The most fuel-efficient way to reach the Moon, it turns out, is to fly straight past it. Not into orbit, not into a landing approach. Past it, skimming within 73 kilometres of the surface before looping back through a gravitational sweet spot halfway between the two worlds. This is the counterintuitive answer that a team of researchers from Portugal, France, and Brazil arrived at after sifting through roughly 30 million simulated routes, a haul that dwarfs anything previously attempted in lunar trajectory planning. The finding, published in the journal Astrodynamics, shaves at least 58.80 metres per second off the fuel cost of the most economical published route, a number that sounds modest until you consider what rocket fuel actually weighs.
The race to return people to the Moon and build permanent infrastructure there is accelerating on several fronts simultaneously. Around 250 missions are expected to launch to the lunar surface after 2030, from scientific probes to cargo runs to crewed outposts, and every kilogram of propellant saved on the journey means more room for the instruments, supplies, or people that justify the expense of going in the first place.
A Gravitational Waypoint Between Worlds
The route the researchers devised does not go straight from Earth orbit to lunar orbit. Instead, it pauses. Roughly 85% of the way between the two bodies sits the L1 Lagrangian point, one of five locations in the Earth-Moon system where the gravitational pulls of the two bodies and the centrifugal forces of the rotating system reach a kind of uneasy equilibrium. L1 is a strange place: a spacecraft parked there is technically in balance but, because the equilibrium is unstable, the slightest nudge sends it tumbling away. This instability is precisely what makes L1 useful for mission planning. Orbits around it (flat, looping paths called Lyapunov orbits) are threaded through with invisible highways called invariant manifolds, surfaces in space along which a spacecraft can drift for free, carried by gravity rather than engines, toward or away from the Lagrangian point itself.
The trick, then, is finding the cheapest on-ramp to one of those highways. And this is where the team’s approach diverges sharply from previous work.
Earlier studies evaluating Earth-to-Moon trajectories via L1 searched through databases of roughly 280,000 candidate routes. Allan Kardec de Almeida Júnior of the University of Coimbra and his colleagues evaluated more than 30 million. The sheer scale was made possible by a mathematical tool called the theory of functional connections (TFC), which recasts trajectory optimisation problems in a form that is far cheaper to compute. Rather than iterating toward a solution numerically, repeatedly tweaking a trajectory until it roughly satisfies the mission constraints, TFC embeds those constraints directly and analytically into the equations of motion. Any candidate solution it generates is already guaranteed to meet the boundary conditions; the optimiser just has to pick the cheapest one from a much larger crowd.
The Wrong Branch Was the Right Answer
The standard assumption in trajectory planning is that a spacecraft heading for L1’s stable manifold from Earth should enter at the branch of the manifold on the Earth’s side of the system. It is the obvious choice: geographically closer, conceptually tidy. The simulations said otherwise. The branch on the Moon’s side of L1 turned out to deliver lower total fuel costs, for a reason that only becomes clear once you look at the geometry: that branch swings close to the Moon, close enough for a gravity assist. “Instead of assuming it’s easier to choose the part of the variate closest to Earth,” says Vitor Martins de Oliveira of the University of São Paulo, a co-author on the study, “we can use systematic analysis with faster methods to try to find nontrivial solutions.”
The resulting trajectory unfolds across three legs. A spacecraft in low Earth orbit at 167 kilometres altitude fires its engines to depart, a burn costing around 3,142 metres per second in velocity change. It then travels for roughly 3.69 days, skimming to within 73 kilometres of the lunar surface. A small second burn near the Moon inserts it into the stable manifold, after which natural dynamics carry it toward the Lyapunov orbit around L1. It can wait there for as long as needed, the orbit’s 13.75-day period allowing the spacecraft to loiter in multiples of that interval until conditions are right to continue. A final set of burns, costing just under 649 metres per second in total, drops it into a circular 100-kilometre orbit around the Moon.
The Moon-leg burn came in just 0.767 metres per second above the theoretical minimum. Almost nowhere left to squeeze on that portion of the trip.
