Astronomical Time Keeping http://www.maa.mhn.de/Scholar/times.html Introduction: Time keeping and construction of calendars are among the oldest branches of astronomy. Up until very recently, no earth-bound method of time keeping could match the accuracy of time determinations derived from observations of the Sun and the planets. All the time units that appear natural to man are caused by astronomical phenomena: The year by Earth's orbit around the Sun and the resulting run of the seasons, the month by the Moon's movement around the Earth and the change of the Moon phases, the day by Earth's rotation and the succession of brightness and darkness. If high precision is required, however, the definition of time units appears to be problematic. Firstly, ambiguities arise for instance in the exact definition of a rotation or revolution. Secondly, some of the basic astronomical processes turn out to be uneven and irregular. A problem known for thousands of years is the non-commensurability of year, month, and day. Neither can the year be precisely expressed as an integer number of months or days, nor does a month contain an integer number of days. To solve these problems, a multitude of time scales and calendars were devised of which the most important will be described below. Sidereal Time The sidereal time is deduced from the revolution of the Earth with respect to the distant stars and can therefore be determined from nightly observations of the starry sky. A sidereal day can be defined in a first approximation as the time interval between two successive passages of the same star through the meridian. Here, the meridian of an observational site is the great circle passing through the two celestial poles and the zenith of the site. Expressed in different words, the meridian is the projection of the circle of the site's geographical longitude onto the celestial sphere if projected from the Earth's centre. The passage through the meridian is thus a more accurate determination of the point in time when -- in colloquial speech -- “the star is due south” (at least for observers on the northern hemisphere). The duration of a sidereal day in units of Universal Time is 23h 56m 04.0905s. To define more precisely the length of a sidereal day and to establish a zero-point for the counting of sidereal time, the terms “hour angle,” “ecliptic,” “celestial equator,” and “vernal equinox” must be introduced. Through any point on the celestial sphere -- for example the position of a star -- and the two celestial poles passes a uniquely defined great circle that in general does not coincide with the meridian but cuts the meridian at the celestial poles. The cutting angle is called the hour angle of the particular point. This angle isn't usually measured in degrees but in hours, minutes and seconds (hence the name). The full circle of 360 degrees corresponds to exactly 24 hours. Because of Earth's rotation, the hour angle grows by 24 hours within one sidereal day. The celestial equator is the set of all points on the celestial sphere that are 90 degrees away from the celestial poles, or -- equivalently -- the projection of Earth's equator onto the celestial sphere, if projected from Earth's centre. The ecliptic is the Sun's path on the celestial sphere, among the stars, during the year. The celestial equator and the ecliptic do not coincide (a consequence of the Earth's rotation axis being tilted) but cross each other in two points one of which is called the vernal equinox.“0 o'clock” sidereal time is defined as the instance when the vernal equinox passes through the meridian. This definition can be generalized to: “sidereal time is the hour angle of the vernal equinox.” Of course, the vernal equinox is a fictitious point on the celestial sphere and cannot be observed directly. From the known coordinates of observed stars, however, the location of the vernal equinox can be deduced. From the above it is also clear that a sidereal day is the interval between two successive passages of the vernal equinox through the meridian. According to this final definition, a sidereal day is shorter by about 9 milliseconds than the approximation given at the beginning. This is a consequence of the fact that due to Earth's precession the vernal equinox is moving with respect to the stars. The above definition refers to the local meridian and therefore leads to a sidereal time that is dependent on the place of observation. To define a global standard of sidereal time, one refers to the meridian of Greenwich and calls the time scale so derived the “Greenwich Mean sidereal Time” (GMST). To convert between GMST and local sidereal time, the geographical longitude of the observation site must be known. From the sidereal time and the celestial coordinates of a star (in particular the right ascension) the hour angle of the star and hence its current apparent position (that is constantly changing because of Earth's rotation) can be computed. Moreover, sidereal time is one of the constituents of Universal Time. Solar Time Solar time follows the apparent revolution of the Sun around the Earth. A solar day is the interval between two successive passages of the Sun through the meridian, or -- colloquially -- from noon to noon. Of course, this apparent revolution only reflects the true rotation of the Earth. However, because in the run of one day the Earth also travels a considerable part of its orbit around the Sun, a complete rotation with respect to the Sun lasts longer than a complete rotation with respect to the stars. Consequently, a true solar day is longer by about 4 minutes than a sidereal day. The reference point of the true solar time again can be expressed as an hour angle. Since the time reading at the Sun's passage through the meridian should be 12 h, though, the true solar time comes out as the hour angle of the anti-sun (which is the fictitious point on the ecliptic opposite to the Sun). A sundial displays the true solar time at its location. The duration of the true solar day varies with the seasons. This is a consequence both of the eccentricity of the Earth's orbit and the obliquity of the ecliptic (the tilt of Earth's rotation axis). Firstly, the Earth moves at different speeds in different parts of its elliptical orbit, according to Kepler's second law, hence the Sun seems to move at different speeds among the stars. Secondly, even with a perfectly circular Earth orbit, the