Comments (4)
qntm
commented on July 19, 2024
____________________________________________________________________________
Limits of validity (at 0h UTC) TAI-UTC (MJD = Modified Julian Day)
____________________________________________________________________________
1961 Jan. 1 - 1961 Aug. 1 1.422 818 0s + (MJD - 37 300) x 0.001 296s
Aug. 1 - 1962 Jan. 1 1.372 818 0s + ""
1962 Jan. 1 - 1963 Nov. 1 1.845 858 0s + (MJD - 37 665) x 0.001 123 2s
1963 Nov. 1 - 1964 Jan. 1 1.945 858 0s + ""
1964 Jan. 1 - April 1 3.240 130 0s + (MJD - 38 761) x 0.001 296s
April 1 - Sept. 1 3.340 130 0s + ""
Sept. 1 - 1965 Jan. 1 3.440 130 0s + ""
1965 Jan. 1 - March 1 3.540 130 0s + ""
March 1 - Jul. 1 3.640 130 0s + ""
Jul. 1 - Sept. 1 3.740 130 0s + ""
Sept. 1 - 1966 Jan. 1 3.840 130 0s + ""
1966 Jan. 1 - 1968 Feb. 1 4.313 170 0s + (MJD - 39 126) x 0.002 592s
1968 Feb. 1 - 1972 Jan. 1 4.213 170 0s + ""
1972 Jan. 1 - Jul. 1 10s
Jul. 1 - 1973 Jan. 1 11s
1973 Jan. 1 - 1974 Jan. 1 12s
1974 Jan. 1 - 1975 Jan. 1 13s
1975 Jan. 1 - 1976 Jan. 1 14s
1976 Jan. 1 - 1977 Jan. 1 15s
1977 Jan. 1 - 1978 Jan. 1 16s
1978 Jan. 1 - 1979 Jan. 1 17s
1979 Jan. 1 - 1980 Jan. 1 18s
1980 Jan. 1 - 1981 Jul. 1 19s
1981 Jul. 1 - 1982 Jul. 1 20s
1982 Jul. 1 - 1983 Jul. 1 21s
1983 Jul. 1 - 1985 Jul. 1 22s
1985 Jul. 1 - 1988 Jan. 1 23s
1988 Jan. 1 - 1990 Jan. 1 24s
1990 Jan. 1 - 1991 Jan. 1 25s
1991 Jan. 1 - 1992 Jul. 1 26s
1992 Jul. 1 - 1993 Jul 1 27s
1993 Jul. 1 - 1994 Jul. 1 28s
1994 Jul. 1 - 1996 Jan. 1 29s
1996 Jan. 1 - 1997 Jul. 1 30s
1997 Jul. 1 - 1999 Jan. 1 31s
1999 Jan. 1 - 2006 Jan. 1 32s
2006 Jan. 1 - 2009 Jan. 1 33s
2009 Jan. 1 - 2012 Jul. 1 34s
2012 Jul. 1 - 2015 Jul. 1 35s
2015 Jul. 1 - 2017 Jan. 1 36s
2017 Jan. 1 - 37s
from t-a-i.
qntm
commented on July 19, 2024
1961 JAN 1 =JD 2437300.5 TAI-UTC= 1.4228180 S + (MJD - 37300.) X 0.001296 S
1961 AUG 1 =JD 2437512.5 TAI-UTC= 1.3728180 S + (MJD - 37300.) X 0.001296 S
1962 JAN 1 =JD 2437665.5 TAI-UTC= 1.8458580 S + (MJD - 37665.) X 0.0011232S
1963 NOV 1 =JD 2438334.5 TAI-UTC= 1.9458580 S + (MJD - 37665.) X 0.0011232S
1964 JAN 1 =JD 2438395.5 TAI-UTC= 3.2401300 S + (MJD - 38761.) X 0.001296 S
1964 APR 1 =JD 2438486.5 TAI-UTC= 3.3401300 S + (MJD - 38761.) X 0.001296 S
1964 SEP 1 =JD 2438639.5 TAI-UTC= 3.4401300 S + (MJD - 38761.) X 0.001296 S
1965 JAN 1 =JD 2438761.5 TAI-UTC= 3.5401300 S + (MJD - 38761.) X 0.001296 S
1965 MAR 1 =JD 2438820.5 TAI-UTC= 3.6401300 S + (MJD - 38761.) X 0.001296 S
1965 JUL 1 =JD 2438942.5 TAI-UTC= 3.7401300 S + (MJD - 38761.) X 0.001296 S
1965 SEP 1 =JD 2439004.5 TAI-UTC= 3.8401300 S + (MJD - 38761.) X 0.001296 S
1966 JAN 1 =JD 2439126.5 TAI-UTC= 4.3131700 S + (MJD - 39126.) X 0.002592 S
1968 FEB 1 =JD 2439887.5 TAI-UTC= 4.2131700 S + (MJD - 39126.) X 0.002592 S
1972 JAN 1 =JD 2441317.5 TAI-UTC= 10.0 S + (MJD - 41317.) X 0.0 S
1972 JUL 1 =JD 2441499.5 TAI-UTC= 11.0 S + (MJD - 41317.) X 0.0 S
1973 JAN 1 =JD 2441683.5 TAI-UTC= 12.0 S + (MJD - 41317.) X 0.0 S
1974 JAN 1 =JD 2442048.5 TAI-UTC= 13.0 S + (MJD - 41317.) X 0.0 S
1975 JAN 1 =JD 2442413.5 TAI-UTC= 14.0 S + (MJD - 41317.) X 0.0 S
1976 JAN 1 =JD 2442778.5 TAI-UTC= 15.0 S + (MJD - 41317.) X 0.0 S
1977 JAN 1 =JD 2443144.5 TAI-UTC= 16.0 S + (MJD - 41317.) X 0.0 S
1978 JAN 1 =JD 2443509.5 TAI-UTC= 17.0 S + (MJD - 41317.) X 0.0 S
1979 JAN 1 =JD 2443874.5 TAI-UTC= 18.0 S + (MJD - 41317.) X 0.0 S
1980 JAN 1 =JD 2444239.5 TAI-UTC= 19.0 S + (MJD - 41317.) X 0.0 S
1981 JUL 1 =JD 2444786.5 TAI-UTC= 20.0 S + (MJD - 41317.) X 0.0 S
1982 JUL 1 =JD 2445151.5 TAI-UTC= 21.0 S + (MJD - 41317.) X 0.0 S
