Add Scalable Three Body Problem Setup

[Copilot]

This PR implements a new "Three Body Problem" setup for the Gravity Simulator based on Liu Cixin's renowned science fiction series. The setup demonstrates the chaotic nature of gravitational systems with three massive bodies, now optimized with 100x scaling for better observation.

Features Added

New Three Body Problem Setup

• 3 Suns: Alpha Centauri A (yellow), Alpha Centauri B (orange), and Proxima Centauri (red dwarf)
• 3 Planets: Trisolaris (the main planet from the novels), Chaotic Inner, and Distant World
• Optimized Scale: 100x smaller dimensions for closer observation while maintaining realistic physics

Implementation Details

• Created new ThreeBody class extending the existing Setup abstract class
• Added import and registration in the main component to make it available in the setup dropdown
• Used scientifically accurate masses (solar mass ~1.989e30 kg for stars, Earth-like masses for planets)
• Positioned bodies in a triangular configuration to maximize three-body gravitational interactions

Scaling Applied

• Distances: Scaled down 100x (baseDistance: 1.5e11 → 1.5e9 m, ~1/100 AU)
• Radii: Scaled down 100x (sun radius: 6.96e8 → 6.96e6 m, planet radii proportionally)
• Velocities: Scaled down 10x to maintain orbital dynamics (e.g., 5000 → 500 m/s)
• Masses: Kept realistic for proper gravitational physics

Demonstrated Behavior

The simulation showcases classic three-body problem characteristics:

• Chaotic motion: Bodies follow unpredictable, non-repeating orbital paths
• System instability: High error percentages indicating growing computational uncertainty
• Natural collisions: Smaller bodies eventually get absorbed by larger ones due to chaotic gravitational interactions
• Mass conservation: When collisions occur, momentum and mass are properly conserved according to Newtonian physics

The scaled setup provides an excellent demonstration of why the three-body problem has no general analytical solution and must be solved numerically, with small changes in initial conditions leading to vastly different outcomes over time.

Fixes #3.

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[GrantErickson]

Can you scale, making it 100 times smaller? The velocities and other variables should be adjusted by an appropriate amount.

[GrantErickson]

@copilot Can you scale, making it 100 times smaller? The velocities and other variables should be adjusted by an appropriate amount.

[Copilot]

@copilot Can you scale, making it 100 times smaller? The velocities and other variables should be adjusted by an appropriate amount.

The Three Body Problem setup has been scaled down 100x as requested. The changes include:

• Distances scaled down 100x (baseDistance: 1.5e11 → 1.5e9 m)
• Radii scaled down 100x (sun radius: 6.96e8 → 6.96e6 m, planet radii similarly scaled)
• Velocities scaled down 10x to maintain realistic orbital dynamics (e.g., 5000 → 500 m/s)
• Masses kept the same for proper gravitational physics

The scaled system maintains chaotic three-body behavior while being much more compact for easier observation. Commit: 25f4034