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2.7 Astronomy and geophysics

2.7.1 Astronomical and atomic time systems

Time systems

The fundamental reference timescale is now international atomic time (TAI). This provides both the standard unit of time (the SI second) and a precise, unambiguous identification of any instant of time, but it is not convenient for general use. There are still valid, practical reasons for continuing to relate the timescales in general use to the rotation of the Earth by the adoption of a system of standard times each of which differs from that for the prime meridian (zero longitude) by an exact number of hours. The standard time for the prime meridian is formally known as coordinated universal time (UTC), but the name Greenwich mean time (GMT) is still in widespread use throughout the world. This timescale differs from TAI by an exact number of seconds in such a way that it corresponds closely (to within 1 s) to universal time (UT) and so can be used directly in astronavigation as a measure of the rotation of the Earth with respect to the celestial sphere.

The rotation of the Earth on its axis is no longer of value for the measurement of precise time since the length of the day is subject to unpredictable variations. The systems of sidereal and solar time, including universal time, that represent this rotation are, however, still of value for astronomical purposes and for the determination of position on the Earth. These timescales may be regarded as angles expressed in time-units at the rate of 1 day of 24 hours for each complete rotation (or l^h = 15°).

Precise measurements of the positions of astronomical objects and the corresponding theories of the motions of bodies in the Solar System require the use of the general theory of relativity for the definition of celestial space–time reference frames. The time-like arguments, or scales of coordinate time, that are used for such purposes are related to TAI, but they are defined so that they maintain continuity with the earlier scales of dynamical time and ephemeris time (ET).

International atomic time and coordinated universal time

Independent atomic timescales based on caesium frequency standards were maintained by several national organisations from 1955 onwards, but the standard timescales continued to be based on universal time (UT) until 1972. The second of UT varies and so offsets in the carrier frequencies of the broadcast transmissions and occasional small adjustments in phase were required. In 1967 the General Conference on Weights and Measures (CGPM) adopted the atomic definition of the second as the unit of time interval; the adopted frequency of the chosen caesium transition gave continuity with the previous use of the ephemeris second. In 1971 the CGPM gave formal recognition to the atomic timescale maintained by the Bureau International de l’Heure (BIH) as international atomic time (TAI); the arbitrary epoch of the scale was chosen so that TAI and UT were coincident at 1958 January 1.0.

The International Bureau of Weights and Measures (BIPM) assumed responsibility for TAI on 1988 January 1. In forming TAI the BIPM combines the results of comparisons of the primary time-standards of three countries and of about 150 secondary time-standards from 30 countries in an attempt to maintain the uniformity of the scale. Transmissions from satellites of the Global Positioning System (GPS) are the main intermediary in the comparisons; a precision of 10–20 ns is routinely achieved. The current estimate (1993) of the uniformity of the scale is 1 part in 10¹³ in frequency so that the accumulated error in epoch is less than 3 μs/year.

The second of TAI is made available directly through the transmissions of coordinated universal time (UTC), which was redefined from the beginning of 1972 as an approximation to UT in which the second markers coincide with those of TAI but the numerical values assigned to them are of an adjacent second of UT. At 0^h 00^m 00^s on 1972 January 1 the difference ΔAT = TAI − UTC was made exactly 10 seconds. ‘Leap seconds’ are added to, or subtracted from, UTC as UT drifts with respect to TAI so that the difference ΔUT = UT − UTC does not normally exceed 0.7 s. The one-second steps are made on the last second of a month, preferably June or December; the date is announced several months in advance on the advice of the International Earth Rotation Service. Estimates of the differences ΔUT are often given by coding in the broadcast time signals that are used for the dissemination of time and frequency.

Differences ΔAT = TAI − UTC

The table gives the dates of the beginning of the periods during which the differences ΔAT took the values indicated.

Relativistic timescales for astronomy

In the context of the general theory of relativity, international atomic time (TAI) may be regarded as a scale of proper time that is appropriate for use for measurements on the surface of the geoid, the equipotential surface for the Earth that corresponds to mean sea level. In astronomy, however, TAI is not used directly, but instead a scale known as terrestrial time (TT), which is equal to TAI + 32^s. 184, is used in order to maintain continuity with ephemeris time (ET), which is the timescale of many theories and ephemerides and which provides a uniform timescale before 1955. In addition it is necessary to introduce scales of coordinate time for use in high-precision theories of the motions of bodies with respect to other space-time reference frames. In particular, scales of geocentric coordinate time (TCG) and barycentric coordinate time (TCB) have been defined for use for motions referred to the centre of the Earth and the barycentre of the Solar System, respectively.

