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3.1. Coordinate-systems and time. Seeber 2.1.PowerPoint Presentation

3.1. Coordinate-systems and time. Seeber 2.1.

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3.1. Coordinate-systems and time. Seeber 2.1.

Z

NON INERTIAL SYSTEM

Mean-rotationaxis

1900.

Gravity-centre

Y- Rotates with

the Earth

CTS:

Conventional Terrestrial System

Greenwich

X

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 !

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.

Ch. 3 POLBEVÆGELSEN

- .

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

Kap. 3

- Polbevægelse, 1994-1997, Fuld linie : middel pol bevægelse, 1900-1996

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".

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

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

Ch. 3, Precession.

- Example: t-t0=0.01 (2001-01-01)
- .

Ch. 3, Nutation – primarily related to the Moon.

- Movement takes place in Ecliptica

Ch. 3, Example for point on Equator.

- Suppose θ=0, xp=yp =1” (30 m)
- .

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.

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.

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

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

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

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

Ch. 3, Clocks and frequency standards.

- With GPS we count cycles. Expect the fequency to be constant.

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.

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