Astronomical Time Keeping


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 solves these problems, a multitude of time scales and calenders were devised of which the most important will be described below.

Siderial Time

The siderial 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 siderial 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 siderial day in units of Universal Time is 23h 56m 04.0905s.
To define more precisely the length of a siderial day and to establish a zero-point for the counting of siderial 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 siderial 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 siderial time is defined as the instance when the vernal equinox passes through the meridian. This definition can be generalized to: ``Siderial 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 siderial day is the interval between two successive passages of the vernal equinox through the meridian. According to this final definition, a siderial 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 siderial time that is dependent on the place of observation. To define a global standard of siderial time, one refers to the meridian of Greenwich and calls the time scale so derived the ``Greenwich Mean Siderial Time'' (GMST). To convert between GMST and local siderial time, the geographical longitude of the observation site must be known.
From the siderial 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, siderial 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 meridan, 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 siderial 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 Sun would move evenly along the ecliptic but its projection onto the celestial equator would move at varying speeds. In spring and autumn, the Sun is close to the crossing points of ecliptic and celestial equator. Its movement from day to day therefore is slanted to the equator, the projected velocity is thus reduced. During summer and winter, however, the Sun is close to a vertex of the ecliptic and moves parallel to the celestial equator, making the projected velocity large. Both effects result in a variation of the 4 minutes correction to the siderial day, with the obliquity of the ecliptic having the slightly larger influence.
To obtain a more even time scale, one defines a fictitious ``Mean Sun''. This Mean Sun takes the same time from one vernal equinox to the next as the true Sun, but it is supposed to move with constant velocity along the celestial equator. Mean Solar Time is therefore the hour angle of the mean anti-sun.
The difference between True and Mean Solar Time is called the equation of time. Because two different effects with different time scales overlap (the eccentricity causes a period of one year, the obliquity of the ecliptic one of half a year), the equation of time has two minima and two maxima per year:

         ~ 11.Feb    ~ -14.5 min
         ~ 14.Mai    ~    +4 min
         ~ 26.Jul    ~  -6.4 min
         ~  3.Nov    ~ +16.3 min
The equation of time also causes asymmetrical shifts of the rising and setting times of the Sun. The earliest sunset, for instance, does not happen on the winter solstice on Dec 22 but about 11 days earlier. The latest sunrise on the other hand happens about 10 days after the winter solstice. For the same reason, morning and afternoon have different lengths on the equinoces on Mar 21 and Sep 23.

Universal Time (UT), Greenwich Time

The Universal Time (UT) was introduced in the year 1926 to replace the Greenwich Mean Time (GMT). At this time, several definitions of GMT were in use, sometimes with considerable differences. The term GMT had thus become useless and was dropped and replaced by a more stringent definition of UT.
For most practical purposes, UT is equivalent to the Mean Solar Time for the Greenwich reference meridian. The relation between UT and local Mean Solar Time is the same as between Greenwich Mean Siderial Time and local Siderial Time. Basically, however, UT is not a solar time in the sense that the observed solar position would be used to define this time. The achievable accuracy for a measurement of the Sun's position is far too insufficient for this purpose. Instead, UT is derived from the more precise Siderial Time by means of a mathematical formula. This formula accounts for the known shape of Earth's orbit with which the position of the fictitious Mean Sun can be calculated. Consequently, UT and Siderial Time are not independent time scales but two forms of the same scale, although with units of different length.
Upon closer inspection, the Universal Time UT has to be differentiated further. The directly observable Siderial Time, converted to the Greenwich reference meridian and subjected to the transformation formula determines the time UT0. Due to the slight movements of the Earth's poles of rotation the difference in geographical longitude between the place of observation and the reference meridian varies. Therefore, the conversion to the reference meridian according to tabulated common longitudes is incorrect. If the pole variation is accounted for, one obtains the time UT1. This timescale is consistent for all places on the Earth but still irregular since the rotational velocity of the Earth is known to be variable. A correction of UT1 for the strongest and most regular variations yields the time UT2. This correction amounts to +/- 30 milliseconds at most. UT2 is the most uniform timescale that can be predicted from Earth's rotation. Because of the availability of time standards that are more precise and easier to obtain (atomic clocks) UT2 has hardly any practical use. The Universal Time commonly adopted in astronomy is therefore the UT1 scale.
UT1 has the advantage of predicting the solar position to sufficient accuracy. Its disadvantage, however, is that the length of a second derived from UT1 varies noticably (caused by the irregularities of Earth's rotation). Therefore, a timescale named Coordinated Universal Time (UTC) was invented in which the SI-second -- as implemented by atomic clocks -- is the unit of time. In addition, it is required that the absolute value of the difference UTC - UT1 never exceeds 0.9 seconds. UTC therefore offers both a highly constant unit of time as well as agreement with the position of the Sun. For this reason, UTC is the basis for all civil time keeping today. It is distributed publicly by DCF77 radio transmitters and other time services, together with an extrapolation of the current time difference DUT1 = UTC - UT1. (This difference has to be extrapolated because UT1 must be determined from observations and cannot be calculated and distributed instantly.)
Since UTC as well as Atomic Time TAI are based on the SI-second, both timescales are basically in step with each other. However, the SI-second does not agree with the UT1-second, therefore UTC drifts with respect to UT1. To account for the above-mentioned requirement about UTC-UT1, leap seconds must occasionally be inserted into or dropped from UTC. This happens -- if necessary -- on Jun 30 or Dec 31 at the end of the last minute of the day. Currently, about two leap seconds must be inserted in an interval of three years. The need for a leap second is determined by the Bureau International de l'Heure (BIH) in Paris, after consultation with several time laboratories.
The need for leap seconds is not caused by the secular slowdown of Earth's rotation (which is less than 2 milliseconds per century) but by irregular variations in this rotation and by the fact that the definition of the SI-second is fixed on the duration of the year 1900 which was shorter than average.

Timezones

The establishment of timezones accounts for the fact that for any given instance the Sun is rising on one place on the Earth, is standing high in the south at noon for another place, and is setting for a third place. Considering these astronomical facts, it makes sense to use different civil timescales at different places on the Earth. Ultimately, however, the adoption of a local timescale is a political decision and is therefore handled differently in individual countries.
A timezone is a region of a common civil timescale that is in general oriented along a meridian of constant geographical longitude. The local time of a timezone usually differs by an integer number of hours from Universal Time, although sporadically other differences occur. The differenz ``local time'' minus ``Universal Time'' is positiv for timezones east of Greenwich and negativ for western timezones (see: Maps of the timezones (230 kb)).
Frequently mentioned timezones are: