Kepler's law
Precession of the perihelion of Mercury
Abstract
Our planet we are living in the solar system.How are the planets working?
This time we are going to study our hypothetical solar system. There are 8 planets, which is similar with earth. And the only force in this problem is gravity. So Kepler's law is our tool.
Background
We can use the equation below
and this is the way we use to approximate the orbit
For our solar system case, the solution can be expressed as
Main body
We can create the simulation of solar system rotation.
This is the data of every planet
The two body problem
We can simply consider a planet-sun system as a two_body problem
Mercury Problem
But for the more precise simulation of the movement of Mercury, we use the force law predicted by general relativity.That is
where the Mm is the mass of Mercury and the a is 1.1x10e-8 AU^2
When beta=2
And beta=2.5
beta=5
And we can see the change in perihelion of Mercury
When alpha=0.0008
When alpha=0.004
Conclusion
When we change beta of the simulation, there will be an obvious procession in the simulation.
When alpha increase, the slope of perihelion of Mercury would become more steep.
Reference
Thanks for Tan shan's code
