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timescales.jl

Astrometry.SOFA.d2dtf — Function
d2dtf(scale::String, ndp::Int, day1::Float64, day2::Float64)

Format for output a 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds).

Input

  • scale – time scale ID (Note 1)
  • ndp – resolution (Note 2)
  • day1 – time as a 2-part Julian Date (Notes 3, 4)
  • day2 – time as a 2-part Julian Date (Notes 3, 4)

Output

  • date – year, month, day in Gregorian calendar (Note 1, 5)

Note

  1. scale identifies the time scale. Only the value "UTC" (in upper case) is significant, and enables handling of leap seconds (see Note 4).

  2. ndp is the number of decimal places in the seconds field, and can have negative as well as positive values, such as:

    ndp resolution -4 1 00 00 -3 0 10 00 -2 0 01 00 -1 0 00 10 0 0 00 01 1 0 00 00.1 2 0 00 00.01 3 0 00 00.001

    The limits are platform dependent, but a safe range is -5 to +9.

  3. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. In the case of UTC, where the use of JD is problematical, special conventions apply: see the next note.

  4. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The ERFA internal convention is that the quasi-JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era there were smaller jumps (in either direction) each time the linear UTC(TAI) expression was changed, and these "mini-leaps" are also included in the ERFA convention.

  5. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See eraDat for further details.

  6. For calendar conventions and limitations, see cal2jd.

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Astrometry.SOFA.dat — Function
dat(year::Integer, month::Integer, day::Integer, subday::Float64)

For a given UTC date, calculate Δ(AT) = TAI-UTC.

Input

  • year – year (Notes 1 and 2) (in UTC)
  • month – month (Note 2)
  • day – day (Notes 2 and 3)
  • fraction – fraction of day (Note 4)

Output

  • Δt – TAI - UTC (in seconds)

Note

  1. UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper to call the function with an earlier date. If this is attempted, zero is returned together with a warning status.

    Because leap seconds cannot, in principle, be predicted in advance, a reliable check for dates beyond the valid range is impossible. To guard against gross errors, a year five or more after the release year of the present function (see the constant IYV) is considered dubious. In this case a warning status is returned but the result is computed in the normal way.

    For both too-early and too-late years, the warning status is +1. This is distinct from the error status -1, which signifies a year so early that JD could not be computed.

  2. If the specified date is for a day which ends with a leap second, the TAI-UTC value returned is for the period leading up to the leap second. If the date is for a day which begins as a leap second ends, the TAI-UTC returned is for the period following the leap second.

  3. The day number must be in the normal calendar range, for example 1 through 30 for April. The "almanac" convention of allowing such dates as January 0 and December 32 is not supported in this function, in order to avoid confusion near leap seconds.

  4. The fraction of day is used only for dates before the introduction of leap seconds, the first of which occurred at the end of 1971. It is tested for validity (0 to 1 is the valid range) even if not used; if invalid, zero is used and status -4 is returned. For many applications, setting fd to zero is acceptable; the resulting error is always less than 3 ms (and occurs only pre-1972).

  5. The status value returned in the case where there are multiple errors refers to the first error detected. For example, if the month and day are 13 and 32 respectively, status -2 (bad month) will be returned. The "internal error" status refers to a case that is impossible but causes some compilers to issue a warning.

  6. In cases where a valid result is not available, zero is returned.

References

  1. For dates from 1961 January 1 onwards, the expressions from the file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.

  2. The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of the 1992 Explanatory Supplement.

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Astrometry.SOFA.dtdb — Function
dtdb(day1::Float64, day2::Float64, ut1::Float64, eastlon::Float64,
     u::Float64, v::Float64)

An approximation to TDB-TT, the difference between barycentric dynamical time and terrestrial time, for an observer on the Earth.

The different time scales - proper, coordinate and realized - are related to each other:

      TAI             <-  physically realized
       :
    offset            <-  observed (nominally +32.184s)
       :
      TT              <-  terrestrial time
       :

rate adjustment (LG) <- definition of TT : TCG <- time scale for GCRS : "periodic" terms <- eraDtdb is an implementation : rate adjustment (LC) <- function of solar-system ephemeris : TCB <- time scale for BCRS : rate adjustment (-L_B) <- definition of TDB : TDB <- TCB scaled to track TT : "periodic" terms <- -eraDtdb is an approximation : TT <- terrestrial time

Adopted values for the various constants can be found in the IERS Conventions (McCarthy & Petit 2003).

