3.1. Coordinate-systems and time. Seeber 2.1.
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Transcript of 3.1. Coordinate-systems and time. Seeber 2.1.
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3.1. Coordinate-systems and time. Seeber 2.1.
NON INERTIAL SYSTEM
CTS:Conventional Terrestrial System
Mean-rotationaxis1900.
Greenwich
X
Y- Rotates withthe Earth
Z
Gravity-centre
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CIS
• Zero-meridian for Bureau Internationale de l’ Heure (BHI) determined so that star-catalogues agree in the mean with observations from astronomical observatories.
• The connection to an Inertial System is determined using knowledge of the Z-axís (Polar motion), rotational velocity and the movement of the Earth Center.
• We obtain an Quasi-Inertial system, CIS.• More correct to use the Sun or the centre of our galaxe
!
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Kap. 3 POLAR MOTION
• Approximatively circular
• Period 430 days (Chandler period)
• Main reason: Axis of Inertia does not co-inside with axis of rotation.
• Rigid Earth: 305 days: Euler-period.
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Ch. 3 POLBEVÆGELSEN
• .
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Kap. 3 POLAR MOVEMENT
• Coordinates for the Polen and Rotational velocity• IERS (http://www.iers.org)• International Earth Rotation and Reference
System service (IAG + IAU)• http://aiuws.unibe.ch/code/erp_pp.gif• Metods:
VLBI (Radio astronomi)LLR (Laser ranging to the Moon)SLR (Satellite Laser ranging)GPS, DORIS
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Kap. 3
• Polbevægelse, 1994-1997, Fuld linie : middel pol bevægelse, 1900-1996
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Kap. 3. International Terrestrial Reference System (ITRS)
• Defined, realised and controlled by IERS ITRS Center. http://www.iers.org/iers/products/itrs/
• Geocentric, mass-centre from total Earth inclusive oceans and atmosphere.
• IERS Reference Pole (IRP) and Reference Meridian (IRM) konsist with BIH directions within +/- 0.005".
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Kap. 3, ITRS.
• Time-wise change of the orientations secured through 0-rotation-condition taking into account horizontal tectonic movements for the whole Earth.
• ITRS realised from estimate of coordinates for set of station with observations of VLBI, LLR, GPS, SLR, and DORIS. See: ftp://lareg.ensg.ign.fr/pub/itrf/old/itrf92.ssc
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Kap. 3
• Paris, 1 July 2003 Bulletin C 26
• INFORMATION ON UTC - TAI
• NO positive leap second will be introduced at the end of December 2003.
• The difference between UTC and the International Atomic Time TAI is :
• from 1999 January 1, 0h UTC, until further notice : UTC-TAI = -32 s
• Leap seconds can be introduced in UTC at the end of the months of December or June, depending on the evolution of UT1-TAI. Bulletin C is mailed every six months, either to announce a time step in UTC, or to confirm that there will be no time step at the next possible date.
• http://www.iers.org/iers/products/eop/leap_second.html
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Kap. 3
•
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Kap. 3 Variationer jord-rotationen.
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Kap. 3
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Ch. 3, Transformation CIS - CTS
• Precession• Nutation• Rotation+• Polar movement
Sun+Moon
CISCTS rSNPr
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Ch. 3, Precession.
• Example: t-t0=0.01 (2001-01-01)
• .
01.-01-2000 J2000, :t
days. 36525 centuries,Julian in )t-(tT
T.in spolynomialorder rd3'by given ,,
)()()(
0
0
323
z
RRzRP
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Ch. 3, Nutation – primarily related to the Moon.• Movement takes place in Ecliptica
4391666723"21'2623
)()()(
ecliptic)(in longitudein nutation
ob. ofnutation ecliptic, theofobliquity
0.
0
131
RRRN
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Ch. 3, Nutation:
• .
0T 0, 0,D :Example
)2-cos(2F0.0977"
)2-2D-2F0.5736cos(cos9.2025"
)2-sin(2F0.2274"-
)222sin("3187.1sin"1996.17
sun thefromMoon theof elongationmean D
node ascendinglunar theof longitude eclipticmean
DF
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Ch. 3, Earth rotation and polar motion (ERP).
• .
100
0cossin
0sincos
1
10
01
:1 - cosv v,- sinv :angles small
)()()(RS
IERS) (from scoordinate- pole ,x
timesiderialapparant Greenwich
312
p
pp
p
p
pp
p
yx
y
x
GASTRyRx
y
GAST
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Ch. 3, Example for point on Equator.
• Suppose θ=0, xp=yp =1” (30 m)
• .
km6371
0
0
1200000/1200000/1
200000/110
200000/101
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Ch. 3, Exercise.
2 May 1994:
x”=0.1843”=0.000000893,
y”=0.3309”=0.0000014651
(x,y,z)=(3513648.63m,778953.56m,5248202.81m)
Compute changes to coordinates.
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Ch. 3, Time requirement
• 1 cm at Equator is 2*10-5 s in rotation
• 1 cm in satellite movement is 10-6 s
• 1 cm in distance measurement is 3*10-11 s
• We must measure better than these quantities.
• Not absolute, but time-differences.
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Ch. 3, Siderial time and UT. (see fig. 2.13).
• Siderial time: Hour-angle of vernal equinox in relationship to the observing instrument
• LAST: Local apparent siderial time: true hour angle
• GAST: LAST for Greenwich
• LMST: Local hour angle of mean equinox
• GMST: LMST for Greenwich
• GMST-GAST=Δψcosε
• LMST-GMST=LAST-GAST=Λ
xp
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Ch. 3, UT
• UT= 12 hours + Greenwich hourangle for the mean sun. Follows siderial time.
• 1 mean siderial day = 1 mean solar day -3m55.909s.
• UT0B is time at observation point B, must be referred to conventional pole
• UT1= UT0B + ΔΛP
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Ch. 3, UT1, GMST and MJD
• .DOY53371MJD
:2005for 2400000.5,-JDMJD
centuriesJulian in counted
,112:01-01-2000J2000 from timeis
......T0.093104
T2866s8640184.81
54841.50416 UT10at
h
2u
u
h
UTT
GMST
u
smh
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Ch. 3, Dynamic time
• ET: Ephemeis time (1952) to make equatins of motion OK.
• TDB= Barycentric time – refers to the Sun
• TDT=Terrestrial time• From general relativity: clock at the earth moving around
the sun varies 0.0016 s due to change in potential of sun (Earth does not move with constant velocity).
• TDB=ET on 1984-01-01
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Ch. 3, GPS Time
• GPS time = UTC 1980-01-05
• Determined from Clocks in GPS satellites
• GPS time – UTC = n * s-C0,
• C0 about 300 ns
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Ch. 3, Clocks and frequency standards.
• With GPS we count cycles. Expect the fequency to be constant.
! tsmeasuremenby determined beMust
......)(
error time.......)()(
but ,)t-(t
intervalin cycles Ncount weIf
1 :clock I)( Ideal
0
0
0
I
agingttDriftBiasttt
ttffftf
f
NTN
fT
ii
iiIi
i
III
iI
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Ch. 3, Praxis, see Seeber, Fig. 2.15.
• Precision quarts crystal: temperature dependent, aging
• Rubidium: good stability, long term
• Cesium: stable both on short term and long term – transportable, commercially available.
• Hydrogen masers: 10-15 stability in periods of 102 to 105 s.
• Pulsars: period e.g. 1.6 ms.