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Compatibility of the IERS earth rotation representation and its relation to the NRO conditions

Compatibility of the IERS earth rotation representation and its relation to the NRO conditions Athanasios Dermanis Department of Geodesy and Surveying The Aristotle University of Thessaloniki. Earth Rotation: Relation of Terrestrial to Celestial Reference System. Celestial Reference System:.

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Compatibility of the IERS earth rotation representation and its relation to the NRO conditions

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  1. Compatibility of the IERS earth rotation representation and its relation to the NRO conditions Athanasios Dermanis Department of Geodesy and Surveying The Aristotle University of Thessaloniki

  2. Earth Rotation: Relation of Terrestrial to Celestial Reference System Celestial Reference System: Terrestrial Reference System: Mathematical model: = orthogonal rotation matrix = earth rotation parameters

  3. To every orthogonal rotation matrix R(t) corresponds a unique rotation vector: defined by Notation: [a] is the antisymmetric matrix with axial vector a

  4. R = QDW: Separation of earth rotation in 3 parts: Q = Precession-Nutation D = Diurnal rotation W = Polar motion Classical model: 9 parameters 7 parameters reduced to 5 by 2 NRO conditions IERS model (IAU 2000): s = s(g,F) = s(xP,yP) NRO conditions: s = s(d,E) = s(X,Y) OSU Report Nr. 245, 1977: 5 parameters Number of independent parameters needed: 3 (geometric description) 6 (dynamic description – state vector)

  5. Characteristics of the IERS earth rotation representation Consequences on model-compatible rotation vector Precession Nutation Q from theory Rotation vector not aligned to common 3rd axis of intermediate systems CIP high frequency terms removed from precession-nutation Diurnal Rotation around R D from observations Magnitude not equal to rate of diurnal rotation angle Polar Motion W

  6. Objective: Construct a compatible representation with a 3 part separation

  7. Objective: Construct a compatible representation with a 3 part separation Find a representation of the same separated form a the IERS representation Involving 2 intermediate reference systems: Intermediate Celestial: Intermediate Terrestrial:

  8. Objective: Construct a compatible representation with a 3 part separation Find a representation of the same separated form a the IERS representation Involving 2 intermediate reference systems: Intermediate Celestial: Intermediate Terrestrial: Subject to the following (natural) compatibility conditions: 2 directional conditions: 1 magnitude condition:

  9. Decomposition of the rotation vector in 3 relative rotation vectors

  10. Decomposition of the rotation vector in 3 relative rotation vectors Relative rotation vectors:

  11. Decomposition of the rotation vector in 3 relative rotation vectors Relative rotation vectors: of Intermediate Celestial with respect to Celestial Defined by:

  12. Decomposition of the rotation vector in 3 relative rotation vectors Relative rotation vectors: of Intermediate Celestial with respect to Celestial of Intermediate Terrestrial with respect to Intermediate Celestial Defined by:

  13. Decomposition of the rotation vector in 3 relative rotation vectors Relative rotation vectors: of Intermediate Celestial with respect to Celestial of Intermediate Terrestrial with respect to Intermediate Celestial of Terrestrial with respect to Intermediate Terrestrial Defined by:

  14. Decomposition of the rotation vector in 3 relative rotation vectors Relative rotation vectors: of Intermediate Celestial with respect to Celestial of Intermediate Terrestrial with respect to Intermediate Celestial of Terrestrial with respect to Intermediate Terrestrial Defined by:

  15. The compatibility conditions In the Intermediate Celestial reference system

  16. The compatibility conditions In the Intermediate Celestial reference system = Celestial Pole (direction of diurnal rotation), e.g. CEP, CIP = Compatible rotation vector (derived from rotation matrix R) = Compatible Celestial Pole (CCP)

  17. The compatibility conditions 7 parameters instead of 3 minimum required = 4 conditions needed !

  18. The compatibility conditions 7 parameters instead of 3 minimum required = 4 conditions needed !

  19. The compatibility conditions 7 parameters instead of 3 minimum required = 4 conditions needed ! 2 direction conditions:

  20. The compatibility conditions 7 parameters instead of 3 minimum required = 4 conditions needed ! 2 direction conditions: 1 magnitude condition:

  21. The compatibility conditions 7 parameters instead of 3 minimum required = 4 conditions needed ! 2 direction conditions: 1 magnitude condition: Missing 4th condition: Ds = arbitrary !

  22. The compatibility conditions 7 parameters instead of 3 minimum required = 4 conditions needed ! 2 direction conditions: 1 magnitude condition: Missing 4th condition: Ds = arbitrary ! 4th condition = arbitrary definition of origin of diurnal rotation angle

  23. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) :

  24. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions:

  25. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions: 1 magnitude condition:

  26. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions: 1 magnitude condition: The 4 independent compatibility conditions 2 direction conditions: 2 NRO conditions:

  27. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions: 1 magnitude condition: The 4 independent compatibility conditions 2 direction conditions: 2 NRO conditions:

  28. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions: 1 magnitude condition: The 4 independent compatibility conditions 2 direction conditions: 2 NRO conditions:

  29. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions: 1 magnitude condition: The 4 independent compatibility conditions 2 direction conditions: 2 NRO conditions:

  30. The NRO conditions in relation to the compatibility conditions The 2 NRO (Non Rotating Origin) conditions: CEO (Celestial Ephemeris Origin) : TEO (Terrestrial Ephemeris Origin) : 2 direction conditions: 1 magnitude condition: The 4 independent compatibility conditions 2 direction conditions: 2 NRO conditions: magnitude condition satisfied !

  31. Explicit form of the 4 compatibility conditions

  32. Explicit form of the 4 compatibility conditions Direction conditions:

  33. Explicit form of the 4 compatibility conditions Direction conditions: NRO conditions:

  34. Explicit form of the 4 compatibility conditions Direction conditions: NRO conditions: Direction conditions + NRO conditions : When , E, d [and s(E,d)] are known then F, g [and s(F,g)] are uniquely determined !

  35. Construct a compatibleseparated model from observations only Analyze observations using a 3 parameter model:

  36. Construct a compatibleseparated model from observations only Analyze observations using a 3 parameter model: Compute rotation vector components, magnitude & directions (CCP components):

  37. Construct a compatibleseparated model from observations only Analyze observations using a 3 parameter model: Compute rotation vector components, magnitude & directions (CCP components): Compute precession-nutation and polar motion angles:

  38. Construct a compatibleseparated model from observations only Analyze observations using a 3 parameter model: Compute rotation vector components, magnitude & directions (CCP components): Compute precession-nutation and polar motion angles: Determine s and s from NRO conditions:

  39. Construct a compatibleseparated model from observations only Analyze observations using a 3 parameter model: Compute rotation vector components, magnitude & directions (CCP components): Compute precession-nutation and polar motion angles: Determine s and s from NRO conditions: Compute diurnal rotation angle:

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