These new scales, (TT, TCG and TCB) were defined in a series of recommendations that were adopted by the International Astronomical Union (IAU) in 1991; they supersede the scales of dynamical time that were recommended by the IAU in 1976.

Ephemeris time

In general terms, ephemeris time is the independent variable of the differential equations for the motions of the Sun, Moon and planets under the influence of their mutual gravitational attractions. Formally, the fundamental epoch and unit of time interval are defined by the first two terms in an adopted expression for the mean longitude of the Sun, although in practice the timescale is determined indirectly from observations of the Moon. The ephemeris second is equal to the SI second to within the limits of accuracy of its determination, and the scale is such that the relation

   ET = TAI + 32^s.184

can be used for most purposes when interpolating ephemerides whose argument is ephemeris time.

Ephemeris time has been superseded by relativistic timescales for current purposes, but for historical purposes the concept of ephemeris time is still valid. ET may be regarded as the backward continuation of TAI − 32^s.184. Current estimates of the annual-mean values of the differences ΔT between universal time and ephemeris time are given in the following table; the values for the earlier epochs depend critically on the value adopted (in this case – 26″/century²) for the tidal term in the expression for the Moon’s mean longitude.

Annual-mean values of ΔT = ET - UT

Sidereal time

Sidereal time represents the orientation of the celestial system of right ascension with respect to the terrestrial system of longitude. Local sidereal time is usually defined as the local hour angle of the equinox (‘First Point of Aries’). An equivalent definition is that it is the right ascension of the local meridian. The direction of the equinox is the line of intersection of the ecliptic (the mean plane of the Earth’s orbit around the Sun) with the plane of the Earth’s equator; it is used as the zero of right ascension. Sidereal time may be determined by observing stars, whose right ascensions are assumed to be known, as they cross the observer’s meridian. The local sidereal time (LST) at a place differs from Greenwich sidereal time (GST) by the longitude of the place measured from the Greenwich meridian according to the expression

   LST = GST + east longitude

where longitude is measured in time-units at the rate of 15° = l ^h.

The precession of the Earth’s axis of rotation around the pole of the ecliptic causes a slow drift of the equinox with respect to the stars. Consequently, the mean length of the sidereal day is slightly shorter than the period of rotation of the Earth with respect to an inertial frame. The luni-solar forces acting on the Earth also cause an oscillatory nutation that is superposed on the precessional drift. It is therefore necessary to distinguish between apparent sidereal time and mean sidereal time, where the latter is free from the quasi-periodic irregularities due to nutation. The obliquity of the ecliptic (the inclination of the ecliptic to the plane of the equator) is also affected by the nutation of the axis of rotation of the Earth. The effects of nutation are computed from an adopted numerical series, the principal terms of which are given in next section.

Observations of local sidereal time are also affected by the motion of the axis of rotation with respect to the axis of figure of the Earth. This ‘polar motion’, which also causes variations in the latitudes of the observing site with respect to the celestial equator, is unpredictable and must be determined from observations at two or more sites. Its principal components are an annual term and a ‘Chandler wobble’, whose period is about 427 days; the amplitude of the polar motion is usually less than 0″.3, corresponding to a displacement of about 9 m on the surface of the Earth.

Universal time

Universal time (UT) is formally defined in terms of Greenwich mean sidereal time (GMST) by a conventional expression (see Section 2.7.2) that ensures continuity with past practice and yet frees UT from irregularities that would arise if UT were defined in terms of the hour angle of the Sun. (In effect, UT is equivalent to 12^h plus the Greenwich hour angle of a fictitious mean sun.) Even so, UT does not provide a uniform timescale since the rate of rotation of the Earth, and hence the length of the day in SI units, is subject to secular, irregular and quasi-periodic changes due to many different causes. During the course of a year the length of the day varies by about 1 ms (i.e. 1 part in 10⁸) about its mean value. During the course of a decade the mean value may change by as much as 4 ms. During the course of a millenium the mean value increases by about 20 ms as a result of ‘tidal friction’.

UT, polar motion and the geodetic positions of the observing sites are now determined mainly from Very Long Baseline Interferometry observations of extra-galactic radio sources, from laser ranging to certain artificial satellites and the Moon, and from the reception of transmissions from satellites of the Global Positioning System (GPS). The results from the various techniques are combined and published by the International Earth Rotation Service, which also publishes the relevant standard constants and models.

Local time and the equation of time

Local mean (solar) time (LMT) differs from UT by the time equivalent of the longitude of the place according to the expression

   LMT = UT + east longitude.

