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For an observer standing on a hill or tower 100 metres (330 ft) above sea level, the horizon is at a distance of 36 kilometres (22 mi). For an observer standing on the roof of the Burj Khalifa, 828 metres (2,717 ft) from ground, and about 834 metres (2,736 ft) above sea level, the horizon is at a distance of 103 kilometres (64 mi).
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;
Without taking into account the refraction through the atmosphere, the radar horizon would be the geometrical distance from the radar to the horizon only taking into account the height of the radar above sea-level, and the radius of the earth (approximately 6.4·10 3 km):
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 ...
At sea level, the Rayleigh atmosphere has an extinction coefficient of approximately 13.2 × 10 −6 m −1 at a wavelength of 520 nm. This means that in the cleanest possible atmosphere, visibility is limited to about 296 km. Visibility perception depends on several physical and visual factors.
A typical example of long-distance observation. The Tatra Mountains as seen from the Łysa Góra, in southeast Poland, at a distance of about 200 km (120 mi).. Long-distance observation is any visual observation, for sightseeing or photography, that targets all the objects, visible from the extremal distance with the possibility to see them closely.
[2] [3] It is also close to the distance to the visible horizon as observed from sea level by a person about six feet tall, so is the limit of what is visible from land. Since the mid-20th century, numerous nations have claimed territorial waters well beyond the traditional three-mile limit.
Using Earth's mean radius of 6371 km, the sea-level air mass at the horizon is = +. The homogeneous spherical model slightly underestimates the rate of increase in air mass near the horizon; a reasonable overall fit to values determined from more rigorous models can be had by setting the air mass to match a value at a zenith angle less than 90°.