The 12th homework

exercise 4.16

物基一班
陈天懿 2013301020146

Abstract

This article use numerical method simulates the three-body system of the sun, Jupiter and Earth.

Background

As we all know, the motion of planets of solar system satisfies the law of universal gravitation. When we calculate the motion of the planets, we ofthen consider the sun is fixed at a point, for its mass is much larger than other planets. But this is just a proximate process. To get more accurate resualt, we must calculate it in the binary system. Mean while, the mass of Jupiter is about $\frac{1}{1000} times the mass of the sun, which is large enough to form a three-body system among Juper, Earth and the sun.

Main

From the picture we can see that the influence of Jupiter is very small compared with sun. When the mass increases, the orbit of Earth becomes chaotic and hard to predict.

At last, let's see the motion of Earth alone under the different mass of Jupiter:



When the mass of Jupiter gets larger, the motion of Earth gets more chaotic, which is the same as the resualt from above.

Conclusion

Actually, the effect of the presence of Jupiter has little influence on the motion of Earth, which corresponds with the reality we can observe. But when we set the mass of Jupiter larger, the chaos will occur, and the motion of Earth will become unpredictable.

see codes here
see codes here

Reference

Computational Physics-Nicholas J. Giordano, Hisao Nakanishi