Sending spacecraft to the moon is not just about reaching it — it’s about how little fuel you can spend doing so. In space missions, even small savings in velocity change can translate into huge cost reductions or extra payload capacity.

A new study published in Astrodynamics suggests that a better route to the moon may already exist — one that uses the hidden structure of gravity itself. 

The study authors have identified a trajectory between Earth and the moon that reduces fuel use by at least 58.80 m/s compared to previously known optimal paths.

“When it comes to space travel, every meter per second equates to a massive amount of fuel consumption,” Allan Kardec de Almeida Júnior, first author of the study and a researcher at the University of Coimbra in Portugal, said. 

Interestingly, this most efficient route is not the most direct one. Instead, the spacecraft first swings closer to the moon before entering a gravitational pathway around a special region called the L1 Lagrange point, where Earth’s and the moon’s gravitational pulls balance each other. 

Mapping millions of possible space routes

The challenge in Earth–moon travel is not a lack of physics; it’s the overwhelming number of possible trajectories. The gravitational field between Earth and the moon creates a complex dynamical system where tiny changes in starting conditions produce very different outcomes.

To overcome this problem, the study authors used a mathematical framework called the theory of functional connections (TFC). Instead of solving the full optimization problem in a brute-force way, TFC allows key physical constraints (like leaving Earth in a tangential burn) to be built directly into the mathematical formulation. This reduces the complexity of the search problem.

The spacecraft’s motion was modeled using the circular restricted three-body problem, which considers only Earth, the moon, and a massless spacecraft. Within this framework, the researchers focused on:

One important region in this system is the L1 Lagrange point. Around this region, spacecraft can move in looping paths known as Lyapunov orbits. These are unstable orbits, meaning a spacecraft would eventually drift away without adjustments, but they are surrounded by natural entry and exit pathways created by gravity. 

These pathways, called stable and unstable manifolds, behave almost like invisible space highways. A spacecraft entering them can travel long distances while using very little fuel because gravity itself helps guide the motion.

“The spacecraft is then transported with no extra costs to the Lyapunov orbit via the system’s natural dynamics,” the study authors added.

Using the TFC method, the researchers simulated around 30 million possible routes through these gravitational pathways (far more than previous studies), allowing them to identify a surprisingly efficient Earth-to-moon transfer trajectory.

The mission was split into two connected segments

In the first segment, Earth to L1 region, the spacecraft leaves a 167 km Earth orbit and enters a stable manifold leading toward L1. Then, in the second segment from L1 to the moon, the spacecraft later departs along an unstable manifold and transitions into lunar orbit.

Instead of testing a small number of possibilities, the method enabled evaluation of around 30 million different trajectories, compared with only ~280,000 in earlier studies. 

This massive search revealed a surprising pattern. The most efficient trajectories were not the ones entering the manifold from the Earth-facing side, but from the opposite side, i.e., after a closer pass toward the moon.

One of the most unexpected results was that the cheapest path involves a close lunar flyby before entering the L1 transfer corridor. This flyby acts like a gravitational assist, reducing the need for engine thrust at key moments.

“It is somewhat counterintuitive that designing transfers from an orbit around the Earth to the right branch of the stable manifold is more cost-effective than using the left branch, given that these are farther away,” the study authors said.

The best Earth-to-L1 segment found in the study requires a total velocity change of 3342.96 m/s, achieved with two carefully timed engine burns. One burn lifts the spacecraft from Earth, and another places it onto the gravitational pathway near the moon. 

After that, gravity does most of the work. Natural gravitational currents help guide the spacecraft with minimal fuel use. From there, the spacecraft can even remain temporarily parked near the L1 region. 

This intermediate orbit is dynamically stable in a controlled sense and can function like a staging area between Earth and lunar destinations.

One fuel-saving route at a time

When the full journey is combined, i.e., from Earth departure to L1 transfer and lunar insertion, the total cost is about 3991.60 m/s over roughly 32 days. While this is not the fastest possible route, it offers operational advantages such as flexible staging, potential communication continuity, and modular mission design.

More importantly, the researchers also found that the L1 to moon segment is extremely close to its theoretical minimum fuel cost. Whereas the Earth to L1 segment is where most savings are still possible. Overall, the method saves at least 58.80 m/s compared to the best known similar trajectories.

In practical terms, that is roughly a 1–2 percent reduction in total mission velocity change, which is the equivalent of shaving a few liters off every hundred liters in a long-distance road trip. 

This difference may appear modest, but in space missions, where every kilogram launched into orbit is expensive, even small reductions can translate into extra payload capacity, lower launch costs, or more operational flexibility.

However, the model has limitations. It ignores the gravitational influence of the Sun and other bodies, which means the results are not tied to specific launch dates. In reality, including solar gravity would likely reveal even cheaper paths, but only during certain time windows when celestial alignments are favorable.

For now, the researchers believe the most important contribution of their study isn’t just this single moon route itself. It is also the computational method behind it — a system capable of scanning tens of millions of possible trajectories and revealing the best.

The study is published in the journal Astrodynamics.