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Two and three body problems
by RS  admin@creationpie.com : 1024 x 640


1. Newton's theories
Newton's theory of gravity was a triumph of human thought and of mathematics. Newton's theory allows the exact mathematical solution of the interrelated motions of two heavenly bodies.

2. Two-body problem
In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. (Wikipedia)

3. Sun and earth
If the sun and earth are considered point masses, then Newton's gravitational equation can be used to determine exactly the attraction and orbit, etc., of the earth around the sun. More precisely, they both go around each other.

Sun and EarthAssume that the bodies are collapsed to points.

The theory works well for sun and earth.

4. Earth and moon
Likewise, if the earth and moon earth are considered point masses, then Newton's gravitational equation can be used to determine exactly the attraction and orbit, etc., of the moon around the earth. More precisely, they both go around each other.

Earth and MoonThe theory works well for earth and moon.

The above are called two body problems.

5. Sun, earth, and moon
However, there is a problem with more than two bodies. Sun, Earth and MoonNo one has ever been able to mathematically solve the three body problem, such as the sun, earth, and moon.

6. Weather prediction
How can a problem such as weather prediction be solved exactly? It can't. Why do we not just approximate it over time to get the solution? We can't.

Any attempt to approximate solutions result in round-off errors that accumulate and can cause the same model to vary widely based in the initial conditions.

7. End of page

by RS  admin@creationpie.com : 1024 x 640