5.4 Space-Time Reference Based on General Relativity
321
which is the relation formula between the coordinate length and the proper length
measured by the local-rest observer using the standard scale length.
For the spatial distance within a small area, when the metric is independent of
time, the spatial integration of formula (5.78) can be carried out directly. Under the
Newtonian limit, the proper length of any two points M (r 1 ) and N (r 2 ) in space is
L =
r 2
r 1
1 +
2GM
rc 2
1
2
dl ≈
r 2
r 1
1 +
GM
rc 2
dl
= r 2 − r 1 +
GM
c 2 ln
r 2 + r 2 · n
r 1 + r 1 · n
,
(5.79)
where n =
r 2 −r 1
r 2 −r 1 .
In formula (5.79), the first term on the right denotes the Euclidean geometric
distance between two points in space, and the second term denotes the distance
correction resulted from the space bending. It is clearly demonstrated that the space
bending is caused by the action of gravitational field.
5.4.4 Timescale of Relativity
In order to study the dynamics of celestial bodies in the solar system more accurately,
the introduction of the timescale of relativity in astronomy was proposed at the 16th
IAU general assembly in 1976. Two kinds of the relativistic timescales, Barycentric
Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT), were defined at
the 17th IAU general assembly in 1979. The TDB refers to the time variables used
in the equations of motion relative to the SSB and in the compiled star catalogue.
The TDT refers to the time variables used in the equations of motion relative to the
Earth’s center of mass and in the catalogues of the apparent positions of the observed
celestial bodies at the Earth’s center. In 1991, at the 21st IAU general assembly,
the space-time forms of the Barycentric Celestial Reference System (BCRS) and
Geocentric Celestial Reference System (GCRS) were proposed, and correspondingly, two new timescales, Barycentric Coordinate Time (TCB) and Geocentric
Coordinate Time (TCG), were defined, respectively. Meanwhile, it was decided in
the IAU general assembly to change the TDT to Terrestrial Time (TT). The TT is
the time reference datum of the apparent ephemeris at the Earth’s center, its difference with the TDT is a proportional constant, and its measurement-selected unit is
consistent with the length of a second in the SI units on the geoid. At 0:0:0.0 TAI
on January 1, 1977, the TT’s reading is 0:0:32.184 on the same day. The TCB refers
to the one-dimensional time component of any space-time coordinate point in the
BCRS, and the TCG refers to the one-dimensional time component of any space-time
coordinate point in the GCRS.
321
which is the relation formula between the coordinate length and the proper length
measured by the local-rest observer using the standard scale length.
For the spatial distance within a small area, when the metric is independent of
time, the spatial integration of formula (5.78) can be carried out directly. Under the
Newtonian limit, the proper length of any two points M (r 1 ) and N (r 2 ) in space is
L =
r 2
r 1
1 +
2GM
rc 2
1
2
dl ≈
r 2
r 1
1 +
GM
rc 2
dl
= r 2 − r 1 +
GM
c 2 ln
r 2 + r 2 · n
r 1 + r 1 · n
,
(5.79)
where n =
r 2 −r 1
r 2 −r 1 .
In formula (5.79), the first term on the right denotes the Euclidean geometric
distance between two points in space, and the second term denotes the distance
correction resulted from the space bending. It is clearly demonstrated that the space
bending is caused by the action of gravitational field.
5.4.4 Timescale of Relativity
In order to study the dynamics of celestial bodies in the solar system more accurately,
the introduction of the timescale of relativity in astronomy was proposed at the 16th
IAU general assembly in 1976. Two kinds of the relativistic timescales, Barycentric
Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT), were defined at
the 17th IAU general assembly in 1979. The TDB refers to the time variables used
in the equations of motion relative to the SSB and in the compiled star catalogue.
The TDT refers to the time variables used in the equations of motion relative to the
Earth’s center of mass and in the catalogues of the apparent positions of the observed
celestial bodies at the Earth’s center. In 1991, at the 21st IAU general assembly,
the space-time forms of the Barycentric Celestial Reference System (BCRS) and
Geocentric Celestial Reference System (GCRS) were proposed, and correspondingly, two new timescales, Barycentric Coordinate Time (TCB) and Geocentric
Coordinate Time (TCG), were defined, respectively. Meanwhile, it was decided in
the IAU general assembly to change the TDT to Terrestrial Time (TT). The TT is
the time reference datum of the apparent ephemeris at the Earth’s center, its difference with the TDT is a proportional constant, and its measurement-selected unit is
consistent with the length of a second in the SI units on the geoid. At 0:0:0.0 TAI
on January 1, 1977, the TT’s reading is 0:0:32.184 on the same day. The TCB refers
to the one-dimensional time component of any space-time coordinate point in the
BCRS, and the TCG refers to the one-dimensional time component of any space-time
coordinate point in the GCRS.