1233:, section II.E.4-5, pages 15β16, including footnote 7, noted that the Jet Propulsion Laboratory spacecraft tracking and data reduction programs of that time (including the Single Precision Orbit Determination Program) used, as ET, the current US atomic clock time A.1 offset by 32.25 seconds. The discussion also noted that the usage was "inaccurate" (the quantity indicated was not identical with any of the other realizations of ET such as ET0, ET1), and that while A.1 gave "certainly a closer approximation to uniform time than ET1" there were no grounds for considering either the atomic clocks or any other measures of ET as (perfectly) uniform. Section II.F, pages 18β19, indicates that an improved time measure of (A.1 + 32.15 seconds), applied in the JPL Double Precision Orbit Determination Program, was also designated ET.
507:, an alternative offered itself. Increasingly, after the calibration in 1958 of the cesium atomic clock by reference to ephemeris time, cesium atomic clocks running on the basis of ephemeris seconds began to be used and kept in step with ephemeris time. The atomic clocks offered a further secondary realization of ET, on a quasi-real time basis that soon proved to be more useful than the primary ET standard: not only more convenient, but also more precisely uniform than the primary standard itself. Such secondary realizations were used and described as 'ET', with an awareness that the time scales based on the atomic clocks were not identical to that defined by the primary ephemeris time standard, but rather, an improvement over it on account of their closer approximation to uniformity. The atomic clocks gave rise to the
1843:
1837:
465:
UT depended on observation. Inspection of the formulae above shows that the (ideally constant) units of ephemeris time have been, for the whole of the twentieth century, very slightly shorter than the corresponding (but not precisely constant) units of mean solar time (which, besides their irregular fluctuations, tend to lengthen gradually). This finding is consistent with the modern results of
Morrison and Stephenson (see article
184:(1927) who wrote "If we accept this hypothesis, then the 'astronomical time', given by the Earth's rotation, and used in all practical astronomical computations, differs from the 'uniform' or 'Newtonian' time, which is defined as the independent variable of the equations of celestial mechanics". De Sitter offered a correction to be applied to the mean solar time given by the Earth's rotation to get uniform time.
671:, replacing UT in the main ephemerides in the issues for 1960 and after. (But the ephemerides in the Nautical Almanac, by then a separate publication for the use of navigators, continued to be expressed in terms of UT.) The ephemerides continued on this basis through 1983 (with some changes due to adoption of improved values of astronomical constants), after which, for 1984 onwards, they adopted the
464:
with the 24.349 seconds of time corresponding to the 1.00" in ΞLs. Clemence's formula (today superseded by more modern estimations) was included in the original conference decision on ephemeris time. In view of the fluctuation term, practical determination of the difference between ephemeris time and
729:
became operational in 1955, and quickly confirmed the evidence that the rotation of the Earth fluctuated irregularly. This confirmed the unsuitability of the mean solar second of
Universal Time as a measure of time interval for the most precise purposes. After three years of comparisons with lunar
518:
The availability of atomic clocks, together with the increasing accuracy of astronomical observations (which meant that relativistic corrections were at least in the foreseeable future no longer going to be small enough to be neglected), led to the eventual replacement of the ephemeris time standard
342:
Clemence's 1948 proposal, however, did not adopt such a correction of mean solar time. Instead, the same numbers were used as in
Newcomb's original uncorrected formula (1), but now applied somewhat prescriptively, to define a new time and time scale implicitly, based on the real position of the Sun:
362:
From the comparison of formulae (2) and (3), both of which express the same real solar motion in the same real time but defined on separate time scales, Clemence arrived at an explicit expression, estimating the difference in seconds of time between ephemeris time and mean solar time, in the sense
257:
During the currency of ephemeris time as a standard, the details were revised a little. The unit was redefined in terms of the tropical year at 1900.0 instead of the sidereal year; and the standard second was defined first as 1/31556925.975 of the tropical year at 1900.0, and then as the slightly
230:
Following this, an astronomical conference held in Paris in 1950 recommended "that in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900.0, that the time reckoned in this unit be designated
172:(1646β1719) it had been believed that the Earth's daily rotation was uniform. But in the later nineteenth and early twentieth centuries, with increasing precision of astronomical measurements, it began to be suspected, and was eventually established, that the rotation of the Earth (
490:
Reasons for the use of lunar measurements were practically based: the Moon moves against the background of stars about 13 times as fast as the Sun's corresponding rate of motion, and the accuracy of time determinations from lunar measurements is correspondingly greater.
482:
Although ephemeris time was defined in principle by the orbital motion of the Earth around the Sun, it was usually measured in practice by the orbital motion of the Moon around the Earth. These measurements can be considered as secondary realizations (in a
494:
When ephemeris time was first adopted, time scales were still based on astronomical observation, as they always had been. The accuracy was limited by the accuracy of optical observation, and corrections of clocks and time signals were published in arrear.
157:), adopted as standard in 1952, was originally designed as an approach to a uniform time scale, to be freed from the effects of irregularity in the rotation of the Earth, "for the convenience of astronomers and other scientists", for example for use in
714:
was obtained from the linear time-coefficient in
Newcomb's expression for the solar mean longitude (above), taken and applied with the same meaning for the time as in formula (3) above. The relation with Newcomb's coefficient can be seen from:
539:
resolved that the theoretical basis for its then-current (since 1952) standard of
Ephemeris Time was non-relativistic, and that therefore, beginning in 1984, Ephemeris Time would be replaced by two relativistic timescales intended to constitute
1389:'ESAE 1961': "Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac" ('prepared jointly by the Nautical Almanac Offices of the United Kingdom and the United States of America', HMSO, London, 1961).
