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Refraction near the horizon is highly variable, principally because of the variability of the temperature gradient near the Earth's surface and the geometric sensitivity of the nearly horizontal rays to this variability. Below the astronomical horizon, refraction is so variable that only crude estimates of astronomical refraction can be made; for example, the observed time of sunrise or sunset can vary by several minutes from day to day. Young [6] [11] distinguished several regions where different methods for calculating astronomical refraction were applicable. A further expansion in terms of the third power of the cotangent of the apparent altitude incorporates H 0, the height of the homogeneous atmosphere, in addition to the usual conditions at the observer: [17] R = ( n 0 − 1 ) ( 1 − H 0 ) cot ⁡ h a − ( n 0 − 1 ) [ H 0 − 1 2 ( n 0 − 1 ) ] cot 3 ⁡ h a . Surveyors, on the other hand, will often schedule their observations in the afternoon, when the magnitude of refraction is minimum.

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Astronomical refraction deals with the angular position of celestial bodies, their appearance as a point source, and through differential refraction, the shape of extended bodies such as the Sun and Moon. Many different formulas have been developed for calculating astronomical refraction; they are reasonably consistent, differing among themselves by a few minutes of arc at the horizon and becoming increasingly consistent as they approach the zenith. As early as 1830, Friedrich Bessel had found that even after applying all corrections for temperature and pressure (but not for the temperature gradient) at the observer, highly precise measurements of refraction varied by ±0. In the upper portion of the sky, with a zenith distance of less than 70° (or an altitude over 20°), various simple refraction formulas based on the index of refraction (and hence on the temperature, pressure, and humidity) at the observer are adequate. Since the amount of atmospheric refraction is a function of the temperature gradient, temperature, pressure, and humidity (the amount of water vapor, which is especially important at mid- infrared wavelengths), the amount of effort needed for a successful compensation can be prohibitive.In the case of the Moon, additional corrections are needed for the Moon's horizontal parallax and its apparent semi-diameter; both vary with the Earth–Moon distance.

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This refraction is due to the velocity of light through air decreasing (the refractive index increases) with increased density. Astronomical or celestial refraction causes astronomical objects to appear higher above the horizon than they actually are. This causes suboptimal seeing conditions, such as the twinkling of stars and various deformations of the Sun's apparent shape soon before sunset or after sunrise. Atmospheric refraction of the light from a star is zero in the zenith, less than 1′ (one arc-minute) at 45° apparent altitude, and still only 5. above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter).A quarter of an hour later the unreasonable visitor disappeared again, only to rise again at 11:40 am, set at 1 pm, rise at 1:10 pm and set lingeringly at 1:20 pm. The sun which had made ‘positively his last appearance’ seven days earlier surprised us by lifting more than half its disk above the horizon on May 8.

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Atmospheric refraction becomes more severe when temperature gradients are strong, and refraction is not uniform when the atmosphere is heterogeneous, as when turbulence occurs in the air. Whenever possible, astronomers will schedule their observations around the times of culmination, when celestial objects are highest in the sky. displaystyle R=(n_{0}-1)(1-H_{0})\cot h_{\mathrm {a} }-(n_{0}-1)[H_{0}-{\frac {1}{2}}(n_{0}-1)]\cot Refraction not only affects visible light rays, but all electromagnetic radiation, although in varying degrees. By convention, sunrise and sunset refer to times at which the Sun's upper limb appears on or disappears from the horizon and the standard value for the Sun's true altitude is −50′: −34′ for the refraction and −16′ for the Sun's semi-diameter.More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction [note 1] if it is understood that actual changes may differ because of unpredictable variations in refraction. If the atmosphere suddenly vanished at this moment, one couldn't see the sun, as it would be entirely below the horizon. On the horizon refraction is slightly greater than the apparent diameter of the Sun, so when the bottom of the sun's disc appears to touch the horizon, the sun's true altitude is negative. where R is the refraction in radians, n 0 is the index of refraction at the observer (which depends on the temperature, pressure, and humidity), and h a is the apparent altitude angle of the astronomical body. If observations of objects near the horizon cannot be avoided, it is possible to equip an optical telescope with control systems to compensate for the shift caused by the refraction.

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Day-to-day variations in the weather will affect the exact times of sunrise and sunset [8] as well as moon-rise and moon-set, and for that reason it generally is not meaningful to give rise and set times to greater precision than the nearest minute. Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. If the dispersion is also a problem (in case of broadband high-resolution observations), atmospheric refraction correctors (made from pairs of rotating glass prisms) can be employed as well. Atmospheric refraction is considered in measuring the position of both celestial and terrestrial objects. Terrestrial refraction usually causes terrestrial objects to appear higher than they actually are, although in the afternoon when the air near the ground is heated, the rays can curve upward making objects appear lower than they actually are.Such refraction can also raise or lower, or stretch or shorten, the images of distant objects without involving mirages.