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View of the ocean with two ships: one in the foreground and one to the left of it on the horizon. Historically, the distance to the visible horizon has long been vital to survival and successful navigation, especially at sea, because it determined an observer's maximum range of vision and thus of communication, with all the obvious consequences for safety and the transmission of information ...
Assuming a perfect sphere with no terrain irregularity, the distance to the horizon from a high altitude transmitter (i.e., line of sight) can readily be calculated. Let R be the radius of the Earth and h be the altitude of a telecommunication station. The line of sight distance d of this station is given by the Pythagorean theorem;
Graphs of distances to the true horizon on Earth for a given height h. s is along the surface of Earth, d is the straight line distance, and ~d is the approximate straight line distance assuming h << the radius of Earth, 6371 km. In the SVG image, hover over a graph to highlight it.
On one side, there is a view of the horizon; on the other side, a view of the celestial object. The advantage of this type is that both the horizon and celestial object are bright and as clear as possible. This is superior at night and in haze, when the horizon and/or a star being sighted can be difficult to see.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
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Horizon distance graphs: Image title: Graphs of distances to the true horizon on Earth for a given height above sea level, h by CMG Lee. s is along the surface of the Earth, d is the straight line distance, and ~d is the approximate straight line distance assuming h << the radius of the Earth, 6371 km. In the SVG image, hover over a graph to ...
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