Calculate the great-circle distance between two geographic coordinates:
d = 2R × arcsin(√(sin²(Δφ/2) + cos(φ₁)cos(φ₂)sin²(Δλ/2)))
Where:
d= distance between two points (meters)R= Earth's radius (6,371,000 meters)φ₁, φ₂= latitude of point 1 and point 2 (radians)Δφ= φ₂ - φ₁ (difference in latitude)Δλ= λ₂ - λ₁ (difference in longitude)
Theoretical maximum range for projectile motion:
R = (v₀² × sin(2θ)) / g
Where:
R= maximum range (meters)v₀= initial velocity (690 m/s for BM-21)θ= launch angle (45° for optimal range)g= gravitational acceleration (9.81 m/s²)
Total flight time for projectile:
t = (2v₀ × sin(θ)) / g
Peak altitude reached by projectile:
h = (v₀² × sin²(θ)) / (2g)
Parametric equations for projectile path:
x(t) = v₀ × cos(θ) × t
y(t) = v₀ × sin(θ) × t - (1/2) × g × t²
- Jane's Infantry Weapons 2023-2024 - BM-21 Grad MLRS specifications
- NATO STANAG 4355 - Artillery ballistic standards
- Soviet Military Technical Manual TM-21 - BM-21 operational parameters
- Katyusha Multiple Rocket Launchers 1941-Present by Steven J. Zaloga
- Artillery Survey and Target Acquisition - NATO standardization agreement
- Ballistics: Theory and Design of Guns and Ammunition by Donald E. Carlucci
- World Geodetic System 1984 (WGS84) - Coordinate reference system
- SRTM Digital Elevation Model - Terrain elevation data
- OpenStreetMap - Geographic coordinate verification
- Classical Mechanics by Herbert Goldstein - Projectile motion theory
- Introduction to Ballistics by Carlucci & Jacobson
- Handbook of Ballistics by Carl Cranz
- Spherical Trigonometry by I.S. Sokolnikoff
- Mathematical Methods for Physicists by Arfken & Weber
- Numerical Methods in Engineering by Steven C. Chapra
- Latitude: 14.355600°N
- Longitude: 103.258600°E
- Source: GPS coordinates, WGS84 datum
- Latitude: 14.6048725°N
- Longitude: 104.643772°E
- Source: PTT Gas Station location, verified via satellite imagery
- Link: https://maps.app.goo.gl/8MVJ35XcKw2hqKgu5
| Parameter | Value | Unit | Source |
|---|---|---|---|
| Earth Radius | 6,371,000 | meters | WGS84 |
| Gravity | 9.81 | m/s² | Standard |
| BM-21 Muzzle Velocity | 690 | m/s | Jane's Infantry Weapons |
| BM-21 Max Range | 15,000 | meters | Military specifications |
| Optimal Launch Angle | 45 | degrees | Ballistics theory |
- Geographic Distance: 142.3 km (Haversine formula)
- BM-21 Maximum Range: 15.0 km (Military specification)
- Range Deficit: 127.3 km
- Impossibility Factor: 9.5× beyond maximum capability
- Physics Violation: 849% over theoretical limits
Mathematical analysis definitively proves that BM-21 rockets launched from Cambodia cannot reach targets in Thailand due to fundamental physics limitations and geographic distance constraints.