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Transformation between Celestial and Terrestrial Frames
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| Fundamentals | |
|---|---|
| Title | Transformation between Celestial and Terrestrial Frames |
| Author(s) | J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain. |
| Level | Basic |
| Year of Publication | 2011 |
Coordinate transformations between CRF and TRF frames are performed by mean of rotations corresponding to Precession, Nutation and Pole movement, briefly described as follows.
- Precession and nutation [forced rotation]: Earth rotation axis (and its equatorial plane) is not kept fixed in space, i.e., in relation to so called ”fixed-stars”, but it rotates about the pole of the ecliptic, as it is shown in figure 1. This movement is due to the effect of the gravitational attraction of the moon and the sun and major planets over the terrestrial ellipsoid. The total movement can be split into a secular component (precession, with a period of 26 000 years) and a periodic component (nutation, with a period of 18.6 years).
- Pole movement [free rotation]: Due to the structure of the earth’s mass distribution and its variation, the earth’s rotation axis is not fixed in relation to the earth’s crust. It moves around on the surface of the earth within a square of about 20 meters in relation to a point with fixed coordinates on earth. This movement has a period of about 430 sidereal days (Chandler period). On the other hand, earth rotation velocity is not constant, but it changes in time (although in very small quantities[footnote 1]), as it was mentioned in the previous section.
The detailed expressions for transformation between the CRF and TRF frames are provided in Transforming celestial to terrestrial. The next equations briefly summarise such transformation: For a given epoch t, the coordinates transformation can be decomposed in a rotation matrices (i.e., orthogonal matrices)[footnote 2] product as:
Notes
- ^ Due to friction of water in shallow seas, atmosphere movements, abrupt displacements in the earth interior (in 1955, the rotation suddenly delayed by 41s · 10−6), etc. Note that TRS system is tied to Greenwich meridian and therefore, it rotates with the earth.
- ^ Note: These matrices verify: RT (θ) = R−1(θ) = R(−θ).