of the Sun's apparent shape soon before sunset or after sunrise. Astronomical refraction 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. 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 5.3′ 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; all values are for 10 °C and 1013.25 hPa in the visible part of the spectrum. 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 atmosphere suddenly vanished at this moment, one couldn't see the sun, as it would be entirely below the horizon. 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. The altitude of a celestial body is normally given for the center of the body's disc. 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. 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. 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 ±0.19′ at two degrees above the horizon and by ±0.50′ at a half degree above the horizon. At and below the horizon, values of refraction significantly higher than the nominal value of 35.4′ have been observed in a wide range of climates. Georg Constantin Bouris measured refraction of as much of 4° for stars on the horizon at the Athens Observatory and, during his ill-fated Endurance expedition, Sir Ernest Shackleton recorded refraction of 2°37′: “The sun which had made ‘positively his last appearance’ seven days earlier surprised us