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second part of the condition shows that the angular momentum of the Earth with
respect to the defined reference system is zero, indicating null rotation of the Earth.
The reference system is defined in such a way that it separates the bodily and partial
movement of the Earth, which is called the ideal TRS. If such a reference system
can be realized, we will be justified in believing that the movement of the observed
station described in this reference system belongs to the motion of the observed
station itself.
In practical applications, the Tisserand condition is approximately realized by
the no-net-rotation (NNR) condition.
Conventional Terrestrial Reference System
In order actually to establish the TRS, we have to choose some physical datum (like
origin, scale, and orientation that involve physical meaning). The choice of the
physical datum, however, is rather inadequate and arbitrary. A convention needs to
be created in order to unify the datum. Hence, the terminology “convention” is used
to describe this specific choice (see Pent and Luzum 2010), which is what the CTRS
is all about.
The definition of the CTRS comprises:
1. Origin: the origin is at the geocenter, which is defined as the center of mass of the
whole Earth, including oceans and atmosphere
2. Scale: the International System of Units (SI) meter is used for its unit of length,
defined in a local Earth frame in the meaning of a relativistic theory of gravitation
3. Orientation: the orientation is consistent with that of the BIH system at 1984.0
4. Time evolution of the orientation: no residual global rotation is created with
regards to the crust
Conventional Terrestrial Reference Frame
The reference frame is a realization of the reference system. Once the CTRS is
chosen, it should be made accessible to all kinds of users. Hence, the system will be
represented by a number of points on the Earth's surface. A globally-distributed set
of 3D Cartesian coordinates infers the location of an origin, the orientation of an
orthogonal set of Cartesian coordinate axes, and a scale parameter. In this sense, the
Conventional Terrestrial Reference Frame (CTRF) is defined as a set of physical
points with precisely determined coordinates in a specific coordinate system as a
realization of the reference system. As a result, the well-known “geodetic control
network” belongs to the concept of the reference frame.
The establishment of the terrestrial reference frame on the deformable Earth can
be realized by transforming parameters and changing coordinates of the stations.
The time-varying station coordinates will be determined repeatedly by the interna-
tional service agency. All the global systematic errors can be reduced to scale,
translation, or rotation errors and fall under the seven transformation parameters.
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