Atmospheric Refraction - Values

Values

Atmospheric refraction is zero in the zenith, less than 1′ (one arcminute) at 45° apparent altitude, and still only 5.3′ at 10° altitude; it quickly increases as altitude decreases, reaching 9.9′ at 5° altitude, 18.4′ at 2° altitude, and 35.4′ at the horizon (Allen 1976, 125); all values are for 10 °C and 101.3 kPa in the visible part of the spectrum.

On the horizon, refraction is slightly greater than the apparent diameter of the Sun. Therefore when it appears that the full disc of the sun is just above the horizon, if it weren't for the atmosphere, no part of the sun's disc would be visible. By convention, sunrise and sunset refer to times at which the Sun’s upper limb appears on or disappears from the horizon; the standard value for the Sun’s true altitude is −50′: −34′ for the refraction and −16′ for the Sun’s semidiameter (the altitude of a celestial body is normally given for the centre of the body’s disc). In the case of the Moon, additional corrections are needed for the Moon’s horizontal parallax and its apparent semidiameter; both vary with the Earth–Moon distance.

Day-to-day variations in the weather will affect the exact times of sunrise and sunset (Schaefer and Liller 1990) as well as moonrise and moonset, and for that reason it generally is not meaningful to give rise and set times to greater precision than the nearest minute (Meeus 1991, 103). 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 (for example Meeus 2002, 315) if it is understood that actual changes may differ because of unpredictable variations in refraction.

Because atmospheric refraction is 34′ on the horizon itself, but only 29′ at 0.5° above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter).