Jul 12, 2024

- Explanation without references to any streaming services
- Focus on the scientific explanation of the three-body problem

**Concept**: Earth and Moon orbit their common center of gravity- This center is 1000 miles beneath Earth's surface
- Causes Earth to jiggle as the Moon orbits

**Equations**: Solved using equations of gravity and mechanics (Isaac Newton)**Application**: Earth-Moon system around the Sun- Ignoring the Moon, it's another two-body system

**Concern**: Jupiter's gravitational tugs on Earth- Worry about system instability leading to chaos

**Newton's Conclusion**: System must be stable since it's still here- Claimed that God occasionally 'fixes' things
- Hint of complexity introduced by a third body

**Developed by**: Lagrange and others, inspired by Newton**Concept**: Two-body system with small, repeated tugs from a third body- Small tugs from Jupiter are averaged out, creating stability

**Outcome**: Solar system is stable in ways Newton hadn't imagined

- Napoleon read books on Celestial Mechanics
- Questioned lack of mention of God; Lagrange replied, "I had no need for that hypothesis"

**Scenario**: Double star system with a third similar mass star- Chaotic orbits result from gravitational interactions
- System becomes unstable; collisions or ejections occur

**Chaos Theory**: Slight differences in initial conditions lead to exponentially different outcomes

**Scenario**: Two larger masses with one much smaller mass- Example: Star Wars (Two stars with a planet)
- The small body doesn't disrupt the system significantly

**Outcome**: Solvable scenario allows stability- Planet sees merged gravity of two stars if far enough away, resulting in stable orbit
- Close proximity causes instability due to gravitational tug-of-war

**Concept**: Even with perturbation theory, long-term system can be chaotic**Example**: Jupiter's interactions with Earth- Very long timescales show eventual chaos

**Main takeaway**: The three-body problem is fundamentally unsolvable- System is innately chaotic and unpredictable
- Approximations and statistical models used for predictions

**Future challenges**: Tracking individual objects through chaotic systems is not feasible beyond statistical modeling

Keep looking up!