Why can't a three/more body problem be reduced to a one-body problem?

In summary, the conversation discusses the analysis of multiple body problems and the challenges of reducing them to an equivalent one body problem. It is suggested that a coordinate transformation may not be effective in solving the problem and that for three bodies, it is necessary to use two independent vectors plus the coordinate of the overall center of mass.
  • #1
neelakash
511
1
We know a two body problem may be analysed as an equivalent one body problem.Why a three/more body problem cannot be reduced to a one-body problem?

I think in that case we do not find an equivalent reduced mass...
Anyone can say something?
 
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  • #2
Try to come up with a coordinate transformation that does any good. Relative coordinates don't work, you need three to specify everything. This is no better than the starting position. Just give it a shot and you'll see.
 
  • #3
For three bodies, you can reduce the independent vectors to two plus the coordinate of the overall center of mass.
 

1. What is a central force?

A central force is a type of force that acts on an object towards a fixed point, known as the center of force. It can be either attractive or repulsive in nature and its magnitude depends only on the distance between the object and the center of force.

2. How is a central force different from other types of forces?

Unlike other types of forces, such as friction or tension, a central force acts towards a fixed point rather than a specific direction. It also has a fixed magnitude that is dependent on the distance between the object and the center of force.

3. What are some common examples of central forces?

Gravitational force, electric force, and magnetic force are all examples of central forces. These forces act towards a central point (such as the center of the Earth for gravitational force) and their magnitude depends on the distance between the objects.

4. How do we measure the strength of a central force?

The strength of a central force is measured by its magnitude, which is determined by the inverse square law. This means that the force decreases as the distance between the objects increases. The unit of measurement for central force is Newtons (N).

5. How does understanding central forces help in scientific research?

Understanding central forces is essential in many scientific fields, such as physics, astronomy, and engineering. It allows us to predict the motion of objects, such as planets or particles, and to design structures that can withstand the forces acting on them. It also helps us to better understand the fundamental laws of nature and how they govern the behavior of objects in our universe.

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