Earth Plus Jupter: A Simple Three_body Problem

郭帅斐

The summary:

In physics, three-body problem is a simple example of chaos. Our erath is stable, so the Sun and the Jupter plus the Earth can not cause chaos. But what if we increase the mass of the Jupter? First, the motion of Earth would not stabe; and finally, the earth go to chaos and fly away. In the program, we make the mass of the Sun as infinite and always at the origin point. Finally, a really threebody model be writted, in which the Sun have a finite mass and can move with the influence of Erath and Jupter.

The psudocode:

The equations are just like the last program, but here we must apply it to 2 or 3 related body, so the psudocode may be a little complicated. But the principles are the same.

The result:

• First, a psedo three-body(where only the Earth and the Jupter can move) model was calculated,the result are as follows:
  When the mass of Jupter is exact, the motion of the two planet is exact:
  
  When we transfer the mass of Jupter to 10 times,the changes are neglectable:
  
  When the mass of Jupter becomes 100 times, the changes can be seen ckearly:
  
  When we change the mass of Jupter to 1000 times, the Earth becomes unstable and fly away!
  
  Now we know why the Earth stable: that's all the environment be the most suitable configuration! Till now, we can admire the owesome of the nature.
• Second, a really three-body model are solved, and gained many strange figures:
  When the distance between the moon and the Earth is small and the velocity of the moon is large, the moon orbit as a planet.
  
  When the distance between the Earth and the moon is large but the velocity of the moon is small, the moon move in a periodic manner:
  
  When the distance betwween the Earth and the moon is small and the velocity of the moon is small, the moon move in a chaotic manner
  
  After all, we have see the different manners of the three-body model.

The conclusion:

We not only see the motion of psudo three-body model through the program two-planet, but also see the motion of real three-body model three the program threebody. There are many beautiful phenomenon in the model.