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Han et al. Satell Navig (2021) 2:18 Page 5 of 10

rotation between the geocentric local inertial frame and the  � σ(t, x ) G � ∂ 2
′
′
3 ′
′
3 ′
�
�
geocentric kinematic non-rotating reference frame, which  j |x − x | ′ d x + 2c 2 ∂t 2 σ(t, x ) � x − x � d x
 w(t, x ) = G


is about 1.92 arc seconds per hundred years and named as � i ′
 j σ (t, x ) 3 ′
i

geodesic precession. Because of the small dynamical efect  w (t, x ) = G |x − x | ′ d x

on the motion of objects, it can be ignored in the usual (6)
cases. here t = TCB , called barycentric coordinate time, and σ
In modern astrometry and space geodesy, there are three and σ denote mass density and fow density respectively,
i
most important space–time reference systems, i.e., the Bar- G is the gravitational constant. Obviously, the potential
ycentric Celestial Reference System (BCRS), the Geocentric functions of the metric are zero at infnity (Deng, 2012).
Celestial Reference System (GCRS) and the Geocentric Ter- Te BCRS can be regarded as a very good inertial reference
restrial Reference System (GTRS). Te origin of BCRS is the system in dynamics. Te stars outside the solar system are
mass center of the Solar System, which takes into account very far away, and the tidal efect generated by them is negligi-
the distributions of all the masses of the Sun and the planets, ble in the solar system. Terefore, it is not difcult to imagine
and the coordinate axes are required to have no spatial rota- that if the observer was at the barycenter of the solar system
tion relative to far-distant celestial bodies. It is mainly used to and moved together without rotation with respect to the far-
study the orbital motion of celestial bodies of the solar system distant celestial bodies, he would have a very fat space, apart
and the observation modeling of distant celestial bodies. Te from the interaction of the celestial bodies in the solar system,
coordinate origin of GCRS is defned at the center of Earth’s and the time given by the carried atomic clock would be also
mass and the spatial axes have no spatial rotation relative to very uniform. Tus, we can regard the solar system as an iso-
BCRS. GCRS is mainly used to study the rotation of the Earth lated system and the BCRS as a space–time reference system
and the orbital motion of artifcial Earth satellites. Te coor- with good inertia characteristics and orthogonal coordinates.
dinate origin of GTRS is the same as GCRS, but the space Te interaction among the celestial bodies in the solar sys-
coordinate axes are fxed to the Earth and rotate daily with it, tem is expressed by the space–time metric determined by the
which is mainly used to describe the locations of ground sta- coordinates.
tions and various geophysical phenomena. Tough IAU2000 Resolution B1.3 has given the form of
Obviously, there exists arbitrariness in the defnition and space–time metric for BCRS, the orientation of the spatial
implementation of these reference systems. If there were no coordinate axes are not given. For this reason, IAU2006 Res-
standards, the results of observation or research given by olution B2 further clarifes that for all practical applications,
diferent teams could not be compared, communicated or unless otherwise stated, the BCRS is assumed to be oriented
shared. To this end, international organizations, such as the according to the ICRS axes.
International Astronomical Union (IAU), the International ICRS is the International Celestial Reference System,
Union of Geodesy and Geophysics (IUGG), and the Inter- which is a realization of BCRS, including the International
national Bureau of Weights and Measures (BIPM) have long Celestial Reference Frame (ICRF) and related standards,
term commitments in the defnition, implementation, and constants, and models. ICRF realizes an ideal reference sys-
coordination of the recommendations for the space–time tem by precise equatorial coordinates of extragalactic radio
reference system and the related physical constants. sources observed with Very Long Baseline Interferometry
According to IAU2000 resolution B1.3, both the BCRS (VLBI). It is established and maintained by the International
and the GCRS are required to meet the harmonic condi- Earth Rotation and Reference Systems Service (IERS). IERS
tions (Petit, 2000; Sofel et al., 2003). Te BCRS space–time was jointly established by IAU and IUGG in 1987. Its basic
metric form can be expressed as: mission is to provide Earth rotation, space reference systems
and related data and standard services for astronomy, geod-

� 2 �
2w 2w −6
 g 00 =− 1 − + + O(c ) esy, and geophysics. Te establishment and maintenance of


 c 2 c 4
 the time scale is the responsibility of BIPM.


 i
4w −5
g 0i =− + O(c ) (5)
 c 3 The geocentric celestial reference system


� �
 Due to the orbital motion of the Earth’s center of mass
 2w
 −4
 g ij = δ ij 1 + + O(c )

c 2 relative to the solar barycenter and the infuence of tidal
forces caused by other celestial bodies of the solar sys-
i
where δij is Kronecker delta, w and w are the Newtonian tem, the Earth cannot be regarded as an isolated body.
and vector potentials of the gravitational feld respec- Te geocentric reference system is very complicated in
tively. Where potential functions