Coordinate-systems and time. Seeber 2.1. NON INERTIAL SYSTEM CTS: Conventional Terrestrial System Mean-rotationaxis Greenwich X Y- Rotates with the Earth Z Gravity-centre

2 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 !

3 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.

4 Ch. 3 POLBEVÆGELSEN.

5 Kap. 3 POLAR MOVEMENT Coordinates for the Polen and Rotational velocity IERS ( International Earth Rotation and Reference System service (IAG + IAU) Metods: VLBI (Radio astronomi) LLR (Laser ranging to the Moon) SLR (Satellite Laser ranging) GPS, DORIS

6 Kap. 3 Polbevægelse, , Fuld linie : middel pol bevægelse,

7 Kap. 3. International Terrestrial Reference System (ITRS) Defined, realised and controlled by IERS ITRS Center. Geocentric, mass-centre from total Earth inclusive oceans and atmosphere. IERS Reference Pole (IRP) and Reference Meridian (IRM) konsist with BIH directions within +/ ".

8 Kap. 3, ITRS. Time-wise change of the orientations secured through 0-rotation-condition taking into account horizontal tektonic 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

9 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 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.

10 Kap. 3

11 Kap. 3 Variationer jord-rotationen.

12 Kap. 3

13 Ch. 3, Transformation CIS - CTS Precession Nutation Rotation+ Polar movement Sun+Moon

14 Ch. 3, Precession. Example: t-t 0 =0.01 ( ).

15 Ch. 3, Nutation – primarily related to the Moon. Movement takes place in Ecliptica

16 Ch. 3, Nutation:.

17 Ch. 3, Earth rotation and polar motion (ERP)..

18 Ch. 3, Example for point on Equator. Suppose θ=0, x p =y p =1” (30 m).

19 Ch. 3, Exercise. 2 May 1994: x”=0.1843”= , y”=0.3309”= (x,y,z)=( m, m, m) Compute changes to coordinates.

20 Ch. 3, Time requirement 1 cm at Equator is 2*10 -5 s in rotation 1 cm in satellite movement is s 1 cm in distance measurement is 3* s We must measure better than these quantities. Not absolute, but time-differences.

21 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

22 Ch. 3, UT UT= 12 hours + Greenwich hourangle for the mean sun. Follows siderial time. 1 mean siderial day = 1 mean solar day - 3 m s. UT0 B is time at observation point B, must be referred to conventional pole UT1= UT0 B + ΔΛ P

23 Ch. 3, UT1, GMST and MJD.

24 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 s due to change in potential of sun (Earth does not move with constant velocity). TDB=ET on

25 Ch. 3, GPS Time GPS time = UTC Determined from Clocks in GPS satellites GPS time – UTC = n * s-C 0, C 0 about 300 ns

26 Ch. 3, Clocks and frequency standards. With GPS we count cycles. Expect the fequency to be constant.

27 Ch. 3, Praxis, see Seeber, Fig 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: stability in periods of 10 2 to 10 5 s. Pulsars: period e.g. 1.6 ms.