Use our Satellite Slant Range Calculator to accurately determine the line-of-sight distance between an earth station and a geostationary or non-geostationary satellite. This essential tool helps in designing communication links and antenna pointing, factoring in satellite altitude and the precise geographic positions of both the earth station and the sub-satellite point for reliable calculations.
Formula:
Slant Range (S) = √(R² + (R+h)² - 2 · R · (R+h) · cos(θ))
Where:
- R = Earth's Mean Radius (approximately 6371 km)
- h = Satellite Altitude above Earth's surface (km)
- θ = Central Angle between Earth Station and Sub-Satellite Point (radians)
θ is calculated using the spherical law of cosines:
θ = arccos(sin(φes)sin(φssp) + cos(φes)cos(φssp)cos(Δλ))
Where:
- φes = Earth Station Latitude (radians)
- φssp = Sub-Satellite Point Latitude (radians)
- Δλ = Absolute difference in Longitude between Earth Station and Sub-Satellite Point (radians)