Analemma

The term analemma (Greek for the pedestal of a sundial ) is most commonly used for the character that generates the Sun at constant Mean local time. This figure is produced for example by photos of the sun ( which also means: to the same zone time in the same place ) one day at the same local time average over a year makes. The superposition of all these sun- images after one year in a photo montage, you can see an elongated eight (see figure): the analemma.

In the gnomonic, the theory of sundials, the analemma is a specified by Vitruvius provision for the construction of sundials.

The positions of the sun as analemma

The analemma leading to the apparent variation of the sun is a result of two motions of the earth. If the orbit of the Earth, an exact circle and would the earth axis perpendicular to the orbital plane, then the sun befände daily at the same instant a uniform running time always at the same point in the sky (also not different in height, because it would be no seasons ). The orbit of the earth, however, is elliptical, and the deviation of the apparent plane of the path of the sun, called ecliptic of the celestial equator ( projection of the equator of the sky ) is approximately 23.5 °. This differs from the sun in one year from this point and sweep once through a figure with the shape of an "8 ", the analemma.

The above photo montage shows throughout the year various positions of the sun about 9 clock CET on about the 8th Eastern Längenengrad and about the 49th degree of north latitude, where the sun is lower, wider part of the double loop ( "8") from early September to opposite the middle of April clockwise, the upper, narrower part from mid-April to early September through it. The deviation from the indicated auxiliary line is expressed using the equation of time pre- or pursue the true solar time ( local apparent time (LAT ) ) from the artificial mean solar time ( " mechanical time " mean time (LMT ) ). The adjacent time equation graph is stretched compared to the above photomontage in width, the analemma is only included schematically in him.

The analemma figure was general meaning only through the invention and use of the principle uniformly ongoing mechanical clock at the end of the Middle Ages. In ancient times, was the apparent movement of the sun itself commonly -used time scale. Your slightly uneven run was accepted or was not known to the general public.

The analemma on sundials

In sundials with point display the Mean time (LMT ) is read, if instead of a straight hour lines analemma " figure eights " are plotted. In order to improve the clarity of this, you divide the "eight - figure" often into two loops, each of which is valid for half a year.

The sundial was shown on September 21, that is, near the equinox, when the date line is a straight line (zodiac sign of Libra and Aries ), photographed. It was about 17 clock in the afternoon (CET ), which is displayed just outside this sundial.

The analemma of Vitruvius

In the ninth of his Ten Books on Architecture Vitruvius indicates how sundials using a figure that he called analemma can be constructed. He describes how the analemma is to draw only when using ruler and compass. His example is for Rome, he begins with the ratio of shadow length to Gnomonhöhe as it is valid there to the equinoxes. The Gnomonspitze located in the center of the circle A, which represents the meridian of the location. From the tangent to the latitude of Rome, ie from the äquinoktialem aspect ratio shadow gnomon ( 8:9; CB: AB) can be the equator and thus the course of the sun beam NAC for high sun, apply at noon. Parallel secants LG and KH to the equator at a distance of 1/15 circumference approximate the respective orbital planes of the sun at the solstices ( declination of the sun ± 24 °). At the winter solstice, the sun of K is projected over A to T. The summer solstice, it is mapped by L on A to R. In the selected view the sun moves on these solstices secant between EI horizon and meridian points L and K once a day up and down. Thus the intersections of S and V of these tracks are with the horizon the constellations at sunrise and sunset. The corresponding time for daily position of the sun can be determined if the respective secant of the sun's path a ( semi-) circle is hit, which is divided into hour angle for each 15 °. The subdivision is already no longer described by Vitruvius. In this diagram the time reading for the sunrise and sunset on the day of summer solstice by the line S - presented SA -SU. For the declination range between summer and winter solstice the Menaeus described by Vitruvius, the monthly or zodiac can be divided. On this the the desired calendar day of the month is applied corresponding position and drawn through this point a parallel to the equator. This gives the secant of the sun's path that day. Its upper intersection with the meridian circle results in the projection beam for the midday sun. In order to determine the position of the sun during the daytime hours, a semi-circle with the corresponding hours division is wrapped around this secant again.