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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 ...
For example, to find the midpoint of the path, substitute σ = 1 ⁄ 2 (σ 01 + σ 02); alternatively to find the point a distance d from the starting point, take σ = σ 01 + d/R. Likewise, the vertex, the point on the great circle with greatest latitude, is found by substituting σ = + 1 ⁄ 2 π. It may be convenient to parameterize the ...
Thus, 32 points of 11.25° each makes a circle of 360°. An object at 022.5° relative would be 'two points off the starboard bow', an object at 101.25° relative would be 'one point abaft the starboard beam' and an object at 213.75° relative would be 'three points on the port quarter'. This method is only used for a relative bearing.
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;
In theory, a person standing on the surface with eyes 1.8 metres (5 ft 11 in) above the ground can see the ground up to about 4.79 kilometres (2.98 mi) away, but a person at the top of the Eiffel Tower at 273 metres (896 ft) can see the ground up to about 58.98 kilometres (36.65 mi) away. [2]
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In astronomical navigation, the intercept method, also known as Marcq St. Hilaire method, is a method of calculating an observer's position on Earth (geopositioning).It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the azimuth line.
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