Exercise12:

Chapter 4 problem 4.16: Three-body motion simulation

Name:戴嘉禾

Number:2013301020073

Abstract

Although each planet in the solar system, astronomers studied movement has been quite thorough, we still have some interesting problems worth exploring. The first is the largest planet in the solar system, the earth gravity of Jupiter makes the sun earth system into three wood system. After the chaos Titan seven. Through the discussion of these issues, we can deepen the understanding of the law and Kepler's law of gravity.

Background discription

Study on the one three body system is a problem worthy of study, it has a chaotic behavior, so it cannot be solved analytically.
In a three body system, the research of planetary motion has many interesting phenomena. Now consider a hypothetical ideal system, the sun, earth and Jupiter form a pseudo celestial system. All the experience of others produced by gravity. Here we study some properties of different mass of jupiter.
The Mass of the sun,the earth and the jupiter are as follows:

By force formula, the total force for each body force on each of its vector and other celestial bodies, for: Here, only the calculation of the sun, earth and jupiter.
Link code 1 is here

Sectional view

3D section:

2 changing the speed of initial conditions, calculation of the motion of the earth:

Sectional view

3D:
It can be found that the center of mass system, keep the total momentum is 0, larger in terms of initial velocity of circular Jupiter, the earth around the sun, but the position of the sun off center.

3.in the center of mass system. It can be concluded that the quality of Jupiter is 10 times bigger, 100 times, and the section of three-dimensional map 1000 times:
3D:
We can see that 10 times the mass of Jupiter, the sun affected is very small.

3D:
We can see that 100 times the mass of Jupiter, the sun circle circle around the earth, the earth, Jupiter.

3D:
We can see that 1000 times the mass of Jupiter, Jupiter from the sun.

Conclusion

Under different conditions, the three body problem will produce different motion.
1 Jupiter has influence on gravity of earth, and with the increase of the mass of Jupiter, this effect will become large, the motion of the earth will become chaotic.
2 When there is more than one star, if one is close to it from the earth, after may revolve around the star motion. If the earth does not favor any stars, the movement will become chaotic.

Acknowlegement and Reference

• Student Yuqiao Wu,Xiao Guo and Shixin Wang.
• Computational physicsNicholas,J.Giordano Hisao Nakanishi.