Horizon: Wikis


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A water horizon, in northern Wisconsin, USA.
View of Earth's horizon as seen from Space Shuttle Endeavour, 2002.
Water horizon (Computer graphics)

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

It is the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting intersection of earth and sky is called the visible horizon. When looking at a sea from a shore, the part of the sea closest to the horizon is called the offing.


Appearance and usage

Historically, the distance to the visible horizon at sea has been extremely important as it represented the maximum range of communication and vision before the development of the radio and the telegraph. Even today, when flying an aircraft under Visual Flight Rules, a technique called attitude flying is used to control the aircraft, where the pilot uses the visual relationship between the aircraft's nose and the horizon to control the aircraft. A pilot can also retain his or her spatial orientation by referring to the horizon.

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. 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.

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 that have an altitude of zero degrees. While similar in ways to the geometrical horizon, in this context a horizon may be considered to be a plane in space, rather than a line on a picture plane.

Distance to the horizon

Three types of horizon.
How far away is the horizon.png

Approximate formulas

The straight line of sight distance d in kilometers to the true horizon on earth is approximately

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 metres (5 ft 7 in) (average eye-level height), the horizon is at a distance of 4.7 kilometres (2.9 mi).
  • For an observer standing on a hill or tower of 100 metres (330 ft) in height, the horizon is at a distance of 36 kilometres (22 mi).
  • For an observer standing at the top of the Burj Khalifa (828 metres (2,717 ft) in height), the horizon is at a distance of 103.75 kilometres (64.47 mi).

For Imperial units, 13 is replaced by 1.5, h is in feet and d is in miles. Thus:

d = \sqrt{1.5h}


  • For observers on the ground with eye-level at h = 5 ft 7 in (5.583 ft), the horizon is at a distance of 2.89 miles (4.65 km).
  • For observers standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 12.25 miles (19.71 km).

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 high-altitude balloons. With the constants as given, both the metric and imperial formulas are precise to within 1 pc (see next section for how to derive formulas of greater precision).

More exact formula

A more 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 (R and h must be in the same units). This formula follows directly from the Pythagorean Theorem (a right triangle can be drawn with vertices at the center of the Earth, your eyes, and the point on the horizon. If h is in meters, h < < R and R is about 6378 km, then the distance in kilometers will be approximately \sqrt{2 (6378) h/1000}=\sqrt{12.756 h}.

This formula is not exact since it assumes a constant earth radius.

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


Solving for s gives the formula


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).

Geometrical horizon distance

Optical adjustments and objects above the horizon

To compute the height of an object visible above the horizon, compute the distance-to-horizon for a hypothetical observer on top of that object, and add it to the real observer's distance-to-horizon. For example, standing on the ground with h = 1.70 m, the horizon is 4.65 km away. For a tower with a height of 100 m, the horizon distance is 35.7 km. Thus an observer on a beach can see the tower as long as it is not more than 40.35 km away. Conversely, if an observer on a boat (h = 1.7 m) can just see the tops of trees on a nearby shore (h = 10 m), they are probably about 16 km away.

Note that the actual visual horizon is slightly farther away than the calculated visual horizon, due to the atmospheric refraction of light rays. 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.

Curvature of the horizon

From a point above the surface the horizon appears slightly bent. There is a basic geometrical relationship between this visual curvature κ, the altitude and the Earth's radius. It is

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

The curvature is the reciprocal of the curvature angular radius in radians. A curvature of 1 appears as a circle of an angular radius of 45° corresponding to an altitude of approximately 2640 km above the Earth's surface. At an altitude of 10 km (33,000 ft, the typical cruising altitude of an airliner) the mathematical curvature of the horizon is about 0.056, the same curvature of the rim of circle with a radius of 10 m that is viewed from 56 cm. However, the apparent curvature is less than that due to refraction of light in the atmosphere and because the horizon is often masked by high cloud layers that reduce the altitude above the visual surface.

See also

External links

Source material

Up to date as of January 22, 2010
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The Horizon
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The Horizon may refer to:

1911 encyclopedia

Up to date as of January 14, 2010

From LoveToKnow 1911

HORIZON (Gr. 6piTcov, dividing), the apparent circle around which the sky and earth seem to meet. At sea this circle is well defined, the line being called the sea horizon, which divides the visible surface of the ocean from the sky. In astronomy the horizon is that great circle of the sphere the plane of which is at right angles to the direction of the plumb line. Sometimes a distinction is made between the rational and the apparent horizon, the former being the horizon as determined by a plane through the centre of the earth, parallel to that through the station of an observer. But on the celestial sphere the great circles of these two planes are coincident, so that this distinction is not necessary (see Astronomy: Spherical). The Dip of the horizon at sea is the angular depression of the apparent sea horizon, or circle bounding the visible ocean, below the apparent celestial horizon as above defined. It is due to the rotundity of the earth, and the height of the observer's eye above the water. The dip of the horizon and its distance in sea-miles when the height of the observer's eye above the sea-level is h feet, are approximately given by the formulae: Dip=o' 97 -slh; Distance =1 m. 17 -(h. The difference between the coefficients o 97 and 1 17 arises from the refraction of the ray, but for which they would be equal.

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Simple English


File:Earth's horizon as seen from Shuttle
View of Earth's horizon as seen from Space Shuttle Endeavour, 2002.

The horizon (from Greek orizein, to limit) is the line that separates earth from sky. But at many places the true horizon cannot be seen as there are trees, buildings, mountains and so forth. The line is then called visible horizon.

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