108:
An impression has sometimes arisen that ephemeris time was in use from 1900: this probably arose because ET, though proposed and adopted in the period 1948β1952, was defined in detail using formulae that made retrospective use of the
220:(1939). Clemence (1948) made it clear that his proposal was intended "for the convenience of astronomers and other scientists only" and that it was "logical to continue the use of mean solar time for civil purposes".
322:
Spencer Jones' work of 1939 showed that differences between the observed positions of the Sun and the predicted positions given by
Newcomb's formula demonstrated the need for the following correction to the formula:
459:
191:(1929), who suggested in effect that observed positions of the Moon, Sun and planets, when compared with their well-established gravitational ephemerides, could better and more uniformly define and determine time.
292:
Ephemeris time was defined in principle by the orbital motion of the Earth around the Sun (but its practical implementation was usually achieved in another way, see below). Its detailed definition was based on
749:
Although this is an independent definition that does not refer to the older basis of ephemeris time, it uses the same quantity as the value of the ephemeris second measured by the cesium clock in 1958. This
603:
only by small periodic terms with an amplitude not exceeding 2 milliseconds of time: it is linearly related to, but distinct (by an offset and constant rate which is of the order of 0.5 s/a) from the
790:
at 1 January 1958 0:00:00. At that time, ΞT was already about 32.18 seconds. The difference between
Terrestrial Time (TT) (the successor to ephemeris time) and atomic time was later defined as follows:
265:, were designed with a relationship that "provides continuity with ephemeris time". ET was used for the calibration of atomic clocks in the 1950s. Close equality between the ET second with the later
745:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
1741:
1664:
359:
each. The 1961 official reference summarized the concept as such: "The origin and rate of ephemeris time are defined to make the Sun's mean longitude agree with
Newcomb's expression"
776:, decreasing from ancient times until the nineteenth century, and increasing since then at a rate corresponding to an increase in the solar day length of 1.7 ms per century (see
334:
Thus, a conventionally corrected form of
Newcomb's formula, incorporating the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:
331:
where "the times of observation are in
Universal time, not corrected to Newtonian time," and 0.0748B represents an irregular fluctuation calculated from lunar observations.
1028:
487:
sense) of the primary definition of ET in terms of the solar motion, after a calibration of the mean motion of the Moon with respect to the mean motion of the Sun.
78:
66:, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.
1657:
678:
Previous to the 1960 change, the 'Improved Lunar Ephemeris' had already been made available in terms of ephemeris time for the years 1952β1959 (computed by
1048:
754:
was later verified by Markowitz (1988) to be in agreement, within 1 part in 10, with the second of ephemeris time as determined from lunar observations.
2195:
261:
Although ET is no longer directly in use, it leaves a continuing legacy. Its successor time scales, such as TDT, as well as the atomic time scale
1650:
668:
314:
at a time, indicated by interval T (in units of Julian centuries of 36525 mean solar days), reckoned from Greenwich Mean Noon on 0 January 1900:
194:
Thus the aim developed, to provide a new time scale for astronomical and scientific purposes, to avoid the unpredictable irregularities of the
368:
1483:
2164:
258:
modified fraction 1/31556925.9747 instead, finally being redefined in 1967/8 in terms of the cesium atomic clock standard (see below).
620:(within 2 milliseconds), but not so closely TCB, can be used as approximations to Terrestrial Time, and via the standard ephemerides T
1915:
1381:
54:, and superseded during the 1970s. This time scale was proposed in 1948, to overcome the disadvantages of irregularly fluctuating
1007:
536:
243:
51:
1534:("Tables of the Motion of the Earth on its Axis and Around the Sun", in "Tables of the Four Inner Planets", vol. 6, part 1, of
1988:
734:
et al. (1958) determined that the ephemeris second corresponded to 9 192 631 770 Β± 20 cycles of the chosen cesium resonance.
1530:
298:
122:
2169:
1444:"Variations in the Rotation of the Earth, Results Obtained with the Dual-Rate Moon Camera and Photographic Zenith Tubes"
180:) showed irregularities on short time scales, and was slowing down on longer time scales. The evidence was compiled by
2124:
2104:
2050:
1935:
1771:
1471:
1431:
636:
605:
561:
90:
42:(itinerary of the trajectory of an astronomical object). In practice it has been used more specifically to refer to:
2426:
1791:
1776:
1714:
1693:
758:
648:
632:
557:
549:
524:
1945:
1756:
783:
737:
Following this, in 1967/68, the General Conference on Weights and Measures (CGPM) replaced the definition of the
667:
Ephemeris time based on the standard adopted in 1952 was introduced into the Astronomical Ephemeris (UK) and the
580:
508:
280:
which have been needed for insertion into current broadcast time scales, to keep them approximately in step with
262:
70:
757:
For practical purposes the length of the ephemeris second can be taken as equal to the length of the second of
58:. The intent was to define a uniform time (as far as was then feasible) based on Newtonian theory (see below:
1548:"On the secular accelerations and the fluctuations of the longitudes of the moon, the sun, Mercury and Venus"
2205:
1983:
1885:
1801:
1796:
1343:
1327:
596:
351:
With this reapplication, the time variable, now given as E, represents time in ephemeris centuries of 36525
210:
162:
639:. The same IAU resolution also stated (in note 4) that the "independent time argument of the JPL ephemeris
552:. Difficulties were recognized, which led to these, in turn, being superseded in the 1990s by time scales
272:
In this way, decisions made by the original designers of ephemeris time influenced the length of today's
2358:
246:
approved this recommendation at its 1952 general assembly. Practical introduction took some time (see
250:); ephemeris time (ET) remained a standard until superseded in the 1970s by further time scales (see
2421:
2185:
2099:
1925:
1786:
1559:
683:
584:
541:
217:
63:
2395:
2190:
2045:
1910:
1862:
1731:
769:
679:
466:
2370:
2144:
2068:
1998:
269:(as defined with reference to the cesium atomic clock) has been verified to within 1 part in 10.
