3'1' Coordinatesystems and time' Seeber 2'1'

1
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
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 (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

6
Kap. 3

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

7
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".

8
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

10
Kap. 3

11
Kap. 3 Variationer jord-rotationen.
12
Kap. 3
13
Ch. 3, Transformation CIS - CTS

• Precession
• Nutation
• Rotation
• Polar movement

SunMoon
14
Ch. 3, Precession.

• Example t-t00.01 (2001-01-01)
• .

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 ?0, xpyp 1 (30 m)
• .

19
Ch. 3,
Exercise.

• 2 May 1994
• x0.18430.000000893,
• y0.33090.0000014651
• (x,y,z)(3513648.63m,778953.56m,5248202.81m)
• Compute changes to coordinates.

20
Ch. 3, Time requirement

• 1 cm at Equator is 210-5 s in rotation
• 1 cm in satellite movement is 10-6 s
• 1 cm in distance measurement is 310-11 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??cose
• LMST-GMSTLAST-GAST?

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
  -3m55.909s.
• UT0B is time at observation point B, must be
  referred to conventional pole
• UT1 UT0B ??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
• TDTTerrestrial 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).
• TDBET on 1984-01-01

25
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

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. 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.