ho·ri·zon
/həˈraɪzən/ Pronunciation Key -
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–noun
1. the line or circle that forms the apparent boundary between earth and sky.
2. Astronomy. a. the small circle of the celestial sphere whose plane is tangent to the earth at the position of a given observer, or the plane of such a circle (sensible horizon).
b. Also called rational horizon. the great circle of the celestial sphere whose plane passes through the center of the earth and is parallel to the sensible horizon of a given position, or the plane of such a circle (celestial horizon).
3. the limit or range of perception, knowledge, or the like.
4. Usually, horizons. the scope of a person's interest, education, understanding, etc.: His horizons were narrow.
5. Geology. a thin, distinctive stratum useful for stratigraphic correlation.
6. any of the series of distinctive layers found in a vertical cross section of any well-developed soil.
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http://dictionary.reference.com/browse/horizons
Question
How far away is the horizon?
Answer
The answer depends on whether you define the distance as the straight, line-of-sight distance (from your eyes to the horizon), or as the distance along the planet's surface from the nearest point on the surface directly beneath your feet (well, straight down to sea level) to the horizon (i.e. the distance that you'd have to walk to get there).
At a height h above the surface of a spherical planet of radius rp:
The straight-line distance to the horizon:
The curved distance along the planet's (sea-level) surface to the horizon:
Of course, for small heights relative to the radius of the planet, these two are approximately equal.
Calculator
Enter the height above the surface and the radius of the planet (Earth is given as an example) to calculate the distance to the horizon using the above two formulae:
Height above surface h = m
Radius of the planet rp = km
Straight-line distance ds = km
Curved-surface distance dc = km
Example: the Earth