1622:
1601:
1592:, (Royal Society, Discussion on Rotation in the Solar System, London, England, Mar. 8, 9, 1984)
1576:
1513:
655:, is essentially a more refined continuation of the older ephemeris time ET and (apart from the
161:
of the Sun (as observed from the Earth), the Moon, and the planets. It was proposed in 1948 by
130:
The ephemeris time of the 1952 standard leaves a continuing legacy, through its historical unit
2218:
2083:
1900:
1631:
1618:
1597:
1547:
1517:
1509:
1501:
1479:
1459:
1455:
1439:
1427:
1415:
1411:
1377:
1347:
1331:
1291:
807:
This difference may be assumed constantβthe rates of TT and TAI are designed to be identical.
731:
110:
1258:
1069:
1044:
994:
842:
838:
2363:
2109:
2088:
2040:
2003:
1816:
1543:
762:
600:
553:
545:
520:
512:
214:
187:
Other astronomers of the period also made suggestions for obtaining uniform time, including
181:
1398:
1271:
583:(JPL) over a long period, and the latest available were adopted for the ephemerides in the
2094:
2073:
1905:
1877:
202:(UT) and any other time scale based on the rotation of the Earth around its axis, such as
55:
2390:
2149:
2139:
2078:
2035:
1867:
1826:
1726:
1698:
1564:"The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets"
1536:
Astronomical Papers prepared for the use of the American Ephemeris and Nautical Almanac
787:
659:
periodic fluctuations) has the same mean rate as that established for ET in the 1950s.
311:
223:
De Sitter and Clemence both referred to the proposal as 'Newtonian' or 'uniform' time.
199:
169:
1502:"Historical values of the Earth's clock error ΔT and the calculation of eclipses"
1360:
635:(TDB) as a current standard. As re-defined in 2006, TDB is a linear transformation of
2415:
2277:
2228:
2213:
2159:
1930:
1766:
1761:
1677:
1525:
1443:
726:
703:
294:
203:
118:
47:
1610:
1589:
1563:
591:
has been in use at that institution since the 1960s. The time scale represented by T
2375:
2262:
2257:
2252:
2239:
1978:
719:
1/31 556 925.9747 = 129 602 768.13 / (360×60×60×36 525×86 400).
504:
224:
188:
105:
Most of the following sections relate to the ephemeris time of the 1952 standard.
1642:
1492:
1373:
213:(1948) made a detailed proposal of this type based on the results of the English
2385:
2380:
2025:
2008:
1940:
1920:
1806:
1688:
777:
303:(1895), implemented in a new way to accommodate certain observed discrepancies:
277:
247:
89:
is closely related to, but distinct (by an offset and constant rate) from, the
2400:
2353:
2337:
2223:
2129:
1950:
1811:
1781:
1719:
281:
195:
898:
For the components of the definition including its retrospective aspect, see
587:
starting in 1984. Although not an IAU standard, the ephemeris time argument T
17:
2297:
2134:
2018:
1993:
1973:
1890:
1842:
1836:
1821:
707:
576:
484:
158:
114:
39:
1495:", NASA Technical Report 32-1306, Jet Propulsion Laboratory, July 15, 1968.
1632:"Ephemeris Time, relativity, and the problem of uniform time in astronomy"
694:
Successive definitions of the unit of ephemeris time are mentioned above (
2332:
2312:
2154:
2060:
1960:
1751:
1746:
773:
134:
which became closely duplicated in the length of the current standard SI
1590:"Long-term changes in the rotation of the earth β 700 B.C. to A.D. 1980"
454:{\displaystyle \delta t=+24^{s}.349+72^{s}.3165T+29^{s}.949T^{2}+1.821B}
2327:
2317:
2247:
2119:
2030:
1895:
723:
647:" (here the IAU source cites), "is for practical purposes the same as
338:
Ls = 279Β° 41' 49".04 + 129,602,771".10T +2".32T +0.0748B . . . . . (2)
2322:
2272:
2267:
751:
738:
511:, and to what was first called Terrestrial Dynamical Time and is now
310:
the basis of the tables (p. 9) includes a formula for the Sun's
273:
266:
135:
85:
ephemeris in widespread current use. The time scale represented by T
1464:
The Earth's Rotation and Reference Frames for Geodesy and Geophysics
1611:"Long-Term Fluctuations in the Earth's Rotation: 700 BC to AD 1990"
2302:
2114:
2013:
1968:
640:
613:
82:
1313:
McCarthy & Seidelmann (2009) Ch. 4, "Variable Earth Rotation"
2307:
2292:
2282:
1736:
1673:
1491:
W G Melbourne, J D Mulholland, W L Sjogren, F M Sturms (1968), "
1406:"Improved Lunar Ephemeris", US Government Printing Office, 1954.
1303:"Improved Lunar Ephemeris", US Government Printing Office, 1954.
