Planets orbit their parent stars while separated by enormous distances – in our solar system, planets are like grains of sand in a region the size of a football field. The time it takes for planets to orbit their suns is not specifically related to each other.
But sometimes, their orbits show striking patterns. For example, astronomers who study six planets orbiting a star 100 light years away, we have just discovered that they orbit their star with an almost rhythmic beat, in perfect synchronization. Each pair of planets completes their orbits in times that are the ratios of whole numbers, allowing the planets to align and exert a gravitational push and pull on each other during their orbit.
This type of gravitational alignment is called orbital resonanceand it is like a harmony between distant planets.
Related: TRAPPIST-1: A guide to the system with 7 Earth-sized exoplanets
I am one astronomer who studies and writes about cosmology. Researchers discovered more than 5,600 exoplanets over the past 30 years, and its extraordinary diversity continues to surprise astronomers.
Harmony of the spheres
Greek mathematician Pythagoras discovered the principles of musical harmony 2,500 years ago by analyzing the sounds of blacksmiths’ hammers and plucked strings.
He believed that mathematics was at the heart of the natural world and proposed that the sun, The Moon and planets emit unique hums based on their orbital properties. He thought that this “music of the spheres” would be imperceptible to the human ear.
Four hundred years ago, Johannes Kepler got this idea. He proposed that musical intervals and harmonies described the movements of the six planets known at the time.
For KeplerO solar system had two basses, Jupiter It is Saturn; a tenor, Mars; two contraltos, Venus It is Earth; and a soprano, Mercury. These functions reflected how long each planet took to orbit the Sun, lower speeds for the outer planets and higher speeds for the inner planets.
He called the book he wrote about these mathematical relationships “The Harmony of the World.” Although these ideas have some similarities to the concept of orbital resonance, planets do not actually make sounds, since they sound cannot travel through the vacuum of space.
Resonance happens when planets or moons have orbital periods that are proportions of whole numbers. The orbital period is the time considered a planet to make a complete circuit around the star. So, for example, two planets orbiting a star would be in 2:1 resonance when one planet took twice as long to orbit the star. Resonance is only seen 5% of planetary systems.
In the solar system, Neptune It is Pluto are in 3:2 resonance. There is also a triple resonance4:2:1, between the three moons of Jupiter: Ganymede, Europe It is I. In the time it takes Ganymede to orbit Jupiter, Europa orbits twice and Io orbits four times. Resonances occur naturally, when planets have orbital periods that are the ratio of whole numbers.
Musical intervals describe the relationship between two musical notes. In the musical analogy, important musical intervals based on the frequency ratios are the fourth, 4:3, the fifth, 3:2, and the octave, 2:1. Anyone who plays the guitar or piano can recognize these intervals.
Orbital resonances can change how gravity influences two bodies, causing them to accelerate, slow down, stabilize in their orbital path and sometimes have their orbits interrupted.
Think about pushing a child on a swing. A planet and a balance have a natural frequency. Give the child a push that matches the rocking motion and he or she will receive a boost. They will also get a boost if you push them every time they are in this position, or every third time. But push them at random times, sometimes with the swing motion and sometimes against it, and they won’t get any push.
For planets, momentum may keep them on their orbital paths, but it is much more likely to disrupt their orbits.
Exoplanets, or planets outside the solar system, present stunning examples of resonance, not just between two objects, but also between resonant “chains” involving three or more objects.
The star Gliese 876 it has three planets with orbit period ratios of 4:2:1, as do Jupiter’s three moons. Kepler223 it has four planets with aspect ratios of 8:6:4:3.
O red dwarf Kepler80 has five planets with proportions of 9:6:4:3:2, and TOI 178 it has six planets, five of which are in a resonant chain with proportions of 18:9:6:4:3.
TRAPPIST-1 is the record holder. There are seven Earth-like planetstwo of which can be habitablewith orbit ratios of 24:15:9:6:4:3:2.
The newest example of a resonant chain is the HD 110067 system. It is about 100 light years away and has six sub-Neptune planets, a common type of exoplanet, with orbit ratios of 54:36:24:16:12:9. The discovery is interesting because most resonance chains are unstable and disappear over time.
Despite these examples, resonant chains are rare and only 1% of all planetary systems exhibit them. Astronomers think planets form in resonance, but small gravitational nudges as they pass stars and wandering planets erase resonance over time. With HD 110067, the resonant chain has survived for billions of years, offering a rare and pristine view of the system as it was when it formed.
Astronomers use a technique called sonification to translate complex visual data into sound. It gives people a different way to enjoy the beautiful images of the Hubble Space Telescopeand was applied to X-ray and gravitational wave data.
With exoplanets, sonification can convey the mathematical relationships of their orbits. Astronomers at the European Southern Observatory have created what they call “music of the spheres”For the TOI 178 system, associating a pentatonic scale sound with each of the five planets.
A similar musical translation was made for TRAPPIST-1 system, with the orbital frequencies increased by a factor of 212 million to bring them into audible range.
Astronomers also created a sonification for the HD 110067 system. People may not agree whether these interpretations sound like real music, but it’s inspiring to see Pythagoras’ ideas come to fruition after 2,500 years.