Input

  • day1 – TBD as part 1 of date (Notes 1-3)
  • day2 – TDB as part 2 of date
  • ut – universal time (UT1, fraction of one day)
  • elong – longitude (east positive, radians)
  • u – distance from Earth spin axis (km)
  • v – distance north of equatorial plane (km)

Output

  • tdbtt – TDB - TT

Note

  1. The date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

       date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)

    The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

    Although the date is, formally, barycentric dynamical time (TDB), the terrestrial dynamical time (TT) can be used with no practical effect on the accuracy of the prediction.

  2. TT can be regarded as a coordinate time that is realized as an offset of 32.184s from International Atomic Time, TAI. TT is a specific linear transformation of geocentric coordinate time TCG, which is the time scale for the Geocentric Celestial Reference System, GCRS.

  3. TDB is a coordinate time, and is a specific linear transformation of barycentric coordinate time TCB, which is the time scale for the Barycentric Celestial Reference System, BCRS.

  4. The difference TCG-TCB depends on the masses and positions of the bodies of the solar system and the velocity of the Earth. It is dominated by a rate difference, the residual being of a periodic character. The latter, which is modeled by the present function, comprises a main (annual) sinusoidal term of amplitude approximately 0.00166 seconds, plus planetary terms up to about 20 microseconds, and lunar and diurnal terms up to 2 microseconds. These effects come from the changing transverse Doppler effect and gravitational red-shift as the observer (on the Earth's surface) experiences variations in speed (with respect to the BCRS) and gravitational potential.

  5. TDB can be regarded as the same as TCB but with a rate adjustment to keep it close to TT, which is convenient for many applications. The history of successive attempts to define TDB is set out in Resolution 3 adopted by the IAU General Assembly in 2006, which defines a fixed TDB(TCB) transformation that is consistent with contemporary solar-system ephemerides. Future ephemerides will imply slightly changed transformations between TCG and TCB, which could introduce a linear drift between TDB and TT; however, any such drift is unlikely to exceed 1 nanosecond per century.

  6. The geocentric TDB-TT model used in the present function is that of Fairhead & Bretagnon (1990), in its full form. It was originally supplied by Fairhead (private communications with P.T.Wallace,

    1. as a Fortran subroutine. The present C function contains an

    adaptation of the Fairhead code. The numerical results are essentially unaffected by the changes, the differences with respect to the Fairhead & Bretagnon original being at the 1e-20 s level.

    The topocentric part of the model is from Moyer (1981) and Murray (1983), with fundamental arguments adapted from Simon et al. 1994. It is an approximation to the expression ( v / c ) . ( r / c ), where v is the barycentric velocity of the Earth, r is the geocentric position of the observer and c is the speed of light.

    By supplying zeroes for u and v, the topocentric part of the model can be nullified, and the function will return the Fairhead & Bretagnon result alone.

  7. During the interval 1950-2050, the absolute accuracy is better than +/- 3 nanoseconds relative to time ephemerides obtained by direct numerical integrations based on the JPL DE405 solar system ephemeris.

  8. It must be stressed that the present function is merely a model, and that numerical integration of solar-system ephemerides is the definitive method for predicting the relationship between TCG and TCB and hence between TT and TDB.

References

Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247 (1990).

IAU 2006 Resolution 3.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Moyer, T.D., Cel.Mech., 23, 33 (1981).

Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).

Seidelmann, P.K. et al., Explanatory Supplement to the Astronomical Almanac, Chapter 2, University Science Books (1992).

Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).

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Astrometry.SOFA.dtf2d — Function
dtf2d(scale::String, year::Int, month::Int, day::Int, hour::Int,
      minute::Int, second::Float64)

Encode date and time fields into 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds).

Input

  • scale – time scale ID (Note 1)
  • year – year in Gregorian calendar (Note 2)
  • month – month in Gregorian calendar (Note 2)
  • day – day in Gregorian calendar (Note 2)
  • hour – hour
  • minute – minute
  • second – seconds

Output

  • day1 – part 1 of Julian Date (Notes 3,4)

-day2 – part 2 of Julian Date (Notes 3,4)

Note

  1. scale identifies the time scale. Only the value "UTC" (in upper case) is significant, and enables handling of leap seconds (see Note 4).

  2. For calendar conventions and limitations, see eraCal2jd.

  3. The sum of the results, d1+d2, is Julian Date, where normally d1 is the Julian Day Number and d2 is the fraction of a day. In the case of UTC, where the use of JD is problematical, special

  4. The sum of the results, d1+d2, is Julian Date, where normally d1 is the Julian Day Number and d2 is the fraction of a day. In the case of UTC, where the use of JD is problematical, special conventions apply: see the next note.

