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The horizon (Ancient Greek ὁ ὁρίζων, /ho horídzôn/, from ὁρίζειν, "to limit") is the apparent line that separates earth from sky.

More precisely, it is the line that divides all of the directions one can possibly look into two categories: those which intersect the Earth's surface, and those which do not. At many locations, the true horizon is obscured by nearby trees, buildings, mountains and so forth. The resulting intersection of earth and sky is instead described as the visible horizon. When looking at a sea from a shore, the part of the sea closest to the horizon is called the offing.

In many contexts, especially perspective drawing, the curvature of the earth is typically disregarded and the horizon is considered the theoretical line to which points on any horizontal plane converge (when projected onto the picture plane) as their distance from the observer increases. Note that, for observers near the ground, the difference between this geometrical horizon (which assumes a perfectly flat, infinite ground plane) and the true horizon (which assumes a spherical Earth surface) is typically imperceptibly small, because of the relative size of the observer. That is, if the Earth were truly flat, there would still be a visible horizon line, and, to ground based viewers, its position and appearance would not be significantly different from what we see on our curved Earth.

In astronomy the horizon is the horizontal plane through (the eyes of) the observer. It is the fundamental plane of the horizontal coordinate system, the locus of points which have an altitude of zero degrees. While similar in ways to the geometrical horizon described above, in this context a horizon may be considered to be a plane in space, rather than a line on a picture plane.

$d\; =\; sqrt\{13h\}$

where h is the height above ground or sea level (in meters) of the eye of the observer. Examples:

- For an observer standing on the ground with h = 1.70 m (average eye-level height), the horizon appears at a distance of 4.7 km.
- For an observer standing on a hill or tower of 100 m in height, the horizon appears at a distance of 36 km.

In the Imperial version of the formula, 13 is replaced by 1.5, h is in feet and d is in miles. Thus:

$d\; =\; sqrt\{1.5h\}$

Examples:

- For observers on the ground with eye-level at h = 5 ft 7 in (5.583 ft), the horizon appears at a distance of 2.89 miles.
- For observers standing on a hill or tower 100 ft in height, the horizon appears at a distance of 12.25 miles.

These formulas may be used when h is much smaller than the radius of the Earth (6371 km), including all views from any mountaintops, airplanes, or even high-altitude balloons. The metric formula is accurate to about 1%; the imperial one is more accurate still.

The exact formula for distance from the viewpoint to the horizon, applicable even for satellites, is

- $d\; =\; sqrt\{2Rh\; +\; h^2\},$

where R is the radius of the Earth (note: both R and h in this equation must be given in the same units, e.g. kilometers, but any consistent units will work).

Another relationship involves the arc length distance s along the curved surface of the Earth to the bottom of object:

- $cosfrac\{s\}\{R\}=frac\{R\}\{R+h\}.$

Solving for s gives the formula

- $s=Rcos^\{-1\}frac\{R\}\{R+h\}.$

The distances d and s are nearly the same when the height of the object is negligible compared to the radius (that is, h<<R).

Note that the actual visual horizon is slightly farther away than the calculated visual horizon, due to the slight refraction of light rays due to the atmospheric density gradient. This effect can be taken into account by using a "virtual radius" that is typically about 20% larger than the true radius of the Earth.

- $kappa=sqrt\{left(frac\{R+h\}\{R\}right)^2-1\}\; .$

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Last updated on Saturday October 04, 2008 at 05:46:29 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday October 04, 2008 at 05:46:29 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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