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The height of the elevated point plus the Earth radius form its hypotenuse. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles.
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.
In geometry, visibility is a mathematical abstraction of the real-life notion of visibility.. Given a set of obstacles in the Euclidean space, two points in the space are said to be visible to each other, if the line segment that joins them does not intersect any obstacles.
Early in World War II, target range and bearing measurements were taken over a period of time and plotted manually on a chart. [14] The speed and course of the target could be computed using the distance the target traveled over an interval of time. During the latter part of World War II, the speed of the target could be measured using radar data.
The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides. [2] [3]: 14
An analemma can be pictured by superimposing photographs taken at the same time of day, a few days apart for a year. An analemma can also be considered as a graph of the Sun's declination, usually plotted vertically, against the equation of time, plotted horizontally. Usually, the scales are chosen so that equal distances on the diagram ...
The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship, = where F is flux (W·m −2), and L is luminosity (W). From this the luminosity distance (in meters ...
Image distance in a spherical mirror + = () Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
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