- vCommons Home
- Angle of Satellite Visibility

# Angle of Satellite Visibility

eng.Angle of Satellite Visibility

The **Angle of Satellite Visibility** calculator computes the angular extent of visibility when an observer can see a satellite based on the altitude (h) of the satellite.

**INSTRUCTIONS**: Choose units and enter the following:

- (
**h**) This is the altitude of the satellite

**Angle of Visibility (η):** The calculator returns the angle in degrees. However this can be automatically converted to compatible units via the pull-down menu.

#### The Math / Science

The Earth's shape is approximated as a sphere in this calculation. USING THE CALCULATOR, `h` is the height of the viewing location.

`delta`is the minimum elevation limit of your line-of-sight to the satellite. the minimum elevation angle could represent obstruction in the line-of-sight. `delta` defaults to 0 degrees.

If you are looking at the horizon from the top of a mountain, the height of the viewing location should be the height of the mountain plus the height of your eye or viewing instrument.

This equation uses the radius of the Earth (`R_E`) and the altitude of the location from which the horizon is observed (`h`).

Since the site line is tangent to the circle, the triangle including angle `alpha` is a right triangle. The angle, `alpha`, can be computed with line through the tangent point having a length equal to the Earth's radius. The hypotenuse of the triangle is then the sum of the radius of the Earth and the altitude of the viewing location.

`R_E` is the radius of the Earth, which is the vCalc constant: Earth - mean spherical radius (Km)

`h` is the height above the Earth's mean radius

cosine (`alpha`) = `R_E / (R_E + h) -> alpha` = acos (`R_E / (R_E + h)`) = η

Once we know the angle `alpha`, we use the fact that both triangles including `alpha` and the triangles including `beta` are all right triangles. So, we can compute `c_1` and `c_2` using the Pythagorean theorem:

`c_1 = tan(alpha) / R_E = `

`c_2 = tan(beta) / R_E `

`c = c_1 + c_2 = tan(alpha) * R_E +tan(beta) * R_E`

`c/R_E = tan(alpha) +tan(beta)`

**EXAMPLE**

If we were to view the horizon from the top of a mountain that is 3 kilometers at its summit, this Central Angle of Horizon equation would tell us the central angle of the tangent point at the horizon is approximately 3.51591974 degrees from the viewing location.

**3D Vector Calculator Functions:**

- Slant Range using Position Vectors
- Slant Range from Elevation Angle (α)
- Slant Range using Subtended Angle (β)
- Distance to Horizon
- Angle of Satellite Visibility
- Grazing Angle
- XYZ to Lat/Lon/Altitude
**k V**- scalar multiplication**V / |V|**- Computes the**Unit Vector****|V|**- Computes the**magnitude of a vector****U + V**- Vector addition**U - V**- Vector subtraction**|U - V|**- Distance between vector endpoints.**|U + V|**- Magnitude of vector sum.**V • U**- Computes the dot product of two vectors**V x U**- Computes the cross product of two vectors**Vector Angle**- Computes the angle between two vectors**Vector Projection**- Compute the vector projection of V onto U.**Vector Rotation**- Compute the result vector after rotating around an axis.**(ρ, θ, φ) to (x,y,z)**- Spherical to Cartesian coordinates**(x,y,z) to (ρ, θ, φ)**- Cartesian to Spherical coordinates**(r, θ, z) to (x,y,z)**- Cylindrical to Cartesian coordinates**(x,y,z) to (r, θ, z)**- Cartesian to Cylindrical coordinates- Central Angle of Horizon
- Great Circle Central Angle
- Distance to Horizon

**Angle of Satellite Visibility**, references 2 equations/constants.

**Equations and Constants **