# 什么是拉格朗日点？

L4和L5点则是一个有趣的结构，它们位于地球和月球轨道形成的等边三角形的对角线上，与地球和月球的连线夹角为60度，形成一个平衡点。在这些拉格朗日点周围，存在许多小行星和尘埃，被称为特洛伊小行星。

## What is a Lagrange point?

Lagrangian points refer to specific points in the gravitational field between two celestial bodies in celestial mechanics, where the gravitational force and centripetal force are perfectly balanced. This allows a small mass to remain stable at these points without external interference. Lagrangian points were first proposed by the French mathematician Joseph-Louis Lagrange in the 18th century.

In the solar system, there are five Lagrangian points between the Earth and the Moon in their gravitational field, known as L1, L2, L3, L4, and L5. L1 is located along the line connecting the Earth and the Moon, approximately 150,000 kilometers from Earth, where the combined gravitational force of the Sun and Earth equals the centripetal force. L2 is located along the extended line connecting the Earth and the Moon, approximately 150,000 kilometers from Earth, where the gravitational forces of the Sun and Earth cancel each other out. L3 is situated in a straight line behind the Earth and the Moon in their orbit, approximately 380,000 kilometers from Earth, where the combined gravitational force of the Earth and the Moon is balanced with the centripetal force on Earth.

L4 and L5, on the other hand, form an interesting structure. They are located along the diagonal line of an equilateral triangle formed by the Earth and the Moon's orbits, with an angle of 60 degrees between the line connecting the Earth and the Moon. These points create a balance. Around these Lagrangian points, there are many asteroids and dust particles known as Trojan asteroids.

Apart from the Earth-Moon system, other planets and satellites in the solar system have similar Lagrangian points. For example, there is a string of stable Lagrangian points between Jupiter and the Sun, known as Jupiter's Trojan points, where some asteroids have been discovered.

The existence of Lagrangian points allows scientists to position objects in specific locations in the universe, which is crucial for selecting stable orbits for space probes and satellites, as well as planning space missions. By studying and utilizing Lagrangian points, scientists can gain a better understanding of celestial mechanics and the mechanisms operating in the universe.