The three-body problem is a problem in classical mechanics that asks how three mass points that interact by weight move.In the field of celestial mechanics, it was first developed around the 18th century as a problem that models the motion of celestial bodies mutually influenced by universal gravitation. It has been studied since. Three bodies, such as the motion of the star/planet/satellite system represented by the “Sun, Earth, and Moon,” the Lagrangian point where three stars are balanced, and the case where three stars with random masses move in free orbits. “Three Bodies” can simulate problems.
Three Bodies
https://three-bodies.sulami.xyz/
When I opened the page, three dots of different colors and sizes appeared. Each point moves in a free trajectory. Each point has numbers “m” and “v”, where m (mass) represents the mass of the point and v (velocity) represents the speed at which the point moves.
Each point basically moves in a straight line at a constant speed, but when two points approach each other, their trajectories change as they are pulled toward each other. The speed of the green dot when moving alone was “0.39”, but in the image below it has increased to “0.75”, which is nearly double, and the speed changes as the points attract each other. You can see that there are. This represents the three-body problem in which universal gravitation is acting on each point, and gravitation affects each trajectory.
As a result of the green and yellow points attracting each other and colliding with each other, “COLLISION” is displayed and the animation stops. Three Bodie simulates the collision of stars of different sizes moving in three free orbits.
By clicking or spacebar, or tapping the screen on a smartphone, three new stars will appear. This time, there are two green dots that are similar in size, and one light blue dot that is about half the mass of the green dots.
When two points approach each other, they are attracted to each other and their orbits change. As shown in the red frame below, the orbits of both points have changed, but the small light blue dot has a large bend, while the green dot’s orbit has changed only slightly. Because the magnitude of gravitational force and the sensitivity to gravitational force differ depending on the mass, they do not move in the same way. In addition, in the first simulation, the two points collided immediately because they were close, but it seems that the force of attraction only changes the trajectory, and in many cases they pass each other and continue moving at a constant speed.
Perhaps because of the large difference in mass, the small light blue dot reacts more sensitively when the green dot approaches. There was also a scene where they turned in a circle.
When two points get close, they only slightly affect each other’s orbits, but when three points get close, each is affected by the gravitational pull of the other two, so you can see complex changes.
However, after approaching, they returned to their respective orbits and resumed linear motion. At least in these three respects, it seems unlikely that the orbit will be balanced and stable.
As a result, the largest green dot collided with the smaller light blue dot at the top of the screen, and the simulation ended.
Three Bodie allows you to deepen your understanding of star orbits and gravitational pull with simple animations by viewing three points with different masses, positions, and orbits each time you retry the simulation.
The code for Three Bodie is published on GitHub.
GitHub – sulami/three-bodies: Three body simulation in Wasm
https://github.com/sulami/three-bodies
Tags: simulate threebody problem difficult mechanical problem models movements mutually influencing celestial bodies Livedoor News
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