This article is the original of Daoist Chen Luoting, **Please indicate the source.
In the three-body free fall law, the collision-free periodic orbit is a very special state. In this state, the three objects orbit and return to their initial positions at equal intervals of time. This state is described as three objects orbiting in a circular orbit that approaches and moves away from each other at equal intervals of time.
Each object in a collision-free periodic orbit has the same velocity and acceleration, and they all complete a complete orbital run at equal intervals. This state is very stable, as any slight disturbance can cause the collapse of the orbit.
To understand the concept of collision-free periodic orbit, let's first understand what is the basic law of three-body free fall.
In this law, three objects fall freely under the action of gravity, and the interaction between them is negligible. In this case, each object has its own acceleration and velocity, but they approach and move away from each other at equal intervals of time.
When three objects are in a collision-free periodic orbit, their path of motion forms an equilateral triangle.
In this triangle, each object moves on its own path and approaches and moves away from each other at equal intervals of time. This state is very stable, as any slight disturbance can cause the collapse of the orbit.
In a collision-free periodic orbit, the velocity and acceleration of each object are the same, and the distance between them is also equal.
Therefore, each object needs the same amount of time to complete a complete orbital run. Also, the period of a collision-free periodic orbit depends on the initial conditions, such as the initial position and velocity of the object.
A collision-free periodic orbit is a special state in the law of three-body free fall, in which three objects orbit in the path of an equilateral triangle and approach and move away from each other at equal intervals of time. This state is very stable, as any slight disturbance can cause the collapse of the orbit.