1

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

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

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 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

Sun+Moon

CISCTS rSNPr

14

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

15

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

16

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

17

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

18

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

19

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.

20

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.

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 -3m55.909s.

• UT0B is time at observation point B, must be referred to conventional pole

• UT1= UT0B + ΔΛP

23

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

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 0.0016 s due to change in potential of sun (Earth does not move with constant velocity).

• TDB=ET 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.

! 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

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.