276:, and in turn, this has a continuing influence on the number of
69:
a modern relativistic coordinate time scale, implemented by the
1646:
1493:
Constants and Related Information for Astrodynamic Calculations
631:
via the JPL ephemerides, IAU resolution 3 of 2006 (re-)defined
62:). Ephemeris time was a first application of the concept of a
2287:
1394:
686:'s theory with modifications recommended by Clemence (1948)).
672:
609:
579:
of sun, moon and planets were developed and calculated at the
347:
Ls = 279Β° 41' 48".04 + 129,602,768".13E +1".089E . . . . . (3)
318:
Ls = 279Β° 41' 48".04 + 129,602,768".13T +1".089T . . . . . (1)
177:
94:
1615:
Royal Society (London), Philosophical Transactions, Series A
1594:
Royal Society (London), Philosophical Transactions, Series A
1361:"Time scales β Their history, definition and interpretation"
1116:
day is left implicit on p. 9 but made explicit on p. 20 of
1047:, citing CIPM recommendation Oct 1956, adopted 1960 by the
1742:
International Earth Rotation and Reference Systems Service
1516:), vol. 35(3) (2004), #120, pp. 327β336 (with addendum at
795:
1977 January 1.000 3725 TT = 1977 January 1.000 0000 TAI,
248:
Use of ephemeris time in official almanacs and ephemerides
698:). The value adopted for the 1956/1960 standard second:
38:) can in principle refer to time in association with any
1416:"Ephemeris time from photographic positions of the moon"
772:; it changes irregularly, but the long-term trend is
651:
defined in this Resolution". Thus the new TDB, like T
371:
239:) for translating mean solar time to ephemeris time.
98:
1374:"Explanatory Supplement to the Astronomical Almanac"
627:
Partly in acknowledgement of the widespread use of T
2346:
2237:
2204:
2178:
2059:
1959:
1876:
1850:
1707:
1434:, Physical Review Letters, vol. 1 (1958), 105β107.
1399:Resolutions adopted by the IAU in 1976 at Grenoble
1204:W Markowitz, R G Hall, L Essen, J V L Parry (1958)
1087:W Markowitz, R G Hall, L Essen, J V L Parry (1958)
453:
93:time scale currently adopted as a standard by the
1460:"Comparisons of ET(Solar), ET(Lunar), UT and TDT"
327:ΔLs = + 1".00 + 2".97T + 1".23T + 0.0748B
1432:"Frequency of cesium in terms of ephemeris time"
1367:, vol. 194 (nos. 1β2) (April 1988), pp. 304β308.
1029:International Committee for Weights and Measures
608:time scale adopted in 1991 as a standard by the
1568:Monthly Notes of the Royal Astronomical Society
1128:
1126:
527:, to which ET can be seen as an approximation.
139:
1338:, vol. 53(6) (1948), issue #1170, pp. 169β179.
1096:
1094:
914:
912:
27:Time standard used in astronomical ephemerides
1658:
503:A few years later, with the invention of the
8:
1577:"Time scales in the JPL and CfA ephemerides"
695:
478:Secondary realizations by lunar observations
251:
1630:G M R Winkler and T C van Flandern (1977),
1462:, in A K Babcock & G A Wilkins (eds.),
1312:
1082:
1080:
1078:
904:'ESAE 1961': 'Explanatory Supplement (1961)
823:'ESAE 1961': 'Explanatory Supplement (1961)
768:The difference between ET and UT is called
1665:
1651:
1643:
1476:TIME From Earth Rotation to Atomic Physics
1061:
1059:
1057:
1049:General Conference on Weights and Measures
986:
984:
982:
980:
978:
953:
951:
1430:, R G Hall, L Essen, J V L Parry (1958),
1332:"On the System of Astronomical Constants"
1243:G M R Winkler and T C van Flandern (1977)
1214:
1212:
882:
880:
867:
865:
863:
515:, defined to provide continuity with ET.
436:
423:
404:
388:
370:
198:scale, and to replace for these purposes
2196:International Commission on Stratigraphy
1466:, IAU Symposia #128 (1988), pp. 413β418.
1164:L V Morrison & F R Stephenson (2004)
1159:
1157:
663:Use in official almanacs and ephemerides
77:, in a series of numerically integrated
1625:), vol. 351 (1995), #1695, pp. 165β202.
815:
669:American Ephemeris and Nautical Almanac
499:Secondary realizations by atomic clocks
1376:, University Science Books, CA, 1992;
702:the fraction 1/31 556 925.9747 of the
519:by more refined time scales including
236:
59:
1609:F R Stephenson, L V Morrison (1995),
1604:), vol. 313 (1984), #1524, pp. 47β70.
1588:F R Stephenson, L V Morrison (1984),
1500:L V Morrison, F R Stephenson (2004),
1372:'ESAA (1992)': P K Seidelmann (ed.),
1027:ESAA 1992, p. 79: citing decision of
562:Barycentric Coordinate Time BCT (TCB)
227:suggested the name 'ephemeris time'.
7:
1506:Journal for the History of Astronomy
1474:& P. Kenneth Seidelmann (2009),
1359:B Guinot and P K Seidelmann (1988),
1352:Journal for the History of Astronomy
1219:B Guinot & P K Seidelmann (1988)
558:Geocentric Coordinate Time GCT (TCG)
235:", and gave Clemence's formula (see
1172:F R Stephenson, L V Morrison (1995)
1168:F R Stephenson, L V Morrison (1984)
835:'ESAA (1992)': P K Seidelmann (ed).
