Some 2,500 years ago, the ancient Greek thinker Pythagoras pondered the “music of the spheres” – the notion that the orbital periods of celestial objects like the moon and the planets represent a mathematical harmony that is equivalent to a pleasing sound.

Now astronomers at the University of Toronto have gone one step further, showing that the same idea may be the secret behind the survival of a distant solar system that scientists say could be a viable candidate in the search for life beyond Earth.

The system, consisting of seven Earth-size planets orbiting the star TRAPPIST-1, made headlines earlier this year because of the sheer number of new worlds discovered in one place, as well as the tantalizing possibility that one or more of the planets fall within a temperature range that would permit water to exist in a liquid state on their surfaces. Water is a key enabler of all life on Earth.

Amid the excitement surrounding the discovery, one puzzling detail was frequently omitted in news reports. The discoverers noted that when they studied the dynamics of the TRAPPIST-1 system, they were unable to understand how it has remained stable over millions of years.

The reason is, if one starts with the masses and separations of the seven planets and applies the laws of gravity to simulate their motions into the future, “it doesn’t take very long before the whole system falls apart and planets start crashing into one another,” said Daniel Tamayo, a post-doctoral researcher at U of T’s Centre for Planetary Sciences.

Clearly that’s not what is happening, otherwise the TRAPPIST-1 system would be long gone by now. Part of the problem is that, with Earth’s distance of 39 light years from TRAPPIST-1, it’s not possible to measure the characteristics of the seven planets’ orbits with enough precision to make a computer simulation work.

Instead, Dr. Tamayo and his collaborators decided to go back in time to simulate how the system formed and see if it would naturally fall into a stable pattern.

They also suspected that the system’s long-term durability must have something to do with the elaborate chain of whole number ratios that exists between the orbital periods of the seven planets – a sequence that looks like this:


Put into words, every time the outermost planet in the system orbits the star twice, the next planet in orbits three times, while the next one in from that orbits four times, and so on, all the way to the innermost planet, which orbits exactly 24 times in the same interval.

Astronomers call such relationships orbital resonances because they mimic the ratios of vibrations between musical notes that resonate together. For example, 1:2 is equivalent to playing two notes on a piano that are one octave apart, while 2:3 corresponds to the musical interval known as a fifth.

When it comes to planets, some kinds of orbital resonances can help make a system more stable. To see if this was the case with TRAPPIST-1, the team ran 1,000 computer simulations of the system’s formation from a swirling disk of gas around a newborn star. Just more than one-third of those produced a system with planets that formed in different locations but that gradually migrated into resonances like those observed at TRAPPIST-1 today.

By running those systems for one billion orbits, they found that all but 3 per cent of those simulations remained stable. In a more detailed analysis of 21 simulated systems that ran up to 10 billion orbits – using up many weeks of supercomputer time in the process – the team found that more than 80 per cent of the systems were stable.

The results also suggest that the seven planets in the system were able to ensure their long-term survival by shifting themselves into orbital harmony.

“It really is like an orchestra that sort of tunes itself,” Dr. Tamayo say.

To illustrate the concept, Matt Russo, at the Canadian Institute for Theoretical Astrophysics, created a video that links the orbits of the planets with musical notes of the appropriate intervals and also adds drum beats to mark when the planets overtake one another as they circle the star.

The end result is surprisingly harmonious, Dr. Tamayo said, particularly when compared with systems that do not have such resonances.

The practical upshot of the study is that it shows that solar systems such as TRAPPIST-1 can form easily and are likely to persist long enough to allow life to emerge – a factor that boosts the chances that similar systems are plentiful throughout the Milky Way galaxy.

“The work sheds light on the origins of this fascinating system,” said Paul Wiegert, an astronomer at Western University who was not involved with the study. Dr. Wiegert added that the study reveals the crucial role of migration during solar system formation – an effect that could play a major role in determining how many habitable worlds exist in the universe.

Ivan Semeniuk – Science reporter
The Globe and Mail
Published Wednesday, May 10, 2017 2:29PM EDT
Last updated Wednesday, May 10, 2017 6:31PM EDT