Local mean time differs from clock time by the time equivalent of the difference in longitude between the place and the appropriate standard meridian, which may not be the nearest standard meridian. This difference will be 1 hour greater when summer (daylight-saving) time is in force. The standard meridians, which differ in longitude by 15°, divide the world into standard time zones, in each of which the time differs from UTC by an integral number of hours.

The time indicated by a simple sundial is known as local apparent (solar) time and it differs from local mean (solar) time by the so-called equation of time. The average amounts by which apparent solar time is in advance of mean solar time are indicated in the following table; the actual amounts for a given day may vary by up to 0^m.3 from these average values.

Equation of time: apparent time – mean time (minutes)

LMT of transit of Sun = 12^h − equation of time.

The principal contributions to the equation of time arise from the eccentricity of the Earth's orbit and from the inclination of the plane of the Earth’s orbit to the plane of the Earth's equator. The equation of time is given to a precision of about l^m by the expression

   + 7^m.6 sin(176°.24 + 0°.9856 d) + 9^m.8 sin(198°.82 + 1°.9712 d),

where d is the interval in days from January 0.

The directions of the stars at a given time are determined by the local sidereal time, which is equal to the right ascension of the stars on the meridian. The following table shows the approximate right ascension of the stars that will be due south at 0^h LMT (midnight) at the beginning of each month. LST gains on LMT by about 4 minutes each day, so that

             LST = LMT + value from table for month + (4 minutes × (day of month − 1),

where LMT is the local clock time plus/minus the correction in time for longitude east/west of the appropriate standard meridian. The value on a given day of the year varies by up to 4 minutes in a four-year cycle.

   At a given LST the local hour angle (LHA) of a star is given by

      LHA = LST − right ascension of star.

Local sidereal time (LST) minus local mean time (LMT) (midnight)

The value of LST – LMT increases by about 4 minutes each day.

G.A.Wilkins

Time and frequency signals

Portable atomic clocks of high accuracy are now available and are used to compare standard clocks in different places. But this has the disadvantage that only occasional comparisons are possible. Time and its reciprocal, frequency, are unique among physical quantities in that the magnitude of the units can be disseminated by radio means without the need for travelling standards. A number of countries operate standard time and frequency broadcast services: these are available for use by anyone within range of the transmitters who has a suitable radio receiver. The majority of the transmissions are in the MF and HF bands (see section 2.5.1) and can be received over distances of some thousands of kilometres. But because variable delays occur when signals are propagated via the ionosphere, the full accuracy can be obtained only by a receiver within ground-wave range.

In Britain, the service is provided by the National Physical Laboratory by a 60 kHz signal from the MSF transmitter at Rugby. This has a carrier derived from an atomic frequency standard, with a stability within ±2 in 10¹² of the nominal frequency. It carries accurate time signals and is related to the national atomic frequency standard at Teddington. Corrections to the radiated frequencies are subsequently available to an accuracy of ±1 in 10¹³. The carrier of the BBC broadcast transmitter on 198 kHz at Droitwich is also stabilised.

In the United States, NIST broadcasts time and frequency signals at a number of frequencies in the HF band from WWVB (Colorado) and WWVH (Hawaii). WWVB also broadcasts at 60 kHz. Some other countries, notably Germany and Japan, also have dedicated time and frequency broadcast services.

In addition, there are a number of types of signal broadcast for other purposes which can be used for accurate time comparisons. These include television signals, Loran-C and others. But in recent years most interest has been aroused by the possibility of using signals from satellites. There are a number of systems which have been used for time comparisons, but perhaps the one which has received most attention has been the US Department of Defense Global Positioning System (GPS) in which the satellites carry atomic clocks. This is a navigation system in which, if you know the time, you can work out where you are from the received signals. But equally, if you know where you are (and where the satellite is) you can determine the time. Many laboratories have made use of this, but it does have the slight disadvantage of being primarily a military system. In an alternative approach, NPL has recently carried out experiments using signals from direct broadcast satellites (DBS) to compare clocks at distances up to 400 km apart with uncertainties of about 100 ns in time and a few parts in 10¹⁴ in frequency. Plans for the intercomparison of national standards via satellite links are now under way.

Clearly, the situation is changing rapidly. Some HF broadcasts have already been abandoned and other broadcasts are likely to follow. It is not possible to give here details of facilities which are likely to remain in use. Anyone wishing to obtain up-to-date information on what is currently available should seek it from their national standards laboratory (NPL in Britain).

A.E.Bailey

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