237:Definition of ephemeris time (1952)
60:Definition of ephemeris time (1952)
930:
855:B Guinot and P K Seidelmann (1988)
599:coordinate time that differs from
25:
1916:Discrete time and continuous time
1638:, vol. 82 (Jan. 1977), pp. 84β92.
752:SI second referred to atomic time
612:. Thus for clocks on or near the
1841:
1835:
1242:
1231:W G Melbourne & others, 1968
1218:
1203:
1199:
1195:
1183:
1163:
1132:
1100:
1086:
1015:
969:
942:
918:
899:
854:
759:Barycentric Dynamical Time (TDB)
550:Barycentric Dynamical Time (TDB)
546:Terrestrial Dynamical Time (TDT)
244:International Astronomical Union
99:JPL ephemeris time argument Teph
1552:Bull. Astron. Inst. Netherlands
1348:"The Concept of Ephemeris Time"
1254:
1196:W Markowitz & others (1955)
1136:
1117:
957:
886:
871:
46:a former standard astronomical
1989:History of timekeeping devices
1570:, vol. 99 (1939), pp. 541β558.
1450:, vol. 64 (1959), pp. 106β113.
1414:, R G Hall, S Edelson (1955),
1230:
1171:
1167:
1:
1554:, vol. 4 (1927), pages 21β38.
568:JPL ephemeris time argument T
1581:Astronomy & Astrophysics
1287:
1148:
1065:
1040:
1011:
990:
903:
834:
822:
595:has been characterized as a
1936:Gravitational time dilation
1772:Barycentric Coordinate Time
1583:, vol. 336 (1998), 381β384.
1354:, vol. 2 (1971), pp. 73β79.
710:at 12 hours ephemeris time.
2443:
1792:Geocentric Coordinate Time
1777:Barycentric Dynamical Time
1715:Coordinated Universal Time
1365:Astronomy and Astrophysics
1010:meeting in Rome 1952: see
690:Redefinition of the second
633:Barycentric Dynamical Time
525:barycentric dynamical time
140:Redefinition of the second
1946:Time-translation symmetry
1833:
1757:International Atomic Time
1684:
1422:, vol. 60 (1955), p. 171.
803:TT β TAI = 32.184 seconds
784:International Atomic Time
581:Jet Propulsion Laboratory
73:ephemeris time argument T
1538:(1895), at pages 1β169).
1014:at sect.1C, p. 9; also
765:or its predecessor TDT.
209:The American astronomer
2206:Astronomical chronology
2179:Archaeology and geology
1886:Absolute space and time
1802:IERS Reference Meridian
1797:International Date Line
1708:International standards
1478:, Wiley-VCH, Weinheim,
1272:"IAU 2006 resolution 3"
1257:; see also ESAA (1992)
906:, esp. pages 69 and 87.
786:(TAI) was set equal to
531:Revision of time scales
306:In the introduction to
146:History (1952 standard)
79:Development Ephemerides
50:adopted in 1952 by the
1255:IAU resolutions (1976)
958:H Spencer Jones (1939)
747:
624:is in widespread use.
455:
2165:Weekday determination
2051:Sundial markup schema
763:Terrestrial Time (TT)
743:
554:Terrestrial Time (TT)
456:
2186:Chronological dating
1926:Theory of relativity
1787:Daylight saving time
1636:Astronomical Journal
1448:Astronomical Journal
1420:Astronomical Journal
1397:resolutions (1976):
1336:Astronomical Journal
1137:Spencer Jones (1939)
1135:, p. 172, following
811:Notes and references
585:Astronomical Almanac
542:dynamical timescales
369:
81:. Among them is the
64:dynamical time scale
2396:Time value of money
2191:Geologic time scale
2046:History of sundials
1911:Cosmological decade
1863:Greenwich Mean Time
1694:Orders of magnitude
1101:Wm Markowitz (1988)
943:G M Clemence (1971)
919:G M Clemence (1948)
902:, esp. p. 172, and
900:G M Clemence (1948)
872:E M Standish (1998)
643:, which is called T
505:cesium atomic clock
34:(often abbreviated
2371:Mental chronometry
1999:Marine chronometer
1851:Obsolete standards
1200:W Markowitz (1959)
1031:(CIPM), Sept 1954.
