Research simulated 30 million different space paths; technique requires less fuel and can make missions cheaper
Researchers have developed a mathematical method that makes it possible to calculate with greater precision the most economical routes for travel between the orbits of different celestial bodies. To demonstrate this, they calculated a path between the Earth’s orbit and that of the Moon that is more efficient than any already described in scientific literature. The study was published in the journal Astrodynamics.
The new route between the 2 celestial bodies demands a fuel consumption 58.80 m/s (meters per second) lower than the cheapest ones already described. The value may seem small given the total estimated cost of the trip – 3,342.96 m/s –, but it has a significant impact on the project’s costs. “When it comes to space travel, every meter per second is equivalent to a gigantic consumption of fuel”points out Allan Kardec de Almeida Júnior, researcher at the University of Coimbra and main author of the work, which also involved the universities of Porto and Évora (Portugal), the Paris Observatory (France) and UPE (University of Pernambuco) and USP (University of São Paulo).
The method is based on the theory of functional connections, which reduces the computational cost of space travel simulations. This allowed scientists to simulate a much larger number of different trajectories and arrive at an answer “more affordable”.
The work used as a reference for the project carried out 280 thousand simulations to reach a result, while Almeida’s research group managed to simulate 30 million different routes.
FROM EARTH TO THE MOON IN ECONOMIC CLASS
The trajectory traced by Almeida and collaborators to take a spacecraft from Earth to lunar orbit was divided into 2 sections. In the 1st, the spacecraft would leave Earth’s orbit and be taken to an orbit around the Lagrangian point L1 – a region between the Earth and the Moon in which the forces exerted by the 2 bodies cancel each other out. For most of this route, the ship would be guided by a “variety”, a natural trajectory that leads to this orbit.
But the path indicated ended up being different from what was expected. Most existing models assume that it would be more efficient to enter the range on the branch closest to Earth, but simulations carried out by the team showed that, in fact, the most economical route was closer to the Moon and entered the range on the opposite side.
Vitor Martins de Oliveira, postdoctoral fellow at IME (Institute of Mathematics, Statistics and Computer Science) at USP and co-author of the work, explains that the search for solutions like this is one of the advantages of using the theory of functional connections: “Instead of assuming that it is easier to get the part of the variety closer to Earth, we can use a systematic analysis with faster methods to try to find solutions that are not so trivial.”
Using a control system, the spacecraft could be maintained in this intermediate orbit for as long as necessary until the mission is ready for the 2nd part of the journey – when it heads to lunar orbit. That “space transfer” It is also an advantage because, while waiting, there is no interruption of communication with either the Earth or the Moon.
“The Artemis 2 mission, for example, spent time without communication with Earth because it was directly behind the Moon. The orbit we recommend is a solution in which the spacecraft maintains uninterrupted communication”highlights Oliveira.
The investigation was supported by Fapesp (projects 21/11306-0 and 22/12785-1). Leonardo Barbosa Torres dos Santos, PhD from Inpe (National Institute for Space Research) with a scholarship from the Foundation, also signed the article.
MORE SAVINGS ON SPECIFIC DATES
Despite being a more economical route than those described previously, the route drawn by Almeida and his collaborators is not the cheapest ticket possible. The simulations used only took into account the gravity of the Moon and Earth, disregarding other celestial bodies, such as the Sun.
Its inclusion could lead to an even greater discount – but it restricts the time window for launch. “It would be necessary to carry out the simulation for a specific position of the Sun. For example, if we simulate the mission launch day on December 23rd, we will obtain results valid only for a mission launched on that date”highlights Almeida.
Even in these cases, the method developed by the team to carry out a greater number of simulations can be applied to find the best trajectory. “The systematic analysis that we apply in our work is something that can be adopted more from now on”suggests the researcher.
This text was published by Agência Fapesp, on April 29, 2026. The content is free for republication, with the source cited, and was adapted to the standard of Poder360.
