GEODETIC REFERENCE SYSTEMS - GPS Satellite Surveying - page 24

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t = ( TT − J2000 . 0 ) [ days ] / 36,525 (2.26)

Th e Julian date (JD) of the fundamental epoch is

JD(J2000.0) = 2,451,545.0TT (2.27)

It follows that t can be computed as

JD + TT [h] / 24 2,451,545.0

36,525

−

t = (2.28)

The Julian date is a convenient counter for mean solar days. Conversion of any
Gregorian calendar date (Y = year, M = month, D = day) to JD is accomplished

by (van Flandern and Pulkkinen, 1979)

[24

JD = 367 × Y − 7 × [Y + ( M + 9 )/ 12] / 4 + 275 × M / 9 + D + 1,721,014 (2.29)

fo r Greenwich noon. This expression is valid for dates since March 1900. The ex-
pr ession is read as a Fortran-type statement; division by integers implies truncation
of the quotients of integers (no decimals are carried). Note that D is an integer.
In order to compute the Greenwich apparent sidereal time (GAST) needed in
(2 .11), we must have the universal time (UT1) for the epoch of observation. The latter
ti me is obtained from UTC (coordinate universal time) of the epoch of observation
an d the UT1-UTC correction. UTC and UT1 will be discussed below. Suffice to say
th at the correction UT1-UTC is a byproduct of the observations; in other words, it is
av ailable from IERS publications. GAST is best computed in three steps. First, we
compute Greenwich mean sidereal time (GMST) at the epoch 0 h UT1,

Lin
—
2.9
——
Nor
*PgE

[24

6 h 41 m 50 s . 54841 8640184 s . 812866T u + 0 s . 093104T u G MST 0 h UT1 = +

(2.30)

6 s . 2 10 − 6 T u

− ×

where T u = d u / 36525 and d u is the number of days elapsed since January 1, 2000,

12 h UT1 (taking on values 1 . 5, etc.). In the second step, we add the difference

in sidereal time that corresponds to UT1 hours of mean time,

± 0 . 5 , ±

GMST = GMST 0 h UT1 + r [ ( UT1 − UTC ) + UTC] (2.31)

10 − 11 T u − 10 − 15 T u r = 1 . 002737909350795 + 5 . 9006 × 5 . 9 × (2.32)

In step 3, we apply the nutation to convert the mean sidereal time to apparent sidereal
time,

0 . 00264 sin 0 . 000063 sin 2

GAST = GMST + ∆ψ cos ε + Ω + Ω (2.33)

The true celestial coordinate system (X), whose third axis coincides with instan-
taneous rotation axis and X and Y axes span true celestial equator, follows from