"""
Example 13: Circular Motion & Orbits (Phase 2.3)
Demonstrates circular motion calculations including:
- Centripetal force
- Orbital mechanics
- Banking angles
- Escape velocity
- Complete orbital analysis
No external services required - uses analytic provider.
"""
import asyncio
from chuk_mcp_physics.tools.circular_motion import (
calculate_centripetal_force,
calculate_banking_angle,
calculate_escape_velocity,
analyze_circular_orbit,
)
async def main():
print("\n" + "=" * 70)
print("CIRCULAR MOTION & ORBITS EXAMPLES (Phase 2.3)")
print("=" * 70)
# Example 1: Centripetal Force - Car turning
print("\n1. Centripetal Force - Car on Curved Road")
print("-" * 70)
result = await calculate_centripetal_force(
mass=1500.0, # kg
velocity=20.0, # m/s (~72 km/h)
radius=50.0, # m
)
print("Scenario: 1500 kg car turning at 20 m/s on 50m radius curve")
print("\nRESULTS:")
print(f" Centripetal force: {result['centripetal_force']:.0f} N")
print(f" Centripetal acceleration: {result['centripetal_acceleration']:.1f} m/s²")
print(f" As fraction of g: {result['centripetal_acceleration'] / 9.81:.2f}g")
print(" Tire friction must provide this force!")
# Example 2: ISS Orbital Period
print("\n\n2. International Space Station Orbit")
print("-" * 70)
result = await analyze_circular_orbit(
altitude=408000.0, # 408 km
planet_mass=5.972e24, # Earth mass
planet_radius=6.371e6, # Earth radius
)
print("ISS Altitude: 408 km above Earth")
print("\nOrbital Properties:")
print(f" Orbital radius: {result['orbital_radius'] / 1000:.0f} km")
print(
f" Orbital velocity: {result['orbital_velocity']:.0f} m/s ({result['orbital_velocity'] * 3.6:.0f} km/h)"
)
print(
f" Period: {result['period_seconds']:.0f} seconds ({result['period_minutes']:.1f} minutes)"
)
print(f" Orbits per day: {86400 / result['period_seconds']:.1f}")
# Example 3: Banking Angle for Highway Curve
print("\n\n3. Optimal Banking Angle - Highway Design")
print("-" * 70)
speeds_kmh = [60, 80, 100, 120]
radius = 200.0 # m
print(f"Curve radius: {radius} m")
print(f"\n{'Speed (km/h)':<15} {'Speed (m/s)':<15} {'Banking Angle':<20}")
print("-" * 70)
for speed_kmh in speeds_kmh:
speed_ms = speed_kmh / 3.6
result = await calculate_banking_angle(velocity=speed_ms, radius=radius)
print(f"{speed_kmh:<15} {speed_ms:<15.1f} {result['angle_degrees']:<20.1f}°")
# Example 4: Escape Velocities
print("\n\n4. Escape Velocities - Various Celestial Bodies")
print("-" * 70)
bodies = [
("Moon", 7.342e22, 1.737e6),
("Earth", 5.972e24, 6.371e6),
("Jupiter", 1.898e27, 6.9911e7),
("Sun", 1.989e30, 6.96e8),
]
print(f"\n{'Body':<15} {'Mass (kg)':<20} {'Radius (km)':<15} {'Escape Velocity':<20}")
print("-" * 70)
for name, mass, radius in bodies:
result = await calculate_escape_velocity(mass=mass, radius=radius)
print(
f"{name:<15} {mass:<20.2e} {radius / 1000:<15.0f} {result['escape_velocity']:.0f} m/s ({result['escape_velocity'] * 3.6:.0f} km/h)"
)
# Example 5: Geostationary Orbit
print("\n\n5. Geostationary Satellite Orbit")
print("-" * 70)
print("Finding altitude for 24-hour orbital period...")
# Geostationary: T = 24 hours = 86400 seconds
# From T² = (4π²/GM) * r³, solve for r
G = 6.674e-11
M_earth = 5.972e24
T_geo = 86400.0
r_orbit = ((G * M_earth * T_geo**2) / (4 * 3.14159**2)) ** (1 / 3)
altitude = r_orbit - 6.371e6
result = await analyze_circular_orbit(
altitude=altitude, planet_mass=M_earth, planet_radius=6.371e6
)
print("\nGeostationary Orbit:")
print(f" Altitude: {altitude / 1000:.0f} km")
print(f" Orbital radius: {result['orbital_radius'] / 1000:.0f} km")
print(f" Orbital velocity: {result['orbital_velocity']:.0f} m/s")
print(f" Period: {result['period_seconds'] / 3600:.1f} hours")
print(" ✓ Stays above same point on Earth's equator!")
print("\n" + "=" * 70)
print("Phase 2.3 Complete! ✓")
print("=" * 70 + "\n")
if __name__ == "__main__":
asyncio.run(main())