Always in Touch with Earth
There is a practical benefit to the L1 waypoint beyond fuel. A spacecraft orbiting the Lagrangian point never disappears behind the Moon from Earth’s perspective; L1 maintains line-of-sight contact with both planets simultaneously. De Oliveira points out that this solved a persistent irritation with other approaches: “The Artemis 2 mission, for example, lost communication with Earth for a while because it was directly behind the moon. The orbit we propose is a solution that maintains uninterrupted communication.” For crewed missions, continuous communication is not an optional comfort but a safety requirement.
The study does have a significant caveat built into its foundations. The mathematical model treats the Earth-Moon system as if the Sun does not exist, a simplification that reduces computational complexity but also means the results apply to any launch date, making them useful as a general baseline for preliminary mission design. Adding solar gravity would almost certainly unlock further savings, but would lock those savings to specific calendar windows. “It’d be necessary to run the simulation for a specific position of the Sun,” Almeida Júnior notes. “For example, if we simulate the mission’s launch date as December 23, we’ll obtain results valid only for a mission launched on that date.” Previous work suggests solar perturbations can deliver around 63 metres per second of additional savings for the right epoch. Station-keeping burns and the energy needed to adjust orbital inclination after launch are also excluded, standard omissions in preliminary trajectory analysis.
What the work really demonstrates, though, is something about methodology rather than just the specific numbers. “When it comes to space travel, every meter per second equates to a massive amount of fuel consumption,” Almeida Júnior says. The total saving of 58.80 metres per second sounds like rounding error on a journey costing roughly 3,991 metres per second end-to-end. But in practical terms it translates directly into payload: cargo, instruments, crew supplies, or margin for the unexpected. “The systematic analysis we applied in our work is something that could be adopted more widely going forward,” he adds, pointing toward applications to other transfer types, including trajectories via the L2 point on the far side of the Moon.
With around 250 lunar missions projected over the coming decade and a half, each one representing its own logistical puzzle, the appetite for cheap routes is not going to diminish. The Moon-first detour that initially looks like the long way round may, mission by mission, turn out to be the most direct path of all.
Read the original research: Earth-Moon transfer via the L1 Lagrangian point using the theory of functional connections, Astrodynamics (2026).
Frequently Asked Questions
Why does flying past the Moon first actually save fuel?
The key is a gravity assist. The most efficient entry point into the natural trajectory leading toward the L1 Lagrangian point turns out to be on the Moon’s side of the system, not Earth’s side. This means the spacecraft swings close to the Moon early in the journey, and the Moon’s gravity provides a free nudge that reduces the total engine burn needed. It is counterintuitive but the mathematics and 30 million simulations all point the same way.
What is the L1 Lagrangian point and why stop there?
L1 is a point in space about 85% of the way from Earth to the Moon where the gravitational pulls of both bodies and the rotational dynamics of the system are in equilibrium. A spacecraft can orbit this point in looping paths called Lyapunov orbits, using very little fuel to stay there. The orbit maintains line-of-sight communication with both Earth and the Moon simultaneously, which makes it an attractive staging post for missions that need to wait before proceeding to the lunar surface.
How does 58.80 metres per second actually translate into mission benefits?
In rocket engineering, fuel savings are multiplicative: carrying less propellant means the vehicle is lighter, which means you needed less fuel to lift it in the first place. A saving of 58.80 metres per second in velocity change can translate into hundreds of kilograms of additional payload capacity depending on the spacecraft. For missions delivering scientific instruments or supplies to a lunar base, that extra margin matters considerably.
Could this route be made even cheaper by including the Sun’s gravity?
Yes, and earlier studies suggest the additional saving could be around 63 metres per second for the right launch date. The catch is that solar gravity is a time-dependent effect: the saving only applies when the Sun is in a specific position relative to Earth and the Moon, so the trajectory has to be recalculated for each launch window. The current work deliberately excludes the Sun to produce a general-purpose result that mission planners can use as a starting point for any date.
Is this approach limited to Earth-Moon missions?
The theory of functional connections method used here is not specific to the Earth-Moon system. The researchers suggest it could be applied to other types of transfers in cislunar space, including routes via the L2 point beyond the Moon, and potentially to trajectories elsewhere in the solar system where Lagrangian point dynamics are relevant.
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