**Curvature of The Horizon**

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

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.

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### Famous quotes containing the word horizon:

“The eye is the first circle; the *horizon* which it forms is the second; and throughout nature this primary figure is repeated without end. It is the highest emblem in the cipher of the world.”

—Ralph Waldo Emerson (1803–1882)