  5. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The ERFA internal convention is that the quasi-JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era there were smaller jumps (in either direction) each time the linear UTC(TAI) expression was changed, and these "mini-leaps" are also included in the ERFA convention.

  6. The warning status "time is after end of day" usually means that the sec argument is greater than 60.0. However, in a day ending in a leap second the limit changes to 61.0 (or 59.0 in the case of a negative leap second).

  7. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See eraDat for further details.

  8. Only in the case of continuous and regular time scales (TAI, TT, TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly speaking. In the other cases (UT1 and UTC) the result must be used with circumspection; in particular the difference between two such results cannot be interpreted as a precise time interval.

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Astrometry.SOFA.taitt — Function
taitt(day1::Float64, day2::Float64)

Time scale transformation: International Atomic Time, TAI, to Terrestrial Time, TT.

Input

  • day1 – TAI as part 1 of Julian Date
  • day2 – TAI as part 2 of Julian Date

Output

  • tt1 – TT as part 1 of Julian Date
  • tt2 – TT as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned (day1,day2) follow suit.

References

  1. McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

  2. Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.taiut1 — Function
taiut1(day1::Float64, day2::Float64, Δt::Float64)

Time scale transformation: International Atomic Time, TAI, to Universal Time, UT1.

Input

  • day1 – TAI as part 1 of Julian Date
  • day2 – TAI as part 2 of Julian Date
  • dta – UT1-TAI in seconds

Output

  • ut11 – UT1 as part 1 of Julian Date
  • ut12 – UT1 as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where tai1 is the Julian Day Number and tai2 is the fraction of a day. The returned (day1,day2) follow suit.

  2. The argument dta, i.e. UT1-TAI, is an observed quantity, and is available from IERS tabulations.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.taiutc — Function
taiutc(day1::Float64, day2::Float64)

Time scale transformation: International Atomic Time, TAI, to Coordinated Universal Time, UTC.

Input

  • day1 – TAI as part 1 of Julian Date (Note 1)
  • day2 – TAI as part 2 of Julian Date

Output

  • utc1 – UTC as part 1 of quasi Julian Date (Notes 1-3)
  • utc2 – UTC as part 2 of quasi Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned (utc1, utc2) form an analogous pair, except that a special convention is used, to deal with the problem of leap seconds - see the next note.

  2. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era there were smaller jumps (in either direction) each time the linear UTC(TAI) expression was changed, and these "mini-leaps" are also included in the ERFA convention.

  3. The function eraD2dtf can be used to transform the UTC quasi-JD into calendar date and clock time, including UTC leap second handling.

  4. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See eraDat for further details.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.tcbtdb — Function
tcbtdb(day1::Float64, day2::Float64)

Time scale transformation: Barycentric Coordinate Time, TCB, to Barycentric Dynamical Time, TDB.

Input

  • day1 – TCB as part 1 of Julian Date
  • day2 – TCB as part 2 of Julian Date

Output

  • tdb1 – TDB as part 1 of Julian Date
  • tdb2 – TDB as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned (tdb1,tdb2) follow suit.

  2. The 2006 IAU General Assembly introduced a conventional linear transformation between TDB and TCB. This transformation compensates for the drift between TCB and terrestrial time TT, and keeps TDB approximately centered on TT. Because the relationship between TT and TCB depends on the adopted solar system ephemeris, the degree of alignment between TDB and TT over long intervals will vary according to which ephemeris is used. Former definitions of TDB attempted to avoid this problem by stipulating that TDB and TT should differ only by periodic effects. This is a good description of the nature of the relationship but eluded precise mathematical formulation. The conventional linear relationship adopted in 2006 sidestepped these difficulties whilst delivering a TDB that in practice was consistent with values before that date.

  3. TDB is essentially the same as Teph, the time argument for the JPL solar system ephemerides.

References

IAU 2006 Resolution B3

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Astrometry.SOFA.tcgtt — Function
tcgtt(day1::Float64, day2::Float64)

Time scale transformation: Geocentric Coordinate Time, TCG, to Terrestrial Time, TT.

Input

  • day1 – TCG as part 1 of Julian Date
  • day2 – TCG as part 2 of Julian Date

Output

  • tt1 – TT as part 1 of Julian Date
  • tt1 – TT as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned (tt1, tt2) follow suit.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

IAU 2000 Resolution B1.9

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Astrometry.SOFA.tdbtcb — Function
tdbtcb(day1::Float64, day2::Float64)

Time scale transformation: Barycentric Dynamical Time, TDB, to Barycentric Coordinate Time, TCB.

