Comments about "N-body problem" in Wikipedia

This document contains comments about the article N-body problem in Wikipedia

• The text in italics is copied from that url
  
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In the last paragraph I explain my own opinion.

Contents

• 1. History
• 2. General formulation
• 3. Special cases
• 3.1 Two-body problem
• 3.2 Three-body problem
• 3.3 Four-body problem
• 3.4 Planetary problem
• 3.5 Central configurations
• 3.6 n-body choreography
• 4. Analytic approaches
• 4.1 Power series solution
• 4.2 A generalized Sundman global solution
• 4.3 Singularities of the n-body problem
• 5. Simulation
• 5.1 Few bodies
• 5.2 Many bodies
• 5.3 Strong gravitation
• 6. Other n-body problems
• 7. See also

Reflection

• Reflection 1 -
• Reflection 2 -
• Reflection 3 -

Introduction

The article starts with the following sentence.

In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.

In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other and using Newton's Law.

The n-body problem in general relativity is considerably more difficult to solve due to additional factors like time and space distortions.

The n-body problem solution using general relativity is considerably more difficult because the solution is more acurate compared with the solution using Newton's Law.

1. History

2. General formulation

3. Special cases

3.1 Two-body problem

3.2 Three-body problem

3.3 Four-body problem

3.4 Planetary problem

3.5 Central configurations

3.6 n-body choreography

4. Analytic approaches

4.1 Power series solution

4.2 A generalized Sundman global solution

4.3 Singularities of the n-body problem

There can be two types of singularities of the n-body problem:

• collisions of two or more bodies, but for which q(t) (the bodies' positions) remains finite. (In this mathematical sense, a "collision" means that two pointlike bodies have identical positions in space.)

The problem is that in real live there can be collisions between two objects, but there never happens something which mathematical is called a singularity. The reason is that objects always have a size. That means the pointlike bodies can never have identical positions.
To bypass this situation, certain steps have to be taken before this situation happens to reduce the problem from a n-body problem to a n-1-body problem, to merge two objects.

5. Simulation

5.1 Few bodies

5.2 Many bodies

5.3 Strong gravitation

6. Other n-body problems

7. See also

Following is a list with "Comments in Wikipedia" about related subjects

• Relativity of Simultaneity Comments
• One-way speed of light Comments

Reflection 1 Comparing Newton's Law with Einstein's Law.

The N-body problem tries to solve or predict the future or positions of a set of masses or pointsize objects.
In general there are two theories to use: Newton's Law or Einstein's Law.

Reflection 2

Reflection 3

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