1. 1999-2000Lecture Notes on Astrometry Earth Rotation Rotation angle: UT1...S Motion of z-axis: Non-Diurnal: Precession...P + Nutation...N Nearly Diurnal: Wobble...W Matrix Expression

2. 1999-2000Lecture Notes on Astrometry Precession/Nutation Non-Diurnal Motion of Earth ’ s z-axis Two Components in Ecliptic RF Longitude, Obliquity Precession: Very Long Periodic 50"/jy, P ~ 26000 jy Nutation: Periodic 18.6 jy, 0.5 jy, 9.3 jy, … Imperfect Current Models Ecliptic Ecliptic Pole z

3. 1999-2000Lecture Notes on Astrometry Precession Hipparcos (~150BC) IAU1976 Precession Formula Lieske et al. (1976, A&A) Dynamical Part: Newcomb ’ s Approach Correction of New Planetary Masses Geodesic Precession Original: Rotation in Ecliptic RF Practical: Rotation in Equatorial RF

4. 1999-2000Lecture Notes on Astrometry Precession (contd.) 3 Precession Angles in Equatorial RF Unit: 1" T =(JD-2451545.0)/36525

5. 1999-2000Lecture Notes on Astrometry Approximate Precession Approximate Precession Matrix Correction Formula

6. 1999-2000Lecture Notes on Astrometry Approx. Precession (contd.) Approximate Precession Angles Precession in Right Ascension/Declination Approximate Correction Formula

7. 1999-2000Lecture Notes on Astrometry Nutation Bradley (1747) IAU1980 Nutation Theory Seidelmann et al. (1981, CM) Rigid Earth: Kinoshita (1977, CM) Non-Rigid Effects: Wahr (1981, GJRAS) Obliquity of Ecliptic (Lieske et al., 1976)

8. 1999-2000Lecture Notes on Astrometry Nutation (contd.) Matrix Expression Nutation in Longitude: Dy Nutation in Obliquity: De Analytic Form

9. 1999-2000Lecture Notes on Astrometry Delauney ’ s Angles 5 Angles used in Nutation Theory Mean Anomaly of Moon Mean Anomaly of Sun Mean Argument of Latitude of Moon Mean Elongaion of Moon from Sun Mean Longitude of Ascending Node of Moon Detailed Expression: Seidelmann et al. (1981)

10. 1999-2000Lecture Notes on Astrometry Approximate Nutation Series Precision: 0.1", Unit: 1"

11. 1999-2000Lecture Notes on Astrometry Approximate Nutation Approximate Nutation Matrix Nutation in Right Ascension/Declination

12. 1999-2000Lecture Notes on Astrometry Approximate Nutation (contd.) Correction Formula

13. 1999-2000Lecture Notes on Astrometry Sidereal Rotation (Almost) Uniform & Diurnal Rotation W 0 = 7.2921150(1) x 10 -5 radian/s Rotation Period = 1 Sidereal Day ~ 365.2422.../366.2422... Day Greenwich (Apparent) Sidereal Time (GAST)

14. 1999-2000Lecture Notes on Astrometry Deviation from Uniform Rotation UTC → UT1 → GMST → G(A)ST DUT1=UT1-UTC: Unpredictable GMST = GMST 0 + r UT1 +... Ratio of ST/UT: r ~1.0027379... GAST = GMST + Dy cos e +... Length of Day (LOD) = 2p/W Earth Orientation Parameter (EOP): DUT1, LOD, x p, y p

15. 1999-2000Lecture Notes on Astrometry Polar Motion (= Wobble) Slow Motion of Pole Position on Earth Symbol: (x p,y p ), Order: 0.1 ” ~30m Period: Annual, Chandler (~14month) Unpredictable: Must be monitored

16. 1999-2000Lecture Notes on Astrometry Earth Orientation Parameter Old: Earth Rotation Parameter (ERP) Current: EOP Pole Offsets = Corr. of Precession/Nutation DUT1,LOD, Polar Motion x p, y p International Earth Rotation Service (IERS) Since 1984, Central Bureau: Paris Obs. Home Page: http://hpiers.obspm.fr/