Could an Electromagnetic field produce the "3-body" problem?

In summary, the "3-body" problem is a difficult problem in physics that involves predicting the motion of three celestial bodies under the influence of their own gravitational forces. An electromagnetic field can affect this problem by introducing an additional force, but it is not the cause of it. Real-life examples of the "3-body" problem include the motion of celestial bodies in our solar system and in other star systems. This problem has been extensively studied in modern science and has led to the development of new mathematical techniques and theories.
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If you know positions and velocitys of bodies and EM-field ((##\vec{E}(t)## and ##\vec{B}(t))##) or (EM-poteintial ##\vec{A}(t)## and it's time deriative ##\frac{\partial \vec{A}}{\partial t}##)) at given time, then you can calculate: EM-field, positions and velocities of bodies on any time.

If you make approximation ##c\to \infty##, then it is just like classical 3-bodie problem, but with additional coulomb force.

If you tried to take into account magnetic force as function of positions of bodies, then the model mignt not be galileo invariant nor lorentz invariant.
 
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FAQ: Could an Electromagnetic field produce the "3-body" problem?

1. How does an electromagnetic field affect the 3-body problem?

An electromagnetic field can affect the 3-body problem by introducing additional forces and interactions between the bodies. This can make the problem more complex and difficult to solve.

2. Can an electromagnetic field alone produce the 3-body problem?

No, an electromagnetic field alone cannot produce the 3-body problem. The 3-body problem is a result of the gravitational interactions between three bodies, and an electromagnetic field does not have the same type of force as gravity.

3. Is the 3-body problem affected by the strength of the electromagnetic field?

Yes, the strength of the electromagnetic field can affect the 3-body problem. A stronger field can introduce stronger forces and interactions between the bodies, making the problem more complex.

4. Are there any real-life examples of the 3-body problem being influenced by an electromagnetic field?

Yes, there are real-life examples of the 3-body problem being influenced by an electromagnetic field. One example is the interaction between the Earth, Moon, and Sun, where the Sun's electromagnetic field affects the orbits of the Earth and Moon.

5. How do scientists study the effects of an electromagnetic field on the 3-body problem?

Scientists study the effects of an electromagnetic field on the 3-body problem through mathematical models and simulations. They can also conduct experiments using electromagnetic fields and three bodies to observe and analyze the interactions between them.

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