Input

  • day1 – TDB as part 1 of Julian Date
  • day2 – TDB as part 2 of Julian Date

Output

  • tcb1 – TCB as part 1 of Julian Date
  • tcb2 – TCB as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tcb1,tcb2 follow suit.

  2. The 2006 IAU General Assembly introduced a conventional linear transformation between TDB and TCB. This transformation compensates for the drift between TCB and terrestrial time TT, and keeps TDB approximately centered on TT. Because the relationship between TT and TCB depends on the adopted solar system ephemeris, the degree of alignment between TDB and TT over long intervals will vary according to which ephemeris is used. Former definitions of TDB attempted to avoid this problem by stipulating that TDB and TT should differ only by periodic effects. This is a good description of the nature of the relationship but eluded precise mathematical formulation. The conventional linear relationship adopted in 2006 sidestepped these difficulties whilst delivering a TDB that in practice was consistent with values before that date.

  3. TDB is essentially the same as Teph, the time argument for the JPL solar system ephemerides.

References

IAU 2006 Resolution B3

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Astrometry.SOFA.tdbtt — Function
tdbtt(day1::Float64, day2::Float64, dtr::Float64)

Time scale transformation: Barycentric Dynamical Time, TDB, to Terrestrial Time, TT.

Input

  • day1 – TDB as part 1 of Julian Date
  • day2 – TDB as part 2 of Julian Date
  • dtr – TDB-TT in seconds

Output

  • tt1 – TT as part 1 of Julian Date
  • tt2 – TT as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tt1,tt2 follow suit.

  2. The argument dtr represents the quasi-periodic component of the GR transformation between TT and TCB. It is dependent upon the adopted solar-system ephemeris, and can be obtained by numerical integration, by interrogating a precomputed time ephemeris or by evaluating a model such as that implemented in the ERFA function eraDtdb. The quantity is dominated by an annual term of 1.7 ms amplitude.

  3. TDB is essentially the same as Teph, the time argument for the JPL solar system ephemerides.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

IAU 2006 Resolution 3

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Astrometry.SOFA.tttai — Function
tttai(day1::Float64, day2::Float64)

Time scale transformation: Terrestrial Time, TT, to International Atomic Time, TAI.

Input

  • day1 – TT as part 1 of Julian Date
  • day2 – TT as part 2 of Julian Date

Output

  • tai1 – TAI as part 1 of Julian Date
  • tai2 – TAI as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tai1,tai2 follow suit.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.tttcg — Function
tttcg(day1::Float64, day2::Float64)

Time scale transformation: Terrestrial Time, TT, to Geocentric Coordinate Time, TCG.

Input

  • day1 – TT as part 1 of Julian Date
  • day2 – TT as part 2 of Julian Date

Output

  • tcg1 – TCG as part 1 of Julian Date
  • tcg2 – TCG as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tcg1,tcg2 follow suit.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

IAU 2000 Resolution B1.9

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Astrometry.SOFA.tttdb — Function
tttdb(day1::Float64, day2::Float64, dtr::Float64)

Time scale transformation: Terrestrial Time, TT, to Barycentric Dynamical Time, TDB.

Input

  • day1 – TT as part 1 of Julian Date
  • day2 – TT as part 2 of Julian Date
  • dtr – TDB-TT in seconds

Output

  • tdb1 – TDB as part 1 of Julian Date
  • tdb2 – TDB as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tdb1,tdb2 follow suit.

  2. The argument dtr represents the quasi-periodic component of the GR transformation between TT and TCB. It is dependent upon the adopted solar-system ephemeris, and can be obtained by numerical integration, by interrogating a precomputed time ephemeris or by evaluating a model such as that implemented in the ERFA function eraDtdb. The quantity is dominated by an annual term of 1.7 ms amplitude.

  3. TDB is essentially the same as Teph, the time argument for the JPL solar system ephemerides.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

IAU 2006 Resolution 3

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Astrometry.SOFA.ttut1 — Function
ttut1(day1::Float64, day2::Float64, dt::Float64)

Time scale transformation: Terrestrial Time, TT, to Universal Time, UT1.

Input

  • day1 – TT as part 1 of Julian Date
  • day2 – TT as part 2 of Julian Date
  • dt – TT-UT1 in seconds

Output

  • ut11 – UT1 as part 1 of Julian Date
  • ut12 – UT1 as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned ut11,ut12 follow suit.

