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.
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 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.
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:
In the Systeme Internationale of units of measurements the
second is defined as the duration of 9 192 631 770 cycles of
a particular hyperfine structure transition in the ground state
of Cesium-133. This definition was chosen to match as best as
possible the length of the ephemeris second that was used before.
The SI-second only defines an abstract atomic time. To obtain
a timescale of practical usabilty a device is required that
attempts to realize the SI-second. Such a device is called an
atomic clock. Real-word atomic clocks do not agree fully with
each another. Therefore, the weighted mean of many atomic clocks
-- distributed over various laboratories on the whole Earth --
is used to define the Atomic Time TAI (french Temps Atomique
International). TAI is currently the best realization of a
timescale based on the SI-second, with a relative accuracy of
+/- 2*10^-14 (as of 1990).
According to the General Relativistic Theory, the time measured
depends on the location on Earth (or more precisely, on the
altitude) and also on the spatial velocity of the clock. TAI
thus refers to a location on sea sevel that rotates with the
Earth.
Ephemeris Time, Dynamical Time Scales (TDT, TDB)
Ephemerides are tables that list the positions of Sun, Moon,
planets and their respectives moons at different times.
Formerly, the positions were given as a function of
Greenwich Mean Time (GMT) which lead to recurring problems,
in particular with predictions for the Moon's motion.
Finally (at about 1930), it was realized that Earth's
rotation is irregular and that any timescale derived from
it must be erratic. However, the application of dynamical
laws of motion -- like for instance Newton's laws of force --
requires a smoothly flowing time as the independent variable.
The Ephemeris Time (ET) was consequently defined as the
timescale that together with the laws of motion correctly
predicts the positions of celestial bodies, and it is
therefore used as the argument in the ephemerides. The
current Ephemeris Time is thus determined by comparing the
observed positions with the ephemerides.
Formally, ET was defined by Newcomb's theory of the Sun.
In 1958, the International Astronomical Union (IAU) at its
10th general assembly stipulated that
The Julian day number -- or simply the Julian day -- is a
continuous count of days, starting with the day 0 that began
on the 1st of January, 4713 BC (in the proleptic Julian
calendar, see below) at 12 o'clock noon. Consequently, a
new Julian day always begins at 12 o'clock noon that
originally gave european astronomers the advantage that all
observations of any particular night happened at the same
Julian day. This property is unimportant today.
The Julian day count can easily be extended to a precise measure
of time by appending the fraction of the day elapsed since
12 o'clock noon. For instance, JD 2 451 605 signifies the
day that will begin on March 1, 2000, 12 o'clock noon whereas
JD 2 451 605.25 means the point of time at 18 o'clock of the
same day. This extension is called the Julian date in many
texts (as for example in the Astronomical Almanac). Other
sources propose to restrict this designation to date specifications
in the Julian calendar to prevent confusion. This proposal
has not carried through, yet.
Julian days were formerly (if nothing else was specified) counted
according to Mean Solar Time, today in UT. Alternatively,
specifications were given in Ephemeris Time which was indicated
by appending the letters JED or JDE. Also today it is sometimes
appropriate to specify Julian Days in another timescale than UT.
The employed timescale should then be appended to the time
specification, for instance JD 2 451 545.0 TDT for Januar 1,
2000, 12 o'clock noon as measured in TDT.
Occasionally, time specifications are given in a Modified Julian
Day format (MJD). The most common definition of a MJD follows
from
The following list mentions books with different demands on knowledge and willingness to learn. It starts with more general or popular-style books and ends with heavy-weight works for specialists.
