by Planets orbit their parent stars separated by vast distances – in our solar system, planets are like grains of sand in a region the size of a football field. The time it takes planets to orbit their sun is not particularly related to each other.
But sometimes, their orbits show striking patterns. For example, astronomers studying six planets orbiting a star 100 light years away have just discovered that they orbit their star with an almost rhythmic beat, in perfect synchronicity. Each pair of planets completes their orbits in times that are in ratio to whole numbers, allowing the planets to align and exert a gravitational push and pull on each other during their orbits.
This type of gravitational alignment is called orbital resonance, and is similar to a harmony between distant planets.
I am an astronomer who studies and writes about cosmology. Researchers have discovered more than 5,600 exoplanets in the past 30 years, and their extraordinary diversity continues to amaze astronomers.
Harmony of the spheres
Greek mathematician Pythagoras discovered the principles of musical harmony 2,500 years ago by analyzing the sounds of blacksmith hammers and plucked stringed instruments.
He believed that mathematics was at the heart of the natural world and proposed that the Sun, Moon and planets emit unique orbits 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 picked up on this idea. He proposed that musical intervals and harmonies would describe the movements of the six planets known at the time.
For Kepler, the solar system had two bosses, Jupiter and Saturn; tenor, Mars; two altos, Venus and Earth; and soprano, Mercury. These roles showed how long it took each planet to orbit the Sun, lower speeds for the outer planets and higher speeds for the inner planets.
He called the book he wrote on these mathematical relationships “The Harmony of the World”. Although these ideas share some similarities with the concept of resonance, planets do not actually make sounds, as sound cannot travel through the vacuum of space.
Orbital resonance
Resonance occurs when planets or moons have orbital periods that are integer ratios. The orbital period is the time it takes for a planet to make one complete circuit of the star. So, for example, two planets orbiting a star would be in 2:1 resonance where one planet takes twice as long as the other planet to orbit the star. Resonance is seen in only 5% of planetary systems.
In the solar system, Neptune and Pluto are in 3:2 resonance. There is also a threefold resonance, 4:2:1, among Jupiter’s three moons: Ganymede, Europa and Io. In the time it takes Ganymede to orbit Jupiter, Europa orbits twice and Io orbits four times. Resonance occurs naturally, when planets have orbital periods equal to the ratio of integers.
Musical intervals describe the relationship between two musical notes. In the musical analogy, important musical intervals based on frequency ratios are the fourth, 4:3, the fifth, 3:2, and the octave, 2:1. Anyone who plays the guitar or piano might recognize these intervals.
Orbital resonance can change the way gravity affects two bodies, causing them to accelerate, decelerate, stabilize on their orbital path and sometimes their orbits are disrupted.
Think of pushing a child on a swing. Both planet and swing have a natural frequency. Push the child to match the speed movement and they will get a boost. They will also get a boost if you push them every other time they are in that position, or every third time. But push them at random times, sometimes with the motion of the swing and sometimes against it, and they get no boost.
For planets, the boost can keep them on track, but it’s more likely to disrupt their orbit.
Exoplanet resonance
Exoplanets, or planets outside the solar system, show excellent examples of resonance, not only between two objects but also between resonant “chains” of three or more objects.
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The star Gliese 876 has three planets with orbital period ratios of 4:2:1, just like Jupiter’s three moons. Kepler 223 has four planets with ratios of 8:6:4:3.
The red dwarf Kepler 80 has five planets with ratios of 9:6:4:3:2, and TOI 178 has six planets, five of which are in a resonant chain with ratios of 18:9:6:4:3.
The record holder is TRAPPIST-1. There are seven Earth-like planets, two of which are potentially habitable, with orbital ratios of 24:15:9:6:4:3:2.
The HD 110067 system is the newest example of a resonant chain. It is about 100 light years away and contains six sub-Neptune planets, a common type of exoplanet, with orbital 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 planetary systems exhibit them. Astronomers think that planets form in resonance, but small gravitational pulls from passing stars and errant planets destroy the resonance over time. With HD 110067, the resonant chain has survived for billions of years, offering a rare and rare view of the system as it was when it formed.
Orbital sonification
Astronomers use a technique called sonification to translate complex visual data into sound. It gives people a different way to appreciate the beautiful images from the Hubble Space Telescope, and has been applied to X-ray data and gravitational waves.
With exoplanets, sonification can convey the mathematical relationships in their orbits. Astronomers at the European Southern Observatory have created what they call “the music of the spheres” for the TOI 178 system by connecting a pentatonic-scale sound to each of the five planets.
A similar musical translation has been made for the TRAPPIST-1 system, and the orbital frequencies have been increased by 212 million to bring them into the audible range.
Astronomers have also created sonification for the HD 110067 system. People may disagree whether these performances sound like actual music, but it’s exciting to see Pythagoras’ thoughts after 2,500 years.
This article is republished from The Conversation, a non-profit, independent news organization that brings you facts and analysis to help you make sense of our complex world.
Written by: Chris Impey, University of Arizona.
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Chris Impey receives funding from the National Science Foundation.
