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Young [6] [11] distinguished several regions where different methods for calculating astronomical refraction were applicable. 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. 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 . above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter).

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If the atmosphere suddenly vanished at this moment, one couldn't see the sun, as it would be entirely below the horizon. 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. Surveyors, on the other hand, will often schedule their observations in the afternoon, when the magnitude of refraction is minimum. 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. Atmospheric refraction is considered in measuring the position of both celestial and terrestrial objects.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.

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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. This refraction is due to the velocity of light through air decreasing (the refractive index increases) with increased density. Between 20° and 5° of the horizon the temperature gradient becomes the dominant factor and numerical integration, using a method such as that of Auer and Standish [12] and employing the temperature gradient of the standard atmosphere and the measured conditions at the observer, is required. 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.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. 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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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. 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. 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. 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.

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. Astronomical or celestial refraction causes astronomical objects to appear higher above the horizon than they actually are. 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. 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.