Post on 25-Dec-2015
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/