931:W de Sitter (1927)
741:by the following:
451:
308:Tables of the Sun,
274:standard SI second
176:the length of the
2427:Time in astronomy
2409:
2408:
2219:Nuclear timescale
1901:Continuous signal
1531:Tables of the Sun
1484:978-3-527-40780-4
509:atomic time scale
357:ephemeris seconds
300:Tables of the Sun
288:Definition (1952)
168:From the time of
124:Tables of the Sun
16:(Redirected from
2434:
2110:Dominical letter
2041:Equation of time
2004:Marine sandglass
1845:
1839:
1817:Terrestrial Time
1674:Time measurement
1667:
1660:
1653:
1644:
1639:
1626:
1605:
1584:
1571:
1555:
1539:
1521:
1496:
1487:
1467:
1451:
1435:
1423:
1407:
1402:
1390:
1385:
1368:
1355:
1339:
1315:
1310:
1304:
1301:
1295:
1285:
1279:
1278:
1276:
1268:
1262:
1252:
1246:
1240:
1234:
1228:
1222:
1216:
1207:
1193:
1187:
1181:
1175:
1161:
1152:
1146:
1140:
1130:
1121:
1110:
1104:
1098:
1089:
1084:
1073:
1063:
1052:
1038:
1032:
1025:
1019:
1004:
998:
988:
973:
967:
961:
955:
946:
940:
934:
928:
922:
916:
907:
896:
890:
887:S Newcomb (1895)
884:
875:
869:
858:
852:
846:
832:
826:
820:
658:
601:Terrestrial Time
521:terrestrial time
513:Terrestrial Time
460:
458:
457:
452:
441:
440:
428:
427:
409:
408:
393:
392:
215:Astronomer Royal
132:ephemeris second
21:
2442:
2441:
2437:
2436:
2435:
2433:
2432:
2431:
2412:
2411:
2410:
2405:
2342:
2233:
2200:
2174:
2055:
1955:
1906:Coordinate time
1878:Time in physics
1872:
1846:
1840:
1831:
1703:
1680:
1671:
1629:
1608:
1587:
1574:
1560:H Spencer Jones
1558:
1542:
1524:
1518:vol. 36, p. 339
1499:
1490:
1472:Dennis McCarthy
1470:
1454:
1438:
1426:
1410:
1405:
1393:
1388:
1371:
1358:
1342:
1326:
1323:
1318:
1311:
1307:
1302:
1298:
1286:
1282:
1274:
1270:
1269:
1265:
1253:
1249:
1241:
1237:
1229:
1225:
1217:
1210:
1194:
1190:
1186:, at pp. 171β3.
1184:Clemence (1948)
1182:
1178:
1162:
1155:
1147:
1143:
1133:Clemence (1948)
1131:
1124:
1111:
1107:
1099:
1092:
1085:
1076:
1064:
1055:
1039:
1035:
1026:
1022:
1016:Clemence (1971)
1005:
1001:
989:
976:
970:Clemence (1948)
968:
964:
956:
949:
941:
937:
929:
925:
917:
910:
897:
893:
885:
878:
870:
861:
853:
849:
833:
829:
821:
817:
813:
692:
665:
656:
654:
646:
630:
623:
619:
594:
590:
575:High-precision
573:
571:
533:
501:
480:
475:
473:Implementations
432:
419:
400:
384:
367:
366:
290:
282:mean solar time
218:H Spencer Jones
196:mean solar time
148:
88:
76:
56:mean solar time
28:
23:
22:
15:
12:
11:
5:
2440:
2438:
2430:
2429:
2424:
2414:
2413:
2407:
2406:
2404:
2403:
2398:
2393:
2391:Time metrology
2388:
2383:
2378:
2373:
2368:
2367:
2366:
2356:
2350:
2348:
2347:Related topics
2344:
2343:
2341:
2340:
2335:
2330:
2325:
2320:
2315:
2310:
2305:
2300:
2295:
2290:
2285:
2280:
2275:
2270:
2265:
2260:
2255:
2250:
2244:
2242:
2235:
2234:
2232:
2231:
2226:
2221:
2216:
2210:
2208:
2202:
2201:
2199:
2198:
2193:
2188:
2182:
2180:
2176:
2175:
2173:
2172:
2167:
2162:
2157:
2152:
2147:
2142:
2137:
2132:
2127:
2122:
2117:
2112:
2107:
2102:
2097:
2092:
2086:
2081:
2076:
2071:
2065:
2063:
2057:
2056:
2054:
2053:
2048:
2043:
2038:
2036:Dialing scales
2033:
2028:
2023:
2022:
2021:
2011:
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1971:
1965:
1963:
1957:
1956:
1954:
1953:
1948:
1943:
1938:
1933:
1928:
1923:
1918:
1913:
1908:
1903:
1898:
1893:
1888:
1882:
1880:
1874:
1873:
1871:
1870:
1868:Prime meridian
1865:
1860:
1858:Ephemeris time
1854:
1852:
1848:
1847:
1834:
1832:
1830:
1829:
1827:180th meridian
1824:
1819:
1814:
1809:
1804:
1799:
1794:
1789:
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1749:
1744:
1739:
1734:
1729:
1724:
1723:
1722:
1711:
1709:
1705:
1704:
1702:
1701:
1696:
1691:
1685:
1682:
1681:
1672:
1670:
1669:
1662:
1655:
1647:
1641:
1640:
1627:
1606:
1585:
1575:E M Standish,
1572:
1556:
1540:
1522:
1497:
1488:
1468:
1452:
1436:
1424:
1408:
1403:
1391:
1386:
1369:
1356:
1340:
1322:
1319:
1317:
1316:
1305:
1296:
1280:
1263:
1247:
1235:
1223:
1208:
1188:
1176:
1153:
1141:
1122:
1118:Newcomb (1895)
1105:
1090:
1074:
1053:
1033:
1020:
999:
974:
962:
947:
935:
923:
908:
891:
876:
859:
857:, at p. 304β5.
