Earth Rotation n n Rotation angle UT 1

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Earth Rotation n n Rotation angle: UT 1. . . S Motion of z-axis:

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

Precession/Nutation n n Non-Diurnal Motion of Earth’s z-axis Two Components in Ecliptic RF n

Precession/Nutation n n Non-Diurnal Motion of Earth’s z-axis Two Components in Ecliptic RF n n Precession: Very Long Periodicz n n Ecliptic Pole 50"/jy, P ~ 26000 jy Nutation: Periodic n n Longitude, Obliquity 18. 6 jy, 0. 5 jy, 9. 3 jy, … Imperfect Current Models 1999 -2000 Ecliptic Lecture Notes on Astrometry

Precession n Hipparcos (~150 BC) IAU 1976 Precession Formula Lieske et al. (1976, A&A)

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

Precession (contd. ) n 3 Precession Angles in Equatorial RF n n Unit: 1"

Precession (contd. ) n 3 Precession Angles in Equatorial RF n n Unit: 1" T =(JD-2451545. 0)/36525 1999 -2000 Lecture Notes on Astrometry

Approximate Precession n Approximate Precession Matrix n Correction Formula 1999 -2000 Lecture Notes on

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

Approx. Precession (contd. ) n Approximate Precession Angles n Precession in Right Ascension/Declination n

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

Nutation n Bradley (1747) IAU 1980 Nutation Theory Seidelmann et al. (1981, CM) n

Nutation n Bradley (1747) IAU 1980 Nutation Theory Seidelmann et al. (1981, CM) n n n Rigid Earth: Kinoshita (1977, CM) Non-Rigid Effects: Wahr (1981, GJRAS) Obliquity of Ecliptic (Lieske et al. , 1976) 1999 -2000 Lecture Notes on Astrometry

Nutation (contd. ) n Matrix Expression n Nutation in Longitude: Dy Nutation in Obliquity:

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

Delauney’s Angles n 5 Angles used in Nutation Theory n n n Mean Anomaly

Delauney’s Angles n 5 Angles used in Nutation Theory n n n 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) 1999 -2000 Lecture Notes on Astrometry

Approximate Nutation Series n Precision: 0. 1", Unit: 1" 1999 -2000 Lecture Notes on

Approximate Nutation Series n Precision: 0. 1", Unit: 1" 1999 -2000 Lecture Notes on Astrometry

Approximate Nutation n Approximate Nutation Matrix n Nutation in Right Ascension/Declination 1999 -2000 Lecture

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

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

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

Sidereal Rotation n n (Almost) Uniform & Diurnal Rotation W 0 = 7. 2921150(1)

Sidereal Rotation n n (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) 1999 -2000 Lecture Notes on Astrometry

Deviation from Uniform Rotation UTC → UT 1 → GMST → G(A)ST n DUT

Deviation from Uniform Rotation UTC → UT 1 → GMST → G(A)ST n DUT 1=UT 1 -UTC: Unpredictable n GMST = GMST 0 + r UT 1 +. . . Ratio of ST/UT: r ~1. 0027379. . . n GAST = GMST + Dy cos e +. . . n Length of Day (LOD) = 2 p/W n Earth Orientation Parameter (EOP): n n DUT 1, LOD, xp, yp 1999 -2000 Lecture Notes on Astrometry

Polar Motion (= Wobble) n n Slow Motion of Pole Position on Earth Symbol:

Polar Motion (= Wobble) n n Slow Motion of Pole Position on Earth Symbol: (xp, yp), Order: 0. 1”~30 m Period: Annual, Chandler (~14 month) Unpredictable: Must be monitored 1999 -2000 Lecture Notes on Astrometry

Earth Orientation Parameter n n n Old: Earth Rotation Parameter (ERP) Current: EOP Pole

Earth Orientation Parameter n n n Old: Earth Rotation Parameter (ERP) Current: EOP Pole Offsets = Corr. of Precession/Nutation DUT 1, LOD, Polar Motion xp, yp International Earth Rotation Service (IERS) n n Since 1984, Central Bureau: Paris Obs. Home Page: http: //hpiers. obspm. fr/ 1999 -2000 Lecture Notes on Astrometry