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Trappist or the harmony of the cosmos

The resonance of the planets

Automatic translation  Automatic translation Updated November 22, 2019

In the confused and turbulent world around us, there are regularities that make sense out of apparent chaos.
For example, we notice that the Earth rotates regularly around the Sun in one year, that the days follow the nights, that the nautilus builds its shell in spirals or that the cells of the bees are hexagonal...
All civilizations have been on the lookout for these patterns, rhythms, repetitions and patterns that amaze and reassure us. This allows us to believe that there is an order or purpose in our observable Universe.
At all times, these regularities, contingent or accidental, have inspired philosophers, physicists, mathematicians and especially musicians.
When we talk about regularities we think about sounds. In music an octave corresponds to a doubling of frequency f, 2f, 3f, etc. These multiple frequencies of a given frequency are called harmonics.
For example, the note do has a frequency of 260 Hz, the next do is 520 Hz. The ground note has a frequency 1.5 times the do, the next ground is equal to 3 times the do, etc. These regularities are sufficient to fix the musical harmony.


The solar system discovered in 2016 by the transits method, is 7.6 billion years old and is located in the constellation of Aquarius at 39.5 light-years.
This system is composed of an ultra-cold dwarf star called TRAPPIST-1a and at least 7 rocky planets (TRAPPIST-1b, TRAPPIST-1c, TRAPPIST-1d, TRAPPIST-1e, TRAPPIST-1f, TRAPPIST-1g, TRAPPIST-1 1h).
Three of them are located in the habitable zone of the star and TRAPPIST-1e has a density close to that of the Earth, and it is probably endowed with an iron core and a liquid or icy ocean.
Using a computer model, scientists simulated planetary orbits and discovered that the 7 planets are in perfect orbital harmony.
In other words, each planet has simple relationships with the orbital periods of its neighbors. When the outermost planet trappist-1h traverses 2 orbits, its neighbor trappist-1g traverses 3 orbits and trappist-1f 4 orbits and tarppist-1e 6 orbits and trappist-1d 9 orbits and trappist-1c 15 orbits and trappist-1b traversed 24 orbits. The entire system moves with great regularity.

 Structure interne d'astéroïde

Image: the star TRAPPIST-1a and its 7 telluric planets represented with their respective sizes (the distance to the star is not respected).

NB: TRAPPIST (Transiting planets and planetesimals small telescope) is a network of 2 robotic telescopes. A telescope is located at the La Silla Observatory (Chile) and the second telescope at Oukaïmeden (Morocco).

The celestial symphony


The planets of the TRAPPIST-1 system are therefore in perfect orbital resonances and these harmonious orbits can be translated musically, with notes. TRAPPIST-1b corresponds to the note b, TRAPPIST-1c corresponds to the note c, TRAPPIST-1d corresponds to the note d, etc.

Trappist-1 Orbital period Music note
Trappist-1b 1.51 days b si
Trappist-1c 2.42 days c do
Trappist-1d 4.05 days d
Trappist-1e 6.10 days e mi
Trappist-1f 9.20 days f fa
Trappist-1g 12.35 days g sol
Trappist-1h 18.76 days a la

Each planet plays a note in orbit as it passes between us and its star, and a rhythmic beat is heard every time it passes its neighbor.
As each planet resonates with its neighbors, the whole system forms a chain of harmonic resonance.
This is what shows (accelerated) this dazzling and melodious animation where the seven planets waltz in almost perfect synchronism.


Video: Rhythmic and harmonious musical vision of transits of planets in front of their star. A team of NASA researchers and musicians has turned the orbits of the seven worlds TRAPPIST-1 into music.
No other known planetary system has so many resonant worlds.
The computer simulations suggest that the planets should have bumped very quickly after their formation. But the resonance apparently saved them, according to Dan Tamayo, Cornell University Ithaca, New York.


The nautilus is a marine mollusk whose shell develops coiled forward, in the form of a spiral.
The interior is partitioned into different boxes and the body of the nautilus occupies the last lodge.
The nautilus moves by reaction by throwing water through a valve (funnel).
Its habitat is the Indian Ocean, the China Sea and the Pacific Ocean.

Constellation of Aquarius

The constellation of Aquarius (water carrier) is crossed by the Sun from February 16 to March 11.
The brightest star in the constellation Aquarius is a red supergiant β Aquarii (Sadalsuud of Arabic Al Sa'd al Su'ud, literally meaning "the luckiest of the lucky ones"), located 612 light-years away. Aquarius is between Capricorn in the west and Pisces in the east.

The light-year (AL) is a unit of measure of distance used in astronomy which corresponds to the distance traveled by the light in the vacuum during a Julian year (365,25 days or 31,557,600 seconds), approximately 10,000 billions of kilometers.
The speed of light in a vacuum is a physical constant of 299,792,458 m / s (about 300,000 km / s).

Habitable zone in astronomy

The circumstellar habitable zone or ecosphere is a theoretical circular tube surrounding a star in which the temperature on the surface of planets in orbit, would allow the appearance of liquid water.
Scientists believe that liquid water is vital because of its role in biochemical reactions.


A harmonic is a component of a periodic sound whose frequency is an integer multiple of a fundamental frequency. If ƒ is the fundamental frequency, the harmonics have frequencies equal to: 2ƒ, 3ƒ, 4ƒ, 5ƒ, and so on. The fundamental note is the la (440 Hz), the harmonic of rank 2 is at 880 Hz, that of rank 3 at 1320 Hz, etc.

Ultra-cold dwarf

An ultra-cold dwarf is a brown dwarf star whose temperature is less than 2,700 Kelvin (temperature of the photosphere of our Sun is 5,781 K).
These very small stars represent about 15% of the main objects of our galaxy.
The small size of the protoplanetary disks that formed the ultra-cold dwarfs mostly hosts a relatively large population of terrestrial planets ranging from the size of Mercury to that of the Earth.

Transit method

When we observe a planetary system by the edge, we can see a planet passing in front of its star (planetary transit) because it will bring down its brightness very slightly.
The transit method consists in detecting these planetary transits many times. If the transit is repeated (period), the presence of a body in orbit around the star is confirmed.
Transit provides the period of revolution and the diameter of the planet (from apparent diameters), the half-major axis of the planet's orbit (using Kepler's third law).
This information with the brightness of the star allows to position the planet in relation to the habitable zone of the star.

Orbital resonance

Orbital resonance occurs when two celestial objects in revolution on their orbits have periods of revolution whose ratio is an integer.
Orbital resonance is commonly rated 1: 1 or 2: 1 or 4: 1, which is the number of times the inner object travels through its orbit as the outer object travels through its own orbit.
In the Solar System, the satellites of Jupiter are in perfect resonance. Ganimede travels 1 orbit while Europe travels 2 and IO 4.

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