Solution of the Two Body Problem

In summary, the conversation is about the unsolvability of the three-body problem and the search for a closed form solution to the two-body problem. The mention of Brun's Theorem and the suggestion to look at ScienceWorld and Landau's text on Mechanics are also discussed. It is mentioned that the three-body problem does have an infinite-series solution, but it converges very slowly and is not practically useful. A link to the Wikipedia page on Sundman's theorem for the three-body problem is also provided.
  • #1
Ed Quanta
297
0
I have been trying to understand why the three body problem is unsolvable for some time now. But I realized that it would probably help to see a closed form solution to the two body problem first. I was wondering if anyone can direct me to such a solution via link or just shed some light on the topic. Peace.
 
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  • #2
Try scienceworlds's Two-Body Problem entry. It's the second thing that came up on google.
 
  • #3
It's done in Landau's text on Mechanics,too.

Daniel.
 
  • #4
Ed Quanta said:
I have been trying to understand why the three body problem is unsolvable for some time now.

Have you gotten as far as Brun's theorem?
 
  • #5
What's Brun's Theorem got to do with it?
I just looked up what it is.
 
  • #7

1. What is the "Two Body Problem" in physics?

The Two Body Problem is a classic problem in physics that involves finding the motion of two bodies, such as planets or stars, that are orbiting around each other under the influence of their mutual gravitational attraction.

2. Why is the "Two Body Problem" important?

The Two Body Problem is important because it is a fundamental problem in classical mechanics and has practical applications in fields such as astronomy and aerospace engineering. It also serves as a foundation for more complex problems involving multiple bodies.

3. How is the "Two Body Problem" solved?

The "Two Body Problem" can be solved using mathematical equations derived from Newton's laws of motion and his law of universal gravitation. These equations can be solved using various techniques, such as numerical methods or analytical methods like Kepler's laws.

4. What are some real-life examples of the "Two Body Problem"?

Some real-life examples of the "Two Body Problem" include the motion of planets around the sun, moons around planets, and binary star systems. The orbits of these bodies can be accurately predicted using the principles of the "Two Body Problem".

5. Are there any limitations to the "Two Body Problem"?

Yes, there are limitations to the "Two Body Problem" as it assumes that the two bodies are point masses with no external forces acting on them. In reality, there are other factors that can affect the motion of objects, such as the gravitational pull of other bodies and the effects of relativity at high speeds. These factors make the problem more complex and require more advanced models and techniques to solve.

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