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3D Representation of the Non-Rotating Origin: Understanding Terrestrial and Celestial Reference Frames

Explore the intricacies of the Terrestrial Reference Frame (TRF) and Celestial Reference Frame (CRF) systems in astronomy. Learn about the Non-Rotating Origin (NRO) and its significance in representing Earth's motion in space. Discover the seamless transformation process from TRF to CIP and delve into the celestial motions associated with different equinoxes. This comprehensive study provides insights into the ideal and less ideal worlds of reference frame transformations.

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3D Representation of the Non-Rotating Origin: Understanding Terrestrial and Celestial Reference Frames

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  1. 3D representation of the Non-Rotating Origin Olivier de Viron and Veronique Dehant Royal Observatory of Belgium Scientific adviser: Nicole Capitaine

  2. The Terrestrial Reference Frame

  3. The Celestial Reference Frame

  4. 2 systems in an ideal world

  5. The less ideal world

  6. TRF Intermediate RS CRF 1. polar motion in Earth 2. Earth rotation 3. Celestial motion of CIP Only the intermediate system is different when using the new or the old formalism. The definition of the TRF and CRF are not affected.

  7. The old-version transformation

  8. 1. From TRF to CIP

  9. 2. To the True equinox of the date

  10. How to go from one equinox another? Z Ecliptic 2 y x g2 Equator 2 Ecliptic 1 Equator 1 g1

  11. How to go from one equinox another? rotation 1 (z) y y x x Z Ecliptic 1 Ecliptic 2 gi Equator 1 g1

  12. How to go from one equinox another? Z Z Rotation2(x) y y Ecliptic 2 gi Equator 1 x

  13. How to go from one equinox to another? Rotation4(z) x x y Z Ecliptic 2 g2 gi Equator 1 Equator 2

  14. How to go from one equinox to another? Z Z Rotation5(x) Ecliptic 2 g2 x Equator 2

  15. How to go from one equinox another? Ecliptic 2 g2 x Equator 2 It took 5 successive steps…

  16. 1 2 3 4 True ecliptic of the date Mean ecliptic of the date Equator at J2000 True equator of the date Mean equator of the date gv g0 Ecliptic at J2000

  17. The new transformation

  18. 1. From TRF to CIP

  19. 2. From the terrestrial NRO

  20. 3. Earth Rotation Angle

  21. 4. To the XCRF projection: s

  22. 5. To CRF: celestial motion of the CIP

  23. What is the NRO 1.Characterized by its motion: no velocity around the CIP equator associated with polar motion or nutation. 2. Not a point in particular, any point of the CIP equator can work. 3. Allows to get rid of the equinox in the change of reference frame.

  24. So, we can take any points we want? 1.Yes, it is not the point it-self that matter, but its motion. 2. But, we want the new system to be consistent with the old one. 3. Thus, the point is chosen to insure continuity.

  25. Conclusions The NRO is defined by its position at the base epoch (continuity) its motion (no motion in the CIP equator associated with polar motion). Only the Intermediate system is involved, no change of the CRF or TRF

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