As the number of known exoplanets mounts to more than 4000, astronomers are finding that more and more lie in full-fledged planetary systems, with as many as five or six planets circling a single star.

It’s not exactly a surprising finding – there’s no reason to believe that our own Solar System is unique – but it does raise an interesting question: what exactly are these other planetary systems like? Do their planets lie in tidy circular orbits all in the same plane, or are they elongated or tilted at odd angles away from each other?

In general, astronomers detect exoplanets indirectly, as they reveal themselves by, for example, causing their star to dim slightly as they pass between us and it, blocking some of its light.

Scientists have been able to tease out an amazing amount of information from these tiny dimmings, but when it comes to these planets’ orbits, often all that’s really known is the size of the planet (revealed by the fraction of its star’s light that it blocks) and the length of its year (revealed by how frequently it passes in front of its star). Even the planet’s mass may be unknown.

In many cases, says Daniel Tamayo, an astronomer/astrophysicist at Princeton University, US, “you’re lucky enough just to detect them, so that leaves a lot of uncertainty about what their orbits look like”.

This means that astronomers find themselves with a whole suite of orbits and planetary masses that fit the data, especially for systems with several planets, all of whose orbits are equally unknown.

But they also know that only a tiny few of these hypothetical configurations are actually feasible. The rest are unstable, producing interactions among the planets that would quickly – at least in astronomical terms – send them crashing into each other.

“The goal is to rule out all the unstable possibilities that would have already collided and couldn’t exist at the present day,” Tamayo says.

This, however, isn’t an easy task. “You can’t come up with simple equations to say this one is going to be right and this one is not,” he says. Instead, it has to be done via computer models that calculate the movements of the planets and their interactions over billions of years – an enormously computer-intensive task. “If you want to try a million configurations, you can’t do that.”

However, as described in a paper in the journal Proceedings of the National Academy of Sciences, his team found a way to speed up the process by using an artificial intelligence algorithm they called SPOCK (Stability of Planetary Orbital Configurations Klassifier).

By training the algorithm to spot patterns that made for stable systems in full-fledged models, Tamayo says, it could then be used to pick out unstable ones more quickly, without having to run full-fledged simulations – speeding up the process by a factor of 100,000.

The algorithm’s name was chosen as a nod to Star Trek. “We called the model SPOCK because the model determines whether systems will ‘live long and prosper’,” he says.

Not that even this process allows astronomers to be sure of any given planetary system’s configuration. There may well be a range of stable configurations that fit the known data. But it does allow them to weed out the clearly unstable ones.

“That allows people to whittle down to configurations that are long-term stable,” Tamayo says.

Hopefully, that will eventually allow astronomers to compare distant planetary systems to our own, looking for clues not only to how planetary systems in general form and evolve, but what makes ours habitable.

“We’re interested in what are their orbital arrangements and what’s typical,” Tamayo says.

Image details

The left-hand image above shows many superimposed orbits for the three planets in Kepler-431 (yellow, red and blue) consistent with observations. Using SPOCK, the researchers removed all unstable configurations that would have resulted in planetary collisions and would not be observable today, leaving only the stable orbits (right-hand image). It took 14 minutes, compared with more than a year of traditional computing time.