A trip to the moon might not need to break the bank, as scientists have discovered a shortcut that could slash the cost of future missions.
Much like flying on a jet, one of the biggest costs associated with getting to our lunar satellite is the fuel.
NASA's Space Launch System rocket uses over two million litres of propellant at an estimated cost of $4bn (£2.8bn) per launch, while the Orion spacecraft needs yet more to navigate to the lunar surface.
However, scientists have now created a mathematical method that could save space agencies cash by finding more fuel–efficient routes.
Space missions measure fuel by the amount it can change the rocket's velocity rather than as a volume, which would change depending on the fuel used.
The researchers' new route requires 58.8 metres per second less fuel than the most efficient paths previously discovered.
That might not sound a lot compared to the journey's total fuel consumption of 3,342.96 metres per second.
However, lead author Dr Allan Kardec de Almeida Júnior, of the University of Coimbra, says: 'When it comes to space travel, every meter per second equates to a massive amount of fuel consumption.'
Scientists have found a new shortcut to the moon that could slash costs for journeys to our lunar satellite
One of the most efficient ways to get to the moon is to take advantage of natural balance points in the solar system known as Lagrange Points.
At each of the five Lagrange Points, the gravitational forces of the Earth, moon, and sun are balanced.
This means that a spaceship can park itself at one of these locations and travel through space without needing to burn any more fuel.
The problem is that orbits around the Lagrange points are inherently unstable, and even tiny differences in trajectory can result in massive differences in outcome.
This makes calculating all the different paths that a spaceship might take through the Lagrange Point between the Earth and the Moon extremely time–consuming.
However, Dr Almeida Júnior and his co–authors have pioneered the use of a new mathematical framework that makes these calculations much easier.
Known as 'the theory of functional connections', their method allowed them to calculate millions rather than thousands of possible trajectories and pick the most efficient.
For their study, Dr Almeida Júnior and his team simulated 30 million different possible ways of reaching the moon to find the best option.
Fuel is one of the most expensive parts of a space mission. The Space Launch System that took the Artemis II crew around the moon uses over two million litres of fuel on launch, while the Orion spacecraft uses yet more to navigate
What is a Lagrange Point?
Lagrange Points are five positions in space where the gravitational pull of two massive bodies — such as the Earth and the Sun — balance perfectly with the motion of an object orbiting them.
This means spacecraft can 'park' there using very little fuel, making the locations ideal for space telescopes and scientific missions.
The five points are named L1 to L5. Some sit directly between or behind planets, while others form stable 'gravitational pockets' where objects can remain for decades.
NASA's James Webb Space Telescope operates around the Sun–Earth L2 point, roughly one million miles from Earth, where it enjoys a stable view deep into the cosmos.
The points are named after 18th Century Italian–French mathematician Joseph–Louis Lagrange, who first described them in 1772.
Their new route defies previous wisdom that suggested the spacecraft should approach the natural orbits leading to the Lagrange Point – known as the L1 variate – from the points closest to Earth.
Counterintuitively, the researchers found that it was actually better to approach these orbits from the side closer to the moon.
Using a control system, a spaceship could stay at this orbit indefinitely until the crew are ready to make the second leg of the journey to the moon.
Dr Almeida Júnior says that this stopping point has the potential to transform space missions into a thriving tourism industry.
He says: 'The strategy proposed in this paper involves orbits around L1, from where people could enjoy a unique perspective: the Earth and Moon can be seen at opposite sides of the ship!
'The spacecraft could stay in this orbit around L1 in multiples of 13 days, when connections with the Moon or Earth could be done to replace the tourists.
'This strategy could then be used in the future as a hub for tourism, but also for mining activities.'
Spotting this unlikely solution was only possible because of the mathematics that let the team calculate such an absurd number of options.
The new route would take the spacecraft away from Earth and into orbit at the 'Lagrange Point' where the gravity of Earth, the moon, and the sun are balanced. From there, the craft can wait until it starts the second leg into lunar orbit
Co–author Dr Vitor Martins de Oliveira, from the University of São Paulo, says: 'Instead of assuming it's easier to choose the part of the variate closest to Earth, we can use systematic analysis with faster methods to try to find nontrivial solutions.'
Exactly how much fuel this would save can vary massively depending on the size of the spaceship, the type of fuel used, how efficient the craft is, and how much cargo it is carrying.
The good news is that the savings will scale with the size of the craft, with heavier ships benefiting from a bigger reduction in fuel volume.
A fully loaded SpaceX Starship with up to 100 tonnes of cargo, for example, could free up a massive volume of fuel by slightly tweaking its route to the lunar surface.
In addition to saving money on fuel, this new path is a tempting option for lunar missions because the spaceship would always be in line of sight from Earth.
That means there would never be a time when mission control loses contact with its astronauts.
Dr de Oliveira says: '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.'
A big advantage of this route is that there would be no blackout period while the spacecraft is hidden from Earth, as there was during the Artemis II mission's lunar transit
However, the researchers admit that their calculations aren't completely realistic, since they only consider the gravity of the Earth and the moon, leaving out the sun's influence.
Even more efficient orbits could be found if the sun were taken into account, but this would put a restriction on the launch window.
Dr Almeida Júnior notes: 'It'd be necessary to run the simulation for a specific position of the Sun.
'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.'
WHO HAS BEEN TO THE MOON?
In total 12 people have walked on the moon.
1 + 2. Apollo 11 - July 21, 1969
Neil Armstrong made history by becoming the first person to set foot on the lunar surface, before he he was followed by crewmate Edwin 'Buzz' Aldrin.
3 + 4. Apollo 12 - November 19 and 20, 1969
Pete Conrad and Alan Bean were the moon walkers on the Apollo 12 mission.
The Apollo 12 crew experienced two lightning strikes just after their Saturn V rocket launched.
5 + 6. Apollo 14 - February 5, 1971
Alan Shepard and Edgar Mitchell were part of the Apollo 14 mission. They launched on January 31, 1971, and landed in the Fra Mauro region of the moon, the original destination for Apollo 13.
7 + 8. Apollo 15 - July 31, 1971
Dave Scott and James Irwin landed on the moon and stayed for three days, until August 2.
9 + 10. Apollo 16 - April 21, 1972
John Young and Charlie Duke were the next men to walk on the moon. When the crew reached lunar orbit, the mission almost had to be aborted because of a problem with the command and service module's main engine.
11 + 12. Apollo 17 - December 11, 1972
The final people to walk on the moon were Eugene (Gene) Cernan and Harrison (Jack) Schmitt.
Before he left the moon, Cernan scratched the initials of his daughter Tracy into the lunar regolith. Since the moon does not experience weather conditions like wind or rain to erode anything away, her initials should stay there for a very long time.
All the men who have been to the moon