847:
837:, especially
827:
814:
812:
809:
805:
804:
800:
799:
730:observations,
721:
720:
712:
711:
691:
688:
664:
661:
652:
644:
628:
621:
617:
592:
588:
572:
569:
566:
532:
529:
500:
497:
479:
476:
474:
471:
461:. . . . . (4)
450:
447:
444:
439:
435:
431:
426:
422:
418:
415:
412:
407:
403:
399:
396:
391:
387:
383:
380:
377:
374:
353:ephemeris days
349:
348:
340:
339:
329:
328:
320:
319:
312:mean longitude
289:
286:
233:ephemeris time
200:Universal Time
170:John Flamsteed
151:Ephemeris time
147:
144:
103:
102:
86:
74:
67:
32:ephemeris time
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2439:
2428:
2425:
2423:
2420:
2419:
2417:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
2365:
2362:
2361:
2360:
2357:
2355:
2352:
2351:
2349:
2345:
2339:
2336:
2334:
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2314:
2311:
2309:
2306:
2304:
2301:
2299:
2296:
2294:
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2264:
2261:
2259:
2256:
2254:
2251:
2249:
2246:
2245:
2243:
2241:
2240:units of time
2236:
2230:
2229:Sidereal time
2227:
2225:
2222:
2220:
2217:
2215:
2214:Galactic year
2212:
2211:
2209:
2207:
2203:
2197:
2194:
2192:
2189:
2187:
2184:
2183:
2181:
2177:
2171:
2170:Weekday names
2168:
2166:
2163:
2161:
2160:Tropical year
2158:
2156:
2153:
2151:
2148:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2125:Intercalation
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2106:
2103:
2101:
2098:
2096:
2093:
2091:(lunar Hijri)
2090:
2087:
2085:
2082:
2080:
2077:
2075:
2072:
2070:
2067:
2066:
2064:
2062:
2058:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2020:
2017:
2016:
2015:
2012:
2010:
2007:
2005:
2002:
2000:
1997:
1995:
1992:
1990:
1987:
1985:
1982:
1980:
1977:
1975:
1972:
1970:
1967:
1966:
1964:
1962:
1958:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1931:Time dilation
1929:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1907:
1904:
1902:
1899:
1897:
1894:
1892:
1889:
1887:
1884:
1883:
1881:
1879:
1875:
1869:
1866:
1864:
1861:
1859:
1856:
1855:
1853:
1849:
1844:
1838:
1828:
1825:
1823:
1820:
1818:
1815:
1813:
1810:
1808:
1805:
1803:
1800:
1798:
1795:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1767:24-hour clock
1765:
1763:
1762:12-hour clock
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1721:
1718:
1717:
1716:
1713:
1712:
1710:
1706:
1700:
1697:
1695:
1692:
1690:
1687:
1686:
1683:
1679:
1675:
1668:
1663:
1661:
1656:
1654:
1649:
1648:
1645:
1637:
1633:
1628:
1624:
1620:
1616:
1612:
1607:
1603:
1599:
1595:
1591:
1586:
1582:
1578:
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1537:
1533:
1532:
1527:
1526:Simon Newcomb
1523:
1519:
1515:
1511:
1507:
1503:
1498:
1494:
1489:
1485:
1481:
1477:
1473:
1469:
1465:
1461:
1457:
1453:
1449:
1445:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1404:
1400:
1396:
1392:
1387:
1383:
1382:0-935702-68-7
1379:
1375:
1370:
1366:
1362:
1357:
1353:
1349:
1345:
1341:
1337:
1333:
1329:
1325:
1324:
1320:
1314:
1309:
1306:
1300:
1297:
1293:
1289:
1284:
1281:
1273:
1267:
1264:
1260:
1256:
1251:
1248:
1244:
1239:
1236:
1232:
1227:
1224:
1220:
1215:
1213:
1209:
1205:
1201:
1197:
1192:
1189:
1185:
1180:
1177:
1173:
1169:
1165:
1160:
1158:
1154:
1150:
1145:
1142:
1138:
1134:
1129:
1127:
1123:
1119:
1115:
1109:
1106:
1102:
1097:
1095:
1091:
1088:
1083:
1081:
1079:
1075:
1071:
1067:
1062:
1060:
1058:
1054:
1050:
1046:
1042:
1037:
1034:
1030:
1024:
1021:
1017:
1013:
1009:
1003:
1000:
996:
992:
987:
985:
983:
981:
979:
975:
971:
966:
963:
959:
954:
952:
948:
944:
939:
936:
932:
927:
924:
920:
915:
913:
909:
905:
901:
895:
892:
888:
883:
881:
877:
873:
868:
866:
864:
860:
856:
851:
848:
844:
840:
836:
831:
828:
824:
819:
816:
810:
808:
802:
801:
798:
794:
793:
792:
789:
785:
781:
779:
775:
771:
766:
764:
760:
755:
753:
746:
742:
740:
735:
733:
728:
727:atomic clocks
725:
718:
717:
716:
709:
705:
704:tropical year
701:
700:
699:
697:
689:
687:
685:
681:
676:
675:ephemerides.
674:
670:
662:
660:
650:
642:
638:
634:
625:
615:
611:
607:
602:
598:
586:
582:
578:
567:
565:
563:
559:
555:
551:
547:
543:
538:
535:In 1976, the
530:
528:
526:
522:
516:
514:
510:
506:
498:
496:
492:
488:
486:
477:
472:
470:
468:
462:
448:
445:
442:
437:
433:
429:
424:
420:
416:
413:
410:
405:
401:
397:
394:
389:
385:
381:
378:
375:
372:
364:
360:
358:
354:
346:
345:
344:
337:
336:
335:
332:
326:
325:
324:
317:
316:
315:
313:
309:
304:
302:
301:
296:
295:Simon Newcomb
287:
285:
283:
279:
275:
270:
268:
264:
259:
255:
253:
249:
245:
240:
238:
234:
228:
226:
221:
219:
216:
212:
207:
205:
204:sidereal time
201:
197:
192:
190:
185:
183:
179:
175:
171:
166:
164:
160:
156:
152:
145:
143:
141:
137:
133:
128:
126:
125:
120:
116:
113:date of 1900
112:
106:
100:
96:
92:
84:
80:
72:
68:
65:
61:
57:
53:
49:
45:
44:
43:
41:
37:
33:
19:
18:Ephemeris day
2376:Decimal time
2105:Astronomical
1984:Complication
1979:Atomic clock
1857:
1635:
1614:
1593:
1580:
1567:
1551:
1535:
1529:
1505:
1475:
1463:
1456:Wm Markowitz
1447:
1419:
1364:
1351:
1344:G M Clemence
1335:
1328:G M Clemence
1321:Bibliography
1308:
1299:
1283:
1266:
1250:
1238:
1226:
1221:, at p. 305.
