# Prospect distance from the ground and line of sight distance between two observers

Calculates the prospect distance from height at observer and line of sight distance between two observers.

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Calculator below computes the prospect distance from height at observer and line of sight distance between two observers. Some theory is placed below the calculator.

### Prospect distance from the ground and line of sight distance between two observers

Observer height in meters

Observable object height in meters

Digits after the decimal point: 3
Prospect distance

Line of sight distance

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Prospect distance
As shown on piture, observer's view is limited by horizon - imaginary line where sky touches the earth. According to picture we can calculate distance to the horizon from Pythagoras theorem.
$d=\sqrt{(R+h)^2-R^2}=\sqrt{h(2R+h)}$
where R - is Earth radius, usually taken as 6378 kilometers.
Atmospheric refraction increases the prospect distance by over 6 percent.
The result formula is
$d=1.06*\sqrt{h(2R+h)}$

Simplified formula, which can be deduced from above, is often used
$d=2.08*\sqrt{h}$, for nautical miles or
$d=3.85*\sqrt{h}$, for kilometers

Line of sight
As shown on picture, line of sight distance is simply addition of two prospect distances.