Astronomical refraction [ edit ] Atmospheric refraction distorting the Sun’s disk into an uneven shape as it sets in the lower horizon. 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. 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. 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.

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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. 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. Whenever possible, astronomers will schedule their observations around the times of culmination, when celestial objects are highest in the sky. Refraction not only affects visible light rays, but all electromagnetic radiation, although in varying degrees. 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.displaystyle R=(n_{0}-1)(1-H_{0})\cot h_{\mathrm {a} }-(n_{0}-1)[H_{0}-{\frac {1}{2}}(n_{0}-1)]\cot 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. 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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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. 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 considered in measuring the position of both celestial and terrestrial objects. 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.