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As The Nautical Almanac notes, "the actual values of …the refraction at low altitudes may, in extreme atmospheric conditions, differ considerably from the mean values used in the tables. above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter). 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. Astronomical or celestial refraction causes astronomical objects to appear higher above the horizon than they actually are. 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.
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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 . 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. 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. 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. 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.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. 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.
Atmospheric refraction - Wikipedia
where R is the refraction in seconds of arc, b is the atmospheric pressure in millimeters of mercury, and t is the temperature in Celsius. Whenever possible, astronomers will schedule their observations around the times of culmination, when celestial objects are highest in the sky. 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. 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. displaystyle R=(n_{0}-1)(1-H_{0})\cot h_{\mathrm {a} }-(n_{0}-1)[H_{0}-{\frac {1}{2}}(n_{0}-1)]\cot 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. 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. 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.
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