Exercise 10:The precession of the perihelion of Mercury

摘要：

本次作业研究了水星近日点的进动问题

背景：

水星近日点的进动

水星轨道

各行星的数据

公式：

  Under Newtonian physics, a two-body system consisting of a lone object orbiting a spherical mass would trace out an ellipse with the spherical mass at a focus. The point of closest approach, called the periapsis (or, because the central body in the Solar System is the Sun, perihelion), is fixed. A number of effects in the Solar System cause the perihelia of planets to precess (rotate) around the Sun. The principal cause is the presence of other planets which perturb one another's orbit. Another (much less significant) effect is solar oblateness.

Under the adjustment of the general relativity, the force law becomes:

the rate of precession functions as alpha.

Because there are relations between the initial velocity and eccentricity, we can change the initial speed to change the eccentricity.

正文：

click here to see the code

1.a simulation of the motion of solar system planets

2.the inverse square law and the stability of planetary orbits

3.precession of the perihelon of mercury

感谢秦大粤同学和徐秋豪同学