5.6 Methods of Large-Scale Navigation
347
where L G = 6.969290134×10
−10 , which is an astronomical constant in the standardized definition of IERS 2000; JD is the Julian day at the corresponding observation
epoch.
(5) Transformation from TCG to TCB
According to the relevant resolution of IAU2000, the complete post-Newtonian
expression for a space-time coordinate point (ct, x E ) in the BCRS has been given,
where t =TCB, and thus the four-dimensional space-time transformation from the
TCG to TCB is expressed as
TCB = TCG +
1
c 2
⎡
⎣
t
t 0
1
2
v
2
E + w 0ext (x E )
dt + v E · (x − x E )
⎤
⎦
−
1
c 4
t
t 0
−
1
8
v
4
E −
3
2
v
2
E w 0ext (x E ) + 4v
i
E w
i
ext (x E ) +
1
2
w
2
0ext (x E )
dt
+
1
c 4
3w 0ext (x E ) +
1
2
v
2
E
[v E · (x − x E )],
(5.103)
where x E and v E are, respectively, the position and velocity vectors of the center
of mass of the Earth in BCRS; v E is the module of vector v E ; w 0ext (x E ) is the total
sum of the Newtonian gravity potentials of celestial bodies of the solar system at the
Earth-center, except for the Earth; w
i
ext (x E ) is the total sum of the vector potentials of
celestial bodies of the solar system at the Earth-center, except for the Earth; t is the
upper limit of integration, representing the TCB; t 0 is the lower limit of integration,
which is at 0:0:0.00 TAI on January 1, 1977.
(6) Transformation from TCB to TDB
Similarly, according to the resolution of the IAU general assembly in 1991, the
transformation from the TCB to TDB is linear, and there is a proportional constant
difference between them, that is,
TDB = TCB − L B × (JD − 2443144.5) × 86400,
(5.104)
where L B = 1.55051976772 × 10
−8 , an astronomical constant in the standardized
definitions of IERS 2000; JD is the Julian day at the observation epoch.
5.6.2.2 Transformation of Time Delays
The pulsar timing model is established in the BCRS using the timescale TCB or TDB.
Through the above timescale transformations, the time of the X-ray photons arriving
at the spacecraft has been transformed from the GPST to TCB. Under the TCB, the
347
where L G = 6.969290134×10
−10 , which is an astronomical constant in the standardized definition of IERS 2000; JD is the Julian day at the corresponding observation
epoch.
(5) Transformation from TCG to TCB
According to the relevant resolution of IAU2000, the complete post-Newtonian
expression for a space-time coordinate point (ct, x E ) in the BCRS has been given,
where t =TCB, and thus the four-dimensional space-time transformation from the
TCG to TCB is expressed as
TCB = TCG +
1
c 2
⎡
⎣
t
t 0
1
2
v
2
E + w 0ext (x E )
dt + v E · (x − x E )
⎤
⎦
−
1
c 4
t
t 0
−
1
8
v
4
E −
3
2
v
2
E w 0ext (x E ) + 4v
i
E w
i
ext (x E ) +
1
2
w
2
0ext (x E )
dt
+
1
c 4
3w 0ext (x E ) +
1
2
v
2
E
[v E · (x − x E )],
(5.103)
where x E and v E are, respectively, the position and velocity vectors of the center
of mass of the Earth in BCRS; v E is the module of vector v E ; w 0ext (x E ) is the total
sum of the Newtonian gravity potentials of celestial bodies of the solar system at the
Earth-center, except for the Earth; w
i
ext (x E ) is the total sum of the vector potentials of
celestial bodies of the solar system at the Earth-center, except for the Earth; t is the
upper limit of integration, representing the TCB; t 0 is the lower limit of integration,
which is at 0:0:0.00 TAI on January 1, 1977.
(6) Transformation from TCB to TDB
Similarly, according to the resolution of the IAU general assembly in 1991, the
transformation from the TCB to TDB is linear, and there is a proportional constant
difference between them, that is,
TDB = TCB − L B × (JD − 2443144.5) × 86400,
(5.104)
where L B = 1.55051976772 × 10
−8 , an astronomical constant in the standardized
definitions of IERS 2000; JD is the Julian day at the observation epoch.
5.6.2.2 Transformation of Time Delays
The pulsar timing model is established in the BCRS using the timescale TCB or TDB.
Through the above timescale transformations, the time of the X-ray photons arriving
at the spacecraft has been transformed from the GPST to TCB. Under the TCB, the