Calculate Mountain View: Visibility of Mountains in a Line

Mountain View

Calculator for the visibility and hiding of mountains from another mountain. You are standing on mountain 1 and are looking to mountain 2 and mountain 3, which are behind each other. Here can be calculated, how many degrees each summit of the other two mountains differs from the plane line of sight and if the third mountain hides behind the second. A positive angle to the line of sight specifies a mountain above it, a negative angle shows, that the mountain is below the plane line of sight. The given Earth radius is an average value in the Alps. If you want to know only the angle to the line of sight of one mountain, leave the fields of mountain 3 empty.

Height mountain 1: meters
Height mountain 2: meters
Height mountain 3: meters
Distance mountain 1 to 2: kilometers
Distance mountain 1 to 3: kilometers
Earth radius: kilometers
Atmospheric refraktion: percent
Angle line of sight mountain 2: degrees
Angle line of sight mountain 3: degrees

The calculation of the angle is done with the law of cosines, the formula is α = arccos( (b² + c² - a²) / 2bc ) - π
where b is the distance of the first summit to Earth's center, c the distance between both mountains and a the distance of the other summit to Earth's center. You can convert length units here.
The atmospheric refraktion changes the apparent location of dictant objects, because atmospheric layers of different densities have a different refraction of light. An average value is 13 percent. During an inversion, the value is negative. The atmospheric refraktion has the effect as if Earth's diameter would be larger at the according value.

Example: You are standing on a 2850 meters high mountain (mountain 1). Mountain 2 is 2530 meters high and 16 kilometers away. Mountain 3, which is behind 2, has a height of 2680 meters at a distance of 42 kilometers. Mountain 2 is 1.22 degrees below the plane line of sight and mountain 3 is 0.42 degrees. So mountain 3 surmounts mountain 2 for 0.8 degrees - which is a bit more than the the full moon with its size of half a degree.

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