Geodesic Distance Calculator
Great Circle Distance: - km
Initial Bearing: -°
Understanding Geodesic Distances
What are Geodesic Distances?
Geodesic distances represent the shortest path between two points on a curved surface, such as the Earth.
Haversine Formula:
a = sin²(Δφ/2) + cos(φ₁)cos(φ₂)sin²(Δλ/2)
c = 2atan2(√a, √(1-a))
d = Rc
where:
- φ is latitude
- λ is longitude
- R is Earth's radius
- d is distance
Types of Distance Measurements
- Great Circle Distance: Shortest path on sphere
- Rhumb Line: Constant bearing path
- Vincenty Formula: Ellipsoidal model
- Karney's Algorithm: Most accurate method
- Lambert's Formula: Cylindrical projection
- Andoyer-Lambert Formula: Quick approximation
- Geodesic Inverse Problem: Path computation
- Spherical Law of Cosines: Simple calculation
Advanced Concepts
Geodesic Curvature
Path bending on surface
Christoffel Symbols
Differential geometry tools
Gauss-Bonnet Theorem
Surface integral relations
Clairaut's Theorem
Constant of motion
Applications
- Navigation: Maritime and aviation routes
- Cartography: Map projections
- GPS Systems: Position calculations
- Geophysics: Earth measurements
- Satellite Orbits: Path planning
- Telecommunications: Signal paths
- Geographic Information Systems (GIS)
- Climate Modeling: Global patterns