Three body problem and numerical method

In summary, a numerical method to solve a three body problem is where you use equations of motion to get an explicit equation. It is very hard to do this and typically requires one force. If you have a solar system with a sun and just one planet, with one moon going around this planet, this would be a three body problem. However, if the planet and moon physically touch one another, they become one body.
  • #1
Rothiemurchus
203
1
What is meant by " a numerical method to solve a three body problem?"
 
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  • #2
3-body usually means based on some physical force...numerical method i would assume to be the numerical integrator that maintains/evolves the system (eg integrator for gravity or potential).
 
  • #3
it means the equation is not separable for the equations of motion to get an explicit equation. You have to iterate to find the solution using eulers method.
 
  • #4
Typically, a three body problem is extremely hard to put into numerical form. If someone has a numerical solution for a three body problem it would have to involve one force, where vectors would be used to solve the problem. The Sun, Earth and moon are a three body problem. The force involved in each case is that of gravitation. Trying to describe the motion of the Earth with a numerical solution is not straight forward. In the case of Hydrogen, one electron orbits a proton- a two body system. Bohr's theory was a solution to this two body problem, it equated electrostatic force or coulomb's law with an inward centripetal force. In the case of Helium, we have two electrons and one nucleus, a three body problem. In this case a solution is extremely difficult, because we have to consider not only the attraction between the electrons and the proton, but also electron-electron repulsion.
In order to be relevant we really need to know what three body problem you are referring too.
 
  • #5
If we had a solar system with a sun and just one planet, with one moon going around this planet, this would be a three body problem.Can we assume that because the sun is large it is a fixed point,and that the moon is small and does not affect the motion of the planet too much, the movement of the planet around the sun is a two body problem?Does a large distance between some masses reduce a problem from being three body to two body? How do we decide when a three body problem has become a two body problem?
Is there some equation that tells us this or is it a subective judgement?
If the planet and moon physically touch one another do they become one body?
 

1. What is the "three body problem" in science?

The three body problem is a mathematical problem in physics that involves predicting the motion of three objects, such as planets or stars, that are affected by each other's gravitational pull. It is a complex problem that has no general analytical solution and requires numerical methods to solve.

2. How is the three body problem related to celestial mechanics?

The three body problem is an important concept in celestial mechanics because it helps us understand the motion of multiple objects in space, such as planets orbiting a star. It also has applications in other fields, such as astrophysics and aerospace engineering.

3. What are numerical methods used for solving the three body problem?

Numerical methods, also known as computational methods, are algorithms or mathematical techniques used to approximate solutions to the three body problem. These methods involve breaking down the problem into smaller, more manageable parts, and using numerical calculations to solve them.

4. What are some challenges in using numerical methods for the three body problem?

One of the main challenges in using numerical methods for the three body problem is the high level of computational complexity and the need for large amounts of computational power. Another challenge is ensuring the accuracy and stability of the solutions, as small errors in calculations can lead to significant deviations in the predicted motion.

5. How are numerical methods for the three body problem continuously improving?

Advancements in computer technology and numerical analysis have led to the development of more sophisticated and accurate methods for solving the three body problem. Researchers are also constantly testing and refining these methods to improve their efficiency and reliability. Additionally, the use of parallel computing and machine learning techniques has also shown promise in solving the three body problem more efficiently.

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