Astronomical dictionary

In the recently popular science fiction film Wandering the Earth, there is a shocking scene: when the Earth "wanders" to Jupiter, part of the atmosphere is attracted by Jupiter's gravity, forming a gas flow, and as the Earth continues to approach the "rigid body Roche limit", the fate of the Earth is also in danger.

Although strict calculations prove that the above scenarios may be exaggerated, what is the Roche limit? When two celestial bodies are close enough to each other and less than the Roche limit of both, will it really cause the material flow of the celestial body or the whole body to be torn apart?

Tidal force causes deformation of celestial bodies

Every object has an interacting gravity, and the celestial body is no exception. When we assume that all objects are a point of negligible size, the matter is very simple: gravity is on the line between two points. However, the gravity between two celestial bodies is much more complex than that between two points: celestial bodies are often very large, so it is not allowed to assume that they are an infinitely small point. In this case, the magnitude and direction of the force exerted by a celestial body on each part of another celestial body must be studied. Obviously, the magnitude and direction of the force exerted by a celestial body on each point of another celestial body are basically different.

As a result, the gravity of one celestial body to another can be divided into two parts: one part causes the two to rotate around the common center or close to each other; The other part pulls or compresses the celestial body in different directions to deform it. The latter is called tidal force.

Our earth is affected by the tidal force of the moon. This force causes the sea water on the earth to be higher than other places in the direction of connection with the moon. With the rotation of the earth and the revolution of the moon, the sea water flows in the horizontal direction, forming tide water. In fact, the moon also has tidal effects on the earth's atmosphere and rocks, which are called "gas tide" and "solid tide" respectively. Our earth also has tidal force on the moon.

In Wandering the Earth, the earth's atmosphere is sucked away by Jupiter, and Jupiter's atmosphere is disturbed by the earth, all of which are gas tides caused by tidal force. In reality, in the binary star system composed of some gas stars, if they are too close, the tidal force will make the gas of one star flow to the other star.

Liquid and solid have different limit values

The strength of tidal force is related to distance. The smaller the distance between celestial bodies, the greater the tidal force, and the more serious the deformation of celestial bodies. In the 19th century, French astronomer Roche calculated and found that when the distance of the celestial body approached a limit value, one of the celestial bodies would be torn apart by the tidal force exerted by the other, which is called the "Roche limit".

Assuming that the mass difference between the two celestial bodies is very large, then the value of the Roche limit is only related to the density of the two celestial bodies and the physical state of the torn object: the value of the Roche limit is the ratio of the density of large celestial bodies to the density of small celestial bodies to the third power, and then multiplied by the radius of large celestial bodies and a multiple. If the torn object is gas, liquid or very loose solid, this multiple is 2.455; If the torn object is a very hard solid, this multiple is 1.26. The latter is the rigid body Roche limit mentioned in the film. The Roche limit is calculated from the center of the celestial body. If you want to calculate the distance between the torn celestial body and the surface of the large celestial body, you should also subtract the radius of the large celestial body itself.

We can give a special example to simply calculate the specific value of the Roche limit. If the density ratio of a large object to a small object is 1, and the Roche limit is 2.455 or 1.26 times the radius of the large object, then when the distance between the object and the surface of the large object is 1.455 or 0.26 times the radius of the large object, it will be torn by the large object.

　　 Jupiter's rings come from torn moons

When the Earth approached Jupiter, all the water was frozen because of the cold. The densities of Jupiter and Earth are 1.326 and 5.514 grams per cubic centimeter respectively, and the ratio to the third power is 0.622. Assuming that the ice and rocks on the earth can be ignored, and the earth is almost all magma and air, then the fluid Roche limit when the earth is close to Jupiter is 1.527 times the radius of Jupiter. Jupiter has a radius of about 70000 kilometers, so when the distance between the earth composed of magma and air and the surface of Jupiter reaches about 40000 kilometers, it will be torn apart by Jupiter. Assuming that the Earth is completely composed of very hard rocks and ice, its Roche limit is 0.784 times the radius of Jupiter, located inside Jupiter, so it will not be torn by Jupiter. For this reason, many people think that the description of the rigid body Roche limit in Wandering Earth is slightly exaggerated.

Since the earth near Jupiter is a mixture of air, ice, rock and magma, when it is very close to Jupiter, although it will not be completely torn apart, the crust will be severely deformed, leading to the earthquake described in the film; In addition, the atmosphere and the magma inside were violently disturbed by Jupiter's huge tidal force, resulting in the eruption of magma and the loss of atmosphere described in the film.

Although the Earth is unlikely to be torn up by Jupiter, there are often some unlucky small bodies in the solar system torn up by Jupiter and hit Jupiter. The most famous event was the collision of Comet Sumek Levy 9 with Jupiter in 1994. Computer simulation shows that the distance between this comet and Jupiter was less than the Roche limit of loose solids in 1992, so it was torn into 21 pieces, which are relatively solid and have not been torn further. From July 16 to 22, 1994, all the fragments of this comet hit Jupiter successively.

Astronomers' research also shows that some giant planets in the solar system will not only capture passing objects, but also tear up some natural satellites close enough. For example, most of Saturn's rings are located within the Roche limit of Saturn's moon, which may be torn up by tidal forces.

(Author's unit: College of Physical Science and Engineering Technology, Guangxi University)