1191:
1179:
1144:
1113:
1112:The unit of
1108:
1036:
1023:
1002:
972:, at p. 171.
965:
938:
926:
894:
850:
839:at pp. 41β42
830:
825:, esp. p. 9.
818:
806:
796:
782:
778:leap seconds
767:
756:
748:
744:
736:
722:
713:
693:
677:
666:
626:
597:relativistic
574:
534:
517:
502:
493:
489:
485:metrological
481:
463:
365:
361:
356:
352:
350:
341:
333:
330:
321:
307:
305:
299:
291:
278:leap seconds
271:
260:
256:
241:
232:
229:
222:
211:G M Clemence
208:
193:
186:
173:
167:
163:G M Clemence
154:
150:
149:
138:(see below:
131:
129:
123:
107:
104:
97:(see below:
35:
31:
29:
2422:Time scales
2386:System time
2381:Metric time
2100:Solar Hijri
2026:Water clock
2009:Radio clock
1941:Time domain
1921:Proper time
1807:Leap second
1689:Chronometry
1544:W de Sitter
1440:W Markowitz
1428:W Markowitz
1412:W Markowitz
1149:ESAE (1961)
1066:ESAA (1992)
1041:ESAA (1992)
1012:ESAE (1961)
991:ESAA (1992)
577:ephemerides
182:W de Sitter
159:ephemerides
2416:Categories
2401:Timekeeper
2354:Chronology
2338:Millennium
2224:Precession
2130:Julian day
1951:T-symmetry
1812:Solar time
1782:Civil time
1114:mean solar
680:W J Eckert
48:time scale
2298:Fortnight
2145:Lunisolar
2135:Leap year
2069:Gregorian
2019:stopwatch
1994:Hourglass
1974:Astrarium
1891:Spacetime
1822:Time zone
1699:Metrology
1678:standards
1623:0080-4614
1602:0080-4614
1514:0021-8286
1292:at p. 612
1288:ESAA 1992
1151:at p. 70.
774:parabolic
739:SI second
732:Markowitz
708:January 0
706:for 1900
657:< 2 ms
373:δ
363:(ET-UT):
355:of 86400
267:SI second
263:IAT (TAI)
225:D Brouwer
115:January 0
40:ephemeris
30:The term
2359:Duration
2333:Saeculum
2313:Olympiad
2155:Solstice
2084:Holocene
2061:Calendar
1961:Horology
1752:ISO 8601
1747:ISO 31-1
1546:(1927),
1528:(1895),
1458:(1988),
1442:(1959),
1346:(1971),
1259:at p. 41
843:at p. 79
252:Revision
189:A Danjon
2328:Century
2318:Lustrum
2248:Instant
2120:Equinox
2089:Islamic
2031:Sundial
1896:Chronon
1202:; also
1166:; also
1070:page 42
1051:(CGPM).
1045:page 80
1006:At the
995:page 79
724:Caesium
696:History
467:ΔT
119:Newcomb
117:and of
2323:Decade
2278:Moment
2273:Minute
2268:Second
2238:Other
2095:Julian
2074:Hebrew
1720:offset
1621:
1600:
1512:
1482:
1380:
1170:, and
1043:, see
993:, see
136:second
2364:music
2303:Month
2263:Jiffy
2258:Shake
2253:Flick
2150:Solar
2140:Lunar
2115:Epact
2079:Hindu
2014:Watch
1969:Clock
1566:, in
1275:(PDF)
1068:, at
684:Brown
682:from
641:DE405
614:geoid
446:1.821
411:.3165
111:epoch
83:DE405
2308:Year
2293:Week
2283:Hour
1737:DUT1
1676:and
1619:ISSN
1598:ISSN
1510:ISSN
1480:ISBN
1378:ISBN
841:and
797:i.e.
560:and
548:and
523:and
430:.949
395:.349
242:The
174:i.e.
2288:Day
1504:,
1395:IAU
1008:IAU
788:UT2
780:).
761:or
673:JPL
653:eph
649:TDB
645:eph
637:TCB
629:eph
622:eph
618:eph
616:, T
610:IAU
606:TCB
593:eph
589:eph
570:eph
537:IAU
469:).
297:'s
254:).
178:day
142:).
121:'s
95:IAU
91:TCB
87:eph
75:eph
71:JPL
52:IAU
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1732:ΞT
1727:UT
1634:,
1613:,
1579:,
1562:,
1550:,
1520:).
1446:,
1418:,
1363:,
1350:,
1334:,
1330:,
1290:,
1211:^
1198:;
1156:^
1125:^
1093:^
1077:^
1056:^
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950:^
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862:^
770:ΞT
564:.
556:,
544::
421:29
402:72
386:24
284:.
206:.
165:.
155:ET
127:.
101:).
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449:B
443:+
438:2
434:T
425:s
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390:s
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379:=
376:t
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