Orbital resonance – the striking gravitational dance performed by planets with aligned orbits

Planets orbit their parent stars while separated by enormous distances. In our solar system, planets are like grains of sand in an area the size of a football field. The time it takes for planets to revolve around their sun has no specific relationship with 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 in an almost rhythmic heartbeat, in perfect synchronization. Each pair of planets completes their orbits in times that are the ratios of whole numbers, allowing the planets to align during their orbit and exert a gravitational pull on the other.

This type of gravitational alignment is called orbital resonance and is like a harmony between distant planets.

I am an astronomer who studies and writes cosmology. Researchers have discovered more than 5,600 exoplanets over the past three decades, and their extraordinary diversity continues to surprise astronomers.

Harmony of the spheres

The Greek mathematician Pythagoras discovered the principles of musical harmony 2,500 years ago by analyzing the sounds of blacksmith hammers and plucked strings.

He believed that mathematics lies at the heart of the natural world and proposed that the sun, moon and planets each emit a unique buzz 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 took up this idea. He proposed that musical intervals and harmonies described the movements of the six then known planets.

Before Kepler, the solar system had two basses, Jupiter and Saturn; a tenor, Mars; two altos, Venus and Earth; and a soprano, Mercury. These roles reflected how long it took for each planet to orbit the sun, slower 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 bear some similarities to the concept of orbital resonance, planets do not actually make sound because sound cannot travel through the vacuum of space.

Orbital resonance

Resonance occurs when planets or moons have orbital periods that are whole number ratios. The orbital period is the time it takes for a planet to make one complete orbit around the star. For example, two planets orbiting a star would be in a 2:1 resonance if one planet takes twice as long as the other to orbit the star. Resonance is seen in only 5% of planetary systems.

Orbital resonance, as seen with Jupiter's moons, occurs when the orbits of planetary bodies align.  For example, Io orbits Jupiter four times in the time it takes Europa to orbit the Earth twice and Ganymede to orbit the Earth once.  <a href=WolfmanSF/Wikimedia Commons” data-src=”https://s.yimg.com/ny/api/res/1.2/a2MH_ZwWnrJuHDnvcAIt2w–/YXBwaWQ9aGlnaGxhbmRlcjt3PTk2MA–/https://images.theconversation.com/files/571674/original/file- 20240126-17-ofefj2.gif?ixlib=rb-1.1.0&q=45&auto=format&w=1440&fit=clip”/>Orbital resonance, as seen with Jupiter's moons, occurs when the orbits of planetary bodies align.  For example, Io orbits Jupiter four times in the time it takes Europa to orbit the Earth twice and Ganymede to orbit the Earth once.  <a href=

In the solar system, Neptune and Pluto are in a 3:2 resonance. There is also a triple resonance, 4:2:1, between Jupiter’s three moons: Ganymede, Europa and Io. In the time it takes for Ganymede to orbit Jupiter, Europa orbits twice and Io four times. Resonances occur naturally when planets happen to have an orbital period that is the ratio of whole numbers.

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 guitar or piano might recognize these intervals.

Orbital resonances can change the way gravity affects two bodies, causing them to speed up, slow down, stabilize on their orbital path, and sometimes disrupt their orbits.

Think of pushing a child on a swing. A planet and a swing both have a natural frequency. Give the child a push that matches the swinging movement and he or she will get a push in the back. They 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 swing motion and sometimes against it, and they get no boost.

For planets, the boost may keep them on their orbits, but it is much more likely to disrupt their orbits.

Resonance of exoplanets

Exoplanets, or planets outside the solar system, exhibit striking examples of resonance not only between two objects, but also between resonant ‘chains’ involving three or more objects.

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The star Gliese 876 has three planets with an orbital period 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.

TRAPPIST-1 is the record holder. It has seven Earth-like planets, two of which are possibly habitable, with orbit ratios of 24:15:9:6:4:3:2.

The latest example of a resonant chain is the HD 110067 system. Located about 100 light-years away, it has 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 all planetary systems exhibit them. Astronomers think planets form in resonance, but small gravitational thrusts from passing stars and wandering planets erase the resonance over time. With HD 110067, the resonance chain has survived for billions of years, providing a rare and pristine view of the system as it was when it formed.

Sonification of the track

Astronomers use a technique called sonification to translate complex visual data into sound. It gives people another way to appreciate the beautiful images from the Hubble Space Telescope, and it has been applied to X-ray data and gravitational waves.

For exoplanets, sonification can convey the mathematical relationships of their orbits. Astronomers at the European Southern Observatory created what they call “music of the spheres” for the TOI 178 system by associating a pentatonic-scale sound with each of the five planets.

A similar musical translation has been made for the TRAPPIST-1 system, with the orbital frequencies scaled up by a factor of 212 million to bring them within audible range.

Astronomers have also sonified the HD 110067 system. People may disagree on whether these renditions sound like real music, but it is inspiring to see Pythagoras’ ideas realized after 2,500 years.

This article is republished from The Conversation, a nonprofit, independent news organization providing facts and analysis to help you understand our complex world.

It was written by: Chris Impey, University of Arizona.

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Chris Impey receives funding from the National Science Foundation.

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