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Memorandum N 1
21.06.997
Arrangement on time and timelike argument

The basic argument is the TT (terrestrial time) according the "Resolution C7 passed at the 1994 Hague General Assembly of the IAU which recommends that J2000.0 be defined at the geocenter and at the date
2000.0 January 1.5 TT = Julian Date 2451545.0 TT."

As a matter of fact each temporal argument has its own julian day (as they are used in the literature) but we shall consider that epoch (that moment of time) fixed in julian days refered to TT, unless otherwise specified. Practically this formula is a determination of the julian days reference point. However to avoid mistakes when programming, we choose within the framework of the project Levante the zero-point of time at 2000.0 January 1.0 TT = Julian Date 2451544.5 TT (Hereafter it is a definition of our Custom Julian date). As a unit we take the day of TT for time and AU for length1).

TAI (temps atomique international)=TT–32.184s. This is the hardware realization of uniform time on the Earth surface got by statistical averaging over a set of atomic clocks, positioned at different places on the Earth surface.

TCG (temps coordinate geocentrique). Timelike coordinate of the four-dimensional reference system, situated at the centre of masses of the Earth. Its connection with TT is given by:TCG=TT+LG(JD–2443144.5), where LG=6.969290310-10. The reference point is given by the resolution A4 of IAU at the Buenos Aires General Assembly.

TCB 2)(temps coordinate baricentrique). Timelike coordinate of the four-dimensional reference system, situated at the centre of masses of the solar system. Its connection with TCG:
TCB=TCG+LC(JD-2443144.5)+c-2ve(xxe) +P, where LG=1.4808268457-8
P — periodic term calculated according to the enclosed fortran algorithm (fbl.f) realizing the FBL model (Fairhead, Bretagnon and Lestrade, 1995, private message for IERS). Enclosed also the file fbl.res. The reference point is given by the resolution A4 of IAU at the Buenos Aires General Assembly.

UT1. The argument, describing rotation of the Earth. The difference UT1-TT is given daily for midnigth (to fix the situation for programming let us say at the beginning of each Custom TT Julian day). At intermediate moments of the time is necessary to do a linear interpolation. It is necessary to create a file of data, containing information on UT1-TT. There exist forecast of difference UT1-TT, using which it is also necessary to prepare the file of the same format. After the period covered by this file it is necessary to prepare the formula giving parabolic extrapolation of the difference according the temporary value of the Earth deceleration (I'll do this). The problem is how to join smoothly this parabolic extrapolation with the data file. As an unsufficient but simple temporary solution we can take the difference UT1-TT equal to the last value in the existing UT1-TT file. Name this file UT1-TT.ini.

GST (Greenwich sidereal time).
GST=GMST+DycoseA+(0.00264"sinW+0.000063"sin2W)
where W is the mean longitude of the ascending node of the lunar orbit. The last two terms (in parentheses) have not been included in the IERS Standards previously. They should not be included in the formula until 1 January 1997 (we consider that starting at 0h TT) when their use will begin. This date is chosen to minimize any discontinuity in UT1 (Capitaine and Gontier (19933))).
GMST is given below, and the calculation of arguments Dy, eA and W will be described in the memorandum on precession-nutation.

Greenwich sidereal time — the time, describing rotation of the Earth. It conditionally corresponds to the angle of the Earth rotational displacement comparatively to the true 0 Aries (true gamma point). Conditionally in the sense that it sufficiently exactly describes this rotation, but not linked to the experimental procedure and determined by this formula by definition.

GMST (Greenwich mean sidereal time).
GMST0h UT1=6h41m50.54841s+8640184.812866sT'u+0.093104sT'u2–6.2s10–6T'u3
with T'u=d'u/36525, and d'u being the number of days elapsed since 2000 January 1, 12h UT1 ( UT1), taking on values 0.5, 1.5, ..., (Aoki et al. (1982)). Here is necessary to note that we have in mind the days of UT1, moreover the interval has the form n+0.5 (nN). This number is positive after 2000 January 1 12h UT1 and negative before, moreover the leap from n+0.5 to n+1.5 occurs after passing 0h UT1.
Further
GMST= GMST0h UT1+rDUT1,
where r is the ratio GMST/UT1 as given by Aoki et al. (1982)4)
r=1.002737909350795+5.900610-11T'u-5.910-15T'u2.
If we calculate time in units of day from 0h 1 January 2000, d'u is simply the whole part of [UT1 – 0.5], and DUT1 is fractional part of [UT1 – 0.5].

Attention! Before 1961 1 january UTC coincides with UT1 by definition.

UTC (universal time coordinated). It is a time on our clocks. Different determinations were entered from 1961 for UTC. Within the period from 1961 to 1972 it went with different velocities (the exact algorithm is available upon request). Besides, the leaps in fraction of a second were regularly inserted. From 1972 this time goes as TT, but 2 times per annum an additional second (leap second) can be inserted at the end of june or december. This second must be inserted so that the difference UT1-TT remains under 0.9 sec. The difference between UTC and TT (or TAI) is given by the file tai-utc.dat (in the folder SER7) by july 1997. This file needs to be renewed twice a year.

NB. MJD=JD–2400000.5. The tai-utc.dat it is better to transform before use.


1. Let be pairs: day – astronomical unit (AU) and seconds SI – metres SI.
2. Let us drop at the beginning the third component in the formula below.
3. Capitaine, N. and Gontier A. -M., 1993, "Accurate procedure for deriving UT1 at a submilliarcsecond accuracy from Greenwich Sidereal Time or from stellar angle," Astron. Astrophys., 275, pp. 645–650.
4. Aoki, S., Guinot, B., Kaplan, G. H., Kinoshita, H., McCarthy, D. D., and Seidelmann, P. K., 1982, ``The New Definition of Universal Time," Astron. Astrophys., 105, pp. 359–361.