Neil deGrasse Tyson Explains The Three Body Problem

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# title: "The Three-Body Problem: Unraveling the Chaos of Celestial Mechanics"

Key takeaways:

1. The three-body problem is a fundamental problem in celestial mechanics that involves the motion of three celestial bodies that interact with each other through gravity.
2. The problem is mathematically chaotic, meaning that small changes in initial conditions can lead to drastically different outcomes.
3. The restricted three-body problem, where one body is much smaller than the other two, is solvable, but the general three-body problem is not.

The Two-Body Problem

• The Moon and Earth orbit their common center of gravity, which is located about 1,000 miles beneath the Earth's surface.
• The two-body problem is perfectly solved using equations of gravity and mechanics.
• Isaac Newton solved the two-body problem, and it has been successfully applied to the Earth-Moon system and the Earth-Sun system.

The Three-Body Problem

• The three-body problem arises when a third body, such as Jupiter, interacts with the Earth and the Sun.
• The three-body problem is mathematically chaotic, meaning that small changes in initial conditions can lead to drastically different outcomes.
• The three-body problem is unsolvable, meaning that it is impossible to predict the exact motion of the three bodies over time.

The Restricted Three-Body Problem

• The restricted three-body problem is a special case where one body is much smaller than the other two.
• The restricted three-body problem is solvable, and it has been applied to the motion of a planet in a double star system.
• The planet's orbit is stable because it is far enough away from the two stars that it only sees one merged gravity.

Chaos and the Three-Body Problem

• The three-body problem is chaotic because small changes in initial conditions can lead to drastically different outcomes.
• The chaos of the three-body problem means that it is impossible to predict the exact motion of the three bodies over time.
• Instead, astronomers use statistical models to predict the behavior of the system over time.

Conclusion

• The three-body problem is a fundamental problem in celestial mechanics that has been studied for centuries.
• The problem is mathematically chaotic, and it has led to important insights into the behavior of celestial systems.
• The three-body problem has been explored in science fiction, and it continues to fascinate scientists and science fiction fans alike.

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