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Earth Rotation

Earth Rotation. Rotation angle: UT1...S Motion of z -axis: Non-Diurnal: Precession...P + Nutation...N Nearly Diurnal: Wobble...W Matrix Expression. Precession/Nutation. Non-Diurnal Motion of Earth ’ s z -axis Two Components in Ecliptic RF Longitude, Obliquity

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Earth Rotation

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

  2. 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 Pole z Ecliptic Lecture Notes on Astrometry

  3. 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 Lecture Notes on Astrometry

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

  5. Approximate Precession • Approximate Precession Matrix • Correction Formula Lecture Notes on Astrometry

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

  7. 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) Lecture Notes on Astrometry

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

  9. 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) Lecture Notes on Astrometry

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

  11. Approximate Nutation • Approximate Nutation Matrix • Nutation in Right Ascension/Declination Lecture Notes on Astrometry

  12. Approximate Nutation (contd.) • Correction Formula Lecture Notes on Astrometry

  13. (Almost) Uniform & Diurnal Rotation W0 = 7.2921150(1) x 10-5 radian/s Rotation Period = 1 Sidereal Day ~ 365.2422.../366.2422... Day Greenwich (Apparent) Sidereal Time (GAST) Sidereal Rotation Lecture Notes on Astrometry

  14. Deviation from Uniform Rotation • UTC → UT1 → GMST → G(A)ST • DUT1=UT1-UTC: Unpredictable • GMST = GMST0 + 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, xp, yp Lecture Notes on Astrometry

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

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

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