  2. The argument dt is classical Delta T.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.ut1tai — Function
ut1tai(day1::Float64, day2::Float64, dta::Float64)

Time scale transformation: Universal Time, UT1, to International Atomic Time, TAI.

Input

  • day1 – UT1 as part 1 of Julian Date
  • day2 – UT1 as part 2 of Julian Date
  • dta – UT1-TAI in seconds

Output

  • tai1 – TAI as part 1 of Julian Date
  • tai2 – TAI as part 2 of Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tai1,tai2 follow suit.

  2. The argument dta, i.e. UT1-TAI, is an observed quantity, and is available from IERS tabulations.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.ut1tt — Function
ut1tt(day1::Float64, day2::Float64, dt::Float64)

Time scale transformation: Universal Time, UT1, to Terrestrial Time, TT.

Input

  • day1 – UT1 as part 1 Julian Date (Note 1)
  • day2 – UT1 as part 2 Julian Date
  • dt – TT-UT1 in seconds (Note 2)

Output

  • tt1 – TT as part 1 Julian Date
  • tt2 – TT as part 2 Julian Date

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned tt1,tt2 follow suit.

  2. The argument dt is classical Delta T.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.ut1utc — Function
ut1utc(day1::Float64, day2::Float64, duts::Float64)

Time scale transformation: Universal Time, UT1, to Coordinated Universal Time, UTC.

Input

  • ut1 – UT1 as part 1 of Julian Date (Note 1)
  • ut2 – UT1 as part 2 of Julian Date
  • duts – Delta UT1: UT1-UTC in seconds (Note 2)

Output

  • utc1 – UTC as part 1 of quasi Julian Date (Notes 3,4)
  • utc2 – UTC as part 2 of quasi Julian Date (Notes 3,4)

Note

  1. day1+day2 is Julian Date, apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day. The returned utc1 and utc2 form an analogous pair, except that a special convention is used, to deal with the problem of leap seconds - see Note 3.

  2. Delta UT1 can be obtained from tabulations provided by the International Earth Rotation and Reference Systems Service. The value changes abruptly by 1s at a leap second; however, close to a leap second the algorithm used here is tolerant of the "wrong" choice of value being made.

  3. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the returned quasi-JD UTC1+UTC2 represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

  4. The function eraD2dtf can be used to transform the UTC quasi-JD into calendar date and clock time, including UTC leap second handling.

  5. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See eraDat for further details.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.utctai — Function
utctai(day1::Float64, day2::Float64)

Time scale transformation: Coordinated Universal Time, UTC, to International Atomic Time, TAI.

Input

  • day1 – UTC as part 1 of quasi Julian Date (Notes 1-4)
  • day2 – UTC as part 2 of quasi Julian Date

Output

  • tai1 – TAI as part 1 of Julian Date (Note 5)
  • tai2 – TAI as part 2 of Julian Date

Note

  1. day1+day2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day.

  2. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era there were smaller jumps (in either direction) each time the linear UTC(TAI) expression was changed, and these "mini-leaps" are also included in the ERFA convention.

  3. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See eraDat for further details.

  4. The function eraDtf2d converts from calendar date and time of day into 2-part Julian Date, and in the case of UTC implements the leap-second-ambiguity convention described above.

  5. The returned TAI1,TAI2 are such that their sum is the TAI Julian Date.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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Astrometry.SOFA.utcut1 — Function
utcut1(day1::Float64, day2::Float64, dut1::Float64)

Time scale transformation: Coordinated Universal Time, UTC, to Universal Time, UT1.

Input

  • day1 – UTC as part 1 of quasi Julian Date (Notes 1-4)
  • day2 – UTC as part 2 of quasi Julian Date
  • dut1 – Delta UT1 = UT1-UTC in seconds (Note 5)

Output

  • ut11 – UT1 as part 1 of Julian Date
  • ut12 – UT1 as part 2 of Julian Date

Note

  1. day1+day2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where day1 is the Julian Day Number and day2 is the fraction of a day.

  2. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

  3. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See eraDat for further details.

  4. The function eraDtf2d converts from calendar date and time of day into 2-part Julian Date, and in the case of UTC implements the leap-second-ambiguity convention described above.

  5. Delta UT1 can be obtained from tabulations provided by the International Earth Rotation and Reference Systems Service. It is the caller's responsibility to supply a dut1 argument containing the UT1-UTC value that matches the given UTC.

  6. The returned ut11,ut12 are such that their sum is the UT1 Julian Date.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

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