“Why are the planets round and never have any other shape?” Eloan (9 years) asks

As soon as one thinks of the shape of a known celestial object, the Earth, the Sun, the Moon, planets, it is the sphere that comes to mind.

But once we have seen the main members of the Sun family, our curiosity can make us visit the other stars. And there, surprise: the general law no longer seems to apply. Mars, for example, has two non-spherical satellites. Their dimensions are in the tens of kilometers, they look like large rocks. Halley’s comet, whose last visit to Earth dates back to 1986, was photographed on this occasion: it is also like a large rock about ten kilometers long.

Why are large celestial bodies spherical while small ones are not? Is there anything in their history that radically separates them from each other?

Asteroids are not spherical – NASA, CC BY (via The Conversation)

Gas and dust …

The answer is yes and depends on how a star system is formed: a star and all the objects that orbit it. The understanding we have of it today is as follows: after a violent event in a galaxy, such as the explosion of a supernova (explosion of a large star at the end of its life), a cloud of gas begins and dust to crumble on itself.

This collapse is accompanied by an increase in temperature at all levels: that of the central star, whose temperature reaches several million degrees; also the rocky planets, which by compressing will reach temperatures of thousands of degrees; and even gas planets further away from the Sun. Our first question becomes this: why is a liquid or gaseous celestial body spherical?

As a result, we can observe around us the shapes that liquids and gases take. Let’s start with a liquid. Here are a number of simple experiments that anyone can do in their kitchen that answer the question.

The example of oil

Experience 1: Pour (gently) a little olive oil into a glass of water; it is well known that oil forms a film on the surface of water.

Experiment 2: Pour (also gently) a little oil into a glass of alcohol; we see that the oil sinks to the bottom of the glass and forms a film at the bottom of the glass.

Oil is less dense than water and denser than alcohol. In the first case, it is exposed to a force called buoyancy greater than its weight, which causes it to float on the surface. In the second, this pressure is not sufficient and the oil remains at the bottom. What happens now if you (gently) pour water into the glass with alcohol? As the water and alcohol are mixed, the density of the mixture increases little by little, the Archimedean thrust of the mixture also increases, and there comes a time when the mixture and the oil have the same density. What shape is the oil at this time?

See: we get beautiful spherical drops of oil floating in the mixture!

Left: oil film at the bottom of a glass of alcohol (the yellow on the surface is only the reflection of the background) - Right: oil droplets in a water-alcohol mixture of the same density as' oil
Left: oil film at the bottom of a glass of alcohol (the yellow on the surface is only the reflection of the background) – Right: oil droplets in a water-alcohol mixture of the same density as the oil – Jacques Treiner (via The Conversation)

What does this experience teach us? The oil molecules attract each other and they are also subject to the Earth’s gravity. When the water-alcohol mixture has the same density as the oil, everything happens as if gravity had been suppressed, since Archimedes’ thrust compensates for the weight, and it is found that the oil acquires a spherical shape under these conditions. This is the most compact shape possible.

The problem of physics has become a geometry problem: what does “the most compact form” mean exactly? It is the shape that for a given volume has the smallest surface, or correspondingly the shape that for a given surface has the largest volume. It can be shown that it is the sphere that meets these two possible definitions.

A fluid that is solely subject to internal forces always assumes a spherical configuration. This is why rocky planets, like Earth formed in a liquid state, have a spherical shape. And also why objects that have always been solid, like asteroids and comets, are not spherical.

What about gaseous celestial bodies? On Earth, a gas occupies all the volume offered to it, gravity is not sufficient to play a role. But when a large mass of gas is involved, then it is different, gravity is able to hold it in a compact form. Starting with the Sun or Jupiter, whose mass is one thousandth of the Sun (and about 300 times that of Earth), or Saturn, whose mass is about 100 times that of Earth.

This analysis is written by Jacques Treiner, theoretical physicist at the University of Paris Cité.
The original article was published on the site of The conversation.

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