Look Angle Calculator

Formula

The formula to calculate the look angle (θ) is:

\[ θ = \cos^{-1}\left(\frac{R + h}{R + d}\right) \]

Where:

\( θ \) is the look angle in degrees
\( R \) is the radius of the Earth in kilometers
\( h \) is the altitude of the satellite in kilometers
\( d \) is the distance to the horizon in kilometers

Definitions

Look Angle: The angle between the line of sight to a satellite and the horizontal plane at the observer’s location. It is crucial for determining the orientation of the antenna needed to establish a link with the satellite.

Example

Let's say the radius of the Earth (R) is 6371 km, the altitude of the satellite (h) is 500 km, and the distance to the horizon (d) is 1000 km. Using the formula:

\[ θ = \cos^{-1}\left(\frac{6371 + 500}{6371 + 1000}\right) \]

We get:

\[ θ \approx 21.22\, \text{degrees} \]

So, the look angle is approximately 21.22 degrees.