The incorporation of solar perturbations in trajectory planning has transformed how we approach mission design, emphasizing not just efficiency but also flexibility, as highlighted in recent simulations.”

In defining an “exit” trajectory from the Earth-Moon system, a unified numerical criterion was established. It includes exceeding a set distance from the barycenter (10 Earth-Moon distances), positive radial velocity, positive generalized energy, and avoidance of collisions with Earth or the Moon.

While for the four-body model, it is technically more accurate to use two-body energy relative to the barycenter, authors demonstrated that at larger distances, it approximates well with generalized energy, allowing a single criterion to be employed when comparing models.

Initial trajectories were obtained using a grid search method. The spacecraft launched from a circular low Earth orbit at 167 km, varying launch angles and initial speed ratios within a narrow range. This approach enabled the creation of global solution maps and identification of areas where trajectories clustered.

Recent missions underscore refining the gravitational slingshot maneuvers around the Moon to maximize energy efficiency, which now often includes real-time computational simulations to predict solar influence on extended mission trajectories, allowing more precise execution of interplanetary routes.

The analysis focused on trajectories with one lunar gravity assist, which were most numerous, forming clear clusters and requiring a near-minimal possible launch impulse. To identify these clusters, the DBSCAN algorithm-a data analysis method that detects arbitrarily shaped clusters without a predefined number of clusters-was applied. This made a transition from visual map analysis to strict classification of trajectory “families” sharing similar dynamics possible. In the three-body model, 19 trajectory families were identified. They differ by the type of lunar gravity maneuver-forward or opposing-and demonstrate stable dynamic patterns.

After the lunar maneuver, generalized energy in this model remains largely unchanged, with major energy redistribution occurring discontinuously during lunar encounters. This practical aspect allowed optimal solutions to be distinguished: minimal transfer time (26 days) belongs to one family, while minimal launch impulse to another.

However, incorporating solar gravity notably complicated the picture. In the four-body model, the number of families increased to 24 and 32, depending on the initial solar phase angle, with some previously existing families disappearing while new ones emerged. A fundamental distinction was in energy: unlike the three-body model, after the lunar maneuver, it no longer conserves and may increase or decrease as the spacecraft moves away from the Earth-Moon system due to constant solar perturbations.

Comparing results highlighted key effects. Solar gravity increases the total number of possible trajectories and qualitatively reorganizes the solution space, yet for single lunar maneuver trajectories with travel times up to 90 days, its impact on the minimal launch impulse remains limited. Authors draw a practical conclusion: in the preliminary design phase, it is permissible to use a simpler three-body model. Still, any trajectory found therein requires mandatory verification in the model accounting for the Sun, as solar perturbations could drastically alter its subsequent behavior.