An alien civilization could shift six or seven planets into a series of carefully-arranged orbits as a signpost advertising its presence. To spot it, we just have to think mathematically.

Several bodies exist in what astronomers call resonant orbits around their parent body. For instance, for every orbit Jupiter’s moon Europa completes, another nearby moon called Io completes two orbits. For every two orbits completed by Europa, Ganymede — the next moon out — completes two, giving them a 4:2:1 resonance. There’s even a planetary system, K2-138, which has an entire fleet of planets in resonance.

In a recent paper in the journal Monthly Notices of the Royal Astronomical Society, planetary scientist Matthew Clement, of the Carnegie Institution for Science Earth and Planets Laboratory, and his colleagues suggest that a sufficiently powerful and motivated alien civilization could arrange entire Solar Systems of planets into resonant orbits with more complex ratios — adding up to a mathematical concept sprinkled throughout nature.

Besides doing it for the aesthetic, this ambitious planet-shuffling could help ET advertise their presence to distant searchers like us — no radio signals or laser beacons needed.

What’s New – It’s theoretically possible, according to Clement and his colleagues, who simulated solar systems with several sets of resonant orbits — including ones whose ratios spell out all the prime numbers up to 11, as well as two other sequences of numbers called the Lazy Caterer’s Sequence and the Fibonacci Sequence (you get each number in the Fibonacci Sequence by adding the last pair of numbers: 1,1, 2, 3, 5, 8, 13, and so on). The simulated Solar Systems turned out to be stable for at least 10 billion years, or about the lifetime of our Sun.

Planets and moons often settle into resonant orbits naturally, like the 4:2:1 resonance of Jupiter’s three innermost moons — or the more complex series of resonances that link the seven TRAPPIST-1 worlds. But some ratios are more common than others. Physics seems especially fond of ratios like 4:3, 3:2, and 2:1, which astronomers call “first-order resonances” because the numbers differ by one.

On the other hand, orbits with so-called “higher-order” resonances – ratios like 7:1 or 13:1 – are much less common in nature. And if the ratios of those orbits spelled out something like the Fibonacci Sequence, which would be immediately recognizable to math nerds across the galaxy, that would almost certainly be a clue that intelligent civilization had a hand (or a tentacle, or a super-intelligent shade of the color blue) in arranging things.

“Extended chains encoding abstract mathematical sequences have not been discovered,” write Clement and his colleagues in their paper, “and thus their detection would be quite curious.”

Here’s The Background – If you were a highly-advanced alien civilization and you wanted to rearrange the orbits of the planets in your star system, how would you do it?

Clement and his colleagues suggest using something about the size of an asteroid, which could be set on the right course to trade gravitational nudges with its larger planetary neighbors, gradually shepherding them into different orbits.

“This actually happens,” Clement tells Inverse. “We are fairly confident that the Solar System’s giant planets moved around significantly after they formed, as they had repeated flybys with leftover debris and with stuff like Pluto.”

Doing the same thing on purpose isn’t entirely the stuff of science fiction, either — Clement says there’s already serious speculation about using gravitational nudges from another small object to steer an asteroid into a closer orbit for mining. And already, we use the same principle to boost spacecraft into more distant orbits (or send them flying out of the Solar System).

But the orbital architecture of companion planets takes patience.

“It would take millions of years to have one asteroid, or a number of asteroids move a planet-sized thing that [necessary] amount of distance,” says Clement. That’s an order of magnitude longer than our species has even existed. “But if you’re a more advanced civilization, maybe you could think on million-year timescales.”

Technically, an extremely advanced alien culture could find a way to apply thrust to a whole planet in order to shift its orbit. Although it’s nearly impossible for us to imagine how, Clement says that in terms of sheer energy requirements, any civilization tech-savvy enough to harness most or all of the energy from its star could pull it off in just over two (Earth) years.

Why It Matters – If we assume that intelligent aliens exist somewhere in the galaxy, our chances of finding them depend on two things: first, whether we’re capable of detecting whatever breadcrumbs they leave us; second, whether their civilizations, or traces of them, are around at the right time to be found. And the solution to both problems could be what Clement and his colleagues call “the orbital architecture of companion planets,” which admittedly sounds like the title of Magrathea’s latest product catalog.

“It stands to reason that if you wanted to set up a system, that could permanently communicate your existence, you could encode that in the orbital periods of planets,” says Clement.

After all, creative planet arrangements last much longer than radio messages, spacecraft carrying golden records, or giant orbiting platforms.

“It is worth considering that any given civilization might only be able to broadcast themselves for a brief window in time,” says Clement.

Some technology can outlast its creators — our radio broadcasts will keep propagating out into space long after we’re gone, for instance, and the Lageos satellites (a pair of laser reflectors in very stable orbits 5,900 kilometers above Earth) will probably stay in orbit longer than Earth will remain habitable. But in a universe that’s 13.8 billion years old, even a shelf-life of a few million years doesn’t guarantee that one planet’s technological relics will overlap in time with another planet’s SETI programs.

Once they’re settled in resonant orbits, however, Clement and his colleagues Solar System-sized signposts will exist for at least 10 billion years — maybe even longer, if the planets in question are far enough from their star to survive its final phase of life.

A cosmic message left encoded in planets’ orbits may also be one of the easiest signals for species like us (tech-savvy enough to build telescopes, but not tech-savvy enough to move entire planets around) to spot. One of the easiest properties of an exoplanet to measure is how long it takes to orbit its star.

“We look for that little blip when a planet passes in front of a star; we wait for it to happen again, and again, and again,” says Clement. “We can measure the orbital period very, very accurately.”

In other words, as far-fetched as it sounds, a Fibonacci Sequence solar system might be the perfect alien signpost.

What’s Next – But although it’s not too early to start looking, it could still be a while before astronomers find anything like the chains of resonant orbits Clement and his colleagues describe.

“With current technology, you know, we can only detect, you know, smaller planets that are close to a star, or very, very large planets that are further from a star,” says Clement. Since planet-arranging aliens would want to start their coded series of orbits far enough from the star to survive its swollen red giant phase, that means they’d want to use larger planets for maximum visibility (although even a Kardashev II civilization presumably has to work with what it actually has, to some extent).

Time is also a factor. More distant planets have longer orbits; Neptune takes more than a century to make a single lap around the Sun.

“If we’re [aliens] trying to detect Saturn or Neptune with current technology, we haven’t been looking at exoplanets for enough time to do this,” says Clement. “We’re still in our infancy is in that we just have not looked at these things for long enough to find [the orbital periods of] some of the further out planets.”