1999-2000 Lecture 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

WSNPR

1999-2000 Lecture 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

1999-2000 Lecture 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

1999-2000 Lecture Notes on Astrometry

Precession (contd.)

3 Precession Angles in Equatorial RF

Unit: 1" T =(JD-2451545.0)/36525

AAA z ,,323 RP

32

018203.0

041833.0

017998.0

09468.1

42665.0

30188.0

2181.2306

3109.2004

2181.2306

TTT

zA

A

A

1999-2000 Lecture Notes on Astrometry

Approximate Precession

Approximate Precession Matrix

Correction Formula

10

01

1

A

A

AA

P AAA z

cos ,sintan APAAP

1999-2000 Lecture Notes on Astrometry

Approx. Precession (contd.)

Approximate Precession Angles

Precession in Right Ascension/Declination

Approximate Correction Formula

TnTm PAPA ,

/jy"3109".2004 ,/jy"4362.4612 PP nm

Tn

Tnm

PP

PPP

cos

,sintan

1999-2000 Lecture 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)

32 001813".000059".0

8150".46448".21'2623

TT

TA

1999-2000 Lecture Notes on Astrometry

Nutation (contd.)

AA ,,131RN

Matrix Expression

Nutation in Longitude: Nutation in Obliquity: Analytic Form

5

1

,cos

sin

jjjk

k kk

kk ΩnAA

A

1999-2000 Lecture 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)

'

F'LLD Ω

1999-2000 Lecture Notes on Astrometry

Approximate Nutation Series

Precision: 0.1", Unit: 1"

0

sin1.0

0

'sin1.0

2cos1.0

2sin2.0

2cos1.0

2sin2.0

'2cos6.0

'2sin3.1

cos2.9

sin2.17

L

L

Ω

Ω

L

L

Ω

Ω

1999-2000 Lecture Notes on Astrometry

Approximate Nutation

Approximate Nutation Matrix

Nutation in Right Ascension/Declination

1

1

1

N

AA sin,cos

1999-2000 Lecture Notes on Astrometry

Approximate Nutation (contd.)

Correction Formula

sincos

,cossintan

N

N

1999-2000 Lecture Notes on Astrometry

Sidereal Rotation

3 S R

(Almost) Uniform & Diurnal Rotation 0 = 7.2921150(1) x 10-5 radian/s Rotation Period = 1 Sidereal Day ~ 365.242

2.../366.2422... Day Greenwich (Apparent) Sidereal Time (GAST)

1999-2000 Lecture Notes on Astrometry

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 + cos + ... Length of Day (LOD) = 2/ Earth Orientation Parameter (EOP):

DUT1, LOD, xp, yp

1999-2000 Lecture Notes on Astrometry

Polar Motion (= Wobble)

2 1p px y W R R

Slow Motion of Pole Position on Earth Symbol: (xp,yp), Order: 0.1”~30m Period: Annual, Chandler (~14month) Unpredictable: Must be monitored

1999-2000 Lecture Notes on Astrometry

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/