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