1983 JUL 1 =JD 2445516.5 TAI-UTC= 22.0 S + (MJD - 41317.) X 0.0 S
1985 JUL 1 =JD 2446247.5 TAI-UTC= 23.0 S + (MJD - 41317.) X 0.0 S
1988 JAN 1 =JD 2447161.5 TAI-UTC= 24.0 S + (MJD - 41317.) X 0.0 S
1990 JAN 1 =JD 2447892.5 TAI-UTC= 25.0 S + (MJD - 41317.) X 0.0 S
1991 JAN 1 =JD 2448257.5 TAI-UTC= 26.0 S + (MJD - 41317.) X 0.0 S
1992 JUL 1 =JD 2448804.5 TAI-UTC= 27.0 S + (MJD - 41317.) X 0.0 S
1993 JUL 1 =JD 2449169.5 TAI-UTC= 28.0 S + (MJD - 41317.) X 0.0 S
1994 JUL 1 =JD 2449534.5 TAI-UTC= 29.0 S + (MJD - 41317.) X 0.0 S
1996 JAN 1 =JD 2450083.5 TAI-UTC= 30.0 S + (MJD - 41317.) X 0.0 S
1997 JUL 1 =JD 2450630.5 TAI-UTC= 31.0 S + (MJD - 41317.) X 0.0 S
1999 JAN 1 =JD 2451179.5 TAI-UTC= 32.0 S + (MJD - 41317.) X 0.0 S
2006 JAN 1 =JD 2453736.5 TAI-UTC= 33.0 S + (MJD - 41317.) X 0.0 S
2009 JAN 1 =JD 2454832.5 TAI-UTC= 34.0 S + (MJD - 41317.) X 0.0 S
2012 JUL 1 =JD 2456109.5 TAI-UTC= 35.0 S + (MJD - 41317.) X 0.0 S
2015 JUL 1 =JD 2457204.5 TAI-UTC= 36.0 S + (MJD - 41317.) X 0.0 S
2017 JAN 1 =JD 2457754.5 TAI-UTC= 37.0 S + (MJD - 41317.) X 0.0 S
from t-a-i.
qntm
commented on July 19, 2024
For example, the line:
1966 JAN 1 =JD 2439126.5 TAI-UTC= 4.3131700 S + (MJD - 39126.) X 0.002592 S
indicates that the following all represent the same instant in time:
- 1966-01-01 00:00:00.000000 UTC
- 1966-01-01 00:00:04.313170 TAI
- Julian date 2439126.5
- Modified Julian date 39126.0
At this instant, TAI was 4.313170 seconds ahead of Unix, and pulling ahead by 0.002592 seconds per day.
By 1968-02-01 00:00:00 UTC, TAI was 6.285682 seconds ahead at 1968-02-01 00:00:06.285682.
However, the next line of data
1968 FEB 1 =JD 2439887.5 TAI-UTC= 4.2131700 S + (MJD - 39126.) X 0.002592 S
indicates that the following all represent the same instants in time:
- 1968-02-01 00:00:00.000000 UTC
- 1968-02-01 00:00:06.185682 TAI
- Julian date 2439887.5
- Modified Julian date 39887
So this means that at 1968-02-01 00:00:00 UTC, TAI suddenly jumped from 6.285682 seconds ahead to only 6.185682 seconds ahead. Since TAI is a fixture and UTC is derived from it, this in fact indicates a deliberately inserted discontinuity in UTC, from which some 0.1 TAI seconds were removed... a removed one-tenth of a leap second, as it were. And you thought there was no such thing!
TAI and UTC continued to drift apart. By 1972-01-01 00:00:00 UTC, TAI was 9.892242 seconds ahead at 1972-01-01 00:00:09.892242. This leads us to beginning of the "modern era" of TAI:
1972 JAN 1 =JD 2441317.5 TAI-UTC= 10.0 S + (MJD - 41317.) X 0.0 S
Here, it is still 1972-01-01 00:00:00 UTC but it is suddenly 1972-01-01 00:00:10 TAI, thanks to the highly irregular insertion of 0.107758 "leap" TAI seconds into UTC. From this moment on,
- UTC and TAI seconds are exactly the same length, and
- the offset between TAI and UTC only changes at discrete intervals, by a whole 1.000000 seconds each time.
from t-a-i.
qntm
commented on July 19, 2024
Done, basically. Give or take some serious thought about precision loss, and exactly how conversions behave at boundaries of leap time insertion/removal...
from t-a-i.
Related Issues (8)
- Improved API for different leap second models HOT 3
- Slightly inaccurate TAI block start times HOT 1
- Unix block start times should always be integer numbers of milliseconds, but aren't
- Need to specify Unix block end times explicitly HOT 1
- Integration with `Temporal`
- Move to ES modules HOT 3
- Support Meta's 17-hour sinusoidal smear? HOT 3
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