Torsten Mayer-Gürr Institute of Geodesy, NAWI Graz Technische Universität Graz
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1 GGOS and Reference Systems errestrial systems and Earth rotation orsten Mayer-Gürr Institute of Geodesy, NAWI Graz echnische Universität Graz orsten Mayer-Gürr 1
2 Celestial systems (Quasi-) inertial system Mean equatorial system at reference eoch t 0 - z: celestial ehemeris ole, CEP(t 0 ) - x: vernal equinox, VE(t 0 ) Precession R z ( za ) R y ( a ) R z ( a ) Mean equatorial system at eoch t - z: mean celestial ehemeris ole, CEP(t) - x: mean vernal equinox, VE(t) Nutation R x ( s ) R z ( ) R x ( s ) rue equatorial system at eoch t - z: true celestial ehemeris ole - x: true vernal equinox orsten Mayer-Gürr 2
3 errestrial systems orsten Mayer-Gürr 3
4 ransformation rue (celestial) equatorial system at eoch t - z: true celestial ehemeris ole (CEP) - x: true vernal equinox Earth rotation R z (GS) rue terrestrial system at eoch t - z: true celestial ehemeris ole (CEP) - x: true Greenwich meridian Polar motion R y ( x ) R x ( y ) Conventional errestrial System (CRS) Mean terrestrial system - z: mean rotation ole - x: mean Greenwich meridian orsten Mayer-Gürr 4
5 Earth Rotation orsten Mayer-Gürr 5
6 Daily Earth Rotation Greenwich Aarent Sidereal ime (GAS) - the true (hour) angle between the true vernal equinox and the true Greenwich meridian. - contains all variations in Earth rotation as well as the motion of the true VE (due to recession and nutation). It is thus not a uniform measure of time. rue VE Greenwich Mean Sidereal ime (GMS) EqE GS GMS Δψ cos ε A Mean VE GS EqE (Equation of the Equinoxes GMS Greenwich orsten Mayer-Gürr 6
7 Daily Earth Rotation Greenwich Aarent Sidereal ime (GAS) - the true (hour) angle between the true vernal equinox and the true Greenwich meridian. - contains all variations in Earth rotation as well as the motion of the true VE (due to recession and nutation). It is thus not a uniform measure of time. rue VE Greenwich Mean Sidereal ime (GMS) EqE GS GMS Δψ cos ε A Mean VE GS EqE (Equation of the Equinoxes GMS Greenwich orsten Mayer-Gürr 7
8 he IERS 1996 heory of Precession/Nutation orsten Mayer-Gürr 8
9 Daily Earth Rotation Greenwich Aarent Sidereal ime (GAS) GS GMS Δψ cos ε A Greenwich Mean Sidereal ime (GMS) 0'' sin Ω 0'' sin 2Ω GMS GMS( 0h, U1) r U1 Solar time -> Siderial time r : 56 h 24 : 00 h orsten Mayer-Gürr 9
10 Daily Earth Rotation Greenwich Aarent Sidereal ime (GAS) GS GMS Δψ cos ε A Greenwich Mean Sidereal ime (GMS) 0'' sin Ω 0'' sin 2Ω GMS GMS( 0h, U1) r U1 Solar time -> Siderial time r GMS( 0h, U1) 6h41m s s s 2 orsten Mayer-Gürr 10
11 U1-AI orsten Mayer-Gürr 11
12 UC-AI orsten Mayer-Gürr 12
13 U1-UC Lea seconds in UC U1 0. 9s orsten Mayer-Gürr 13
14 Daily Earth Rotation Greenwich Aarent Sidereal ime (GAS) GS GMS Δψ cos ε A Greenwich Mean Sidereal ime (GMS) 0'' sin Ω 0'' sin 2Ω GMS GMS( 0h, U1) r U1 Solar time -> Siderial time r GMS( 0h, U1) 6h41m s s s 2 Universal time U1 UC U1 Must be observed orsten Mayer-Gürr 14
15 Excess of length of day (LOD) Angular velocity: with the nominal rate N N 1 LOD /86400s rad/s d dt 2 GMS 86400s orsten Mayer-Gürr 15
16 Excess of length of day (LOD) Angular velocity: with the nominal rate N N 1 LOD /86400s rad/s d dt 2 GMS 86400s orsten Mayer-Gürr 16
17 ransformation rue equatorial system at eoch t - z: true celestial ehemeris ole (CEP) - x: true vernal equinox Earth rotation R z (GS) rue terrestrial system at eoch t - z: true celestial ehemeris ole (CEP) - x: true Greenwich meridian Polar motion R y ( x ) R x ( y ) Conventional errestrial System (CRS) Mean terrestrial system - z: mean rotation ole - x: mean Greenwich meridian orsten Mayer-Gürr 17
18 Polar motion orsten Mayer-Gürr 18
19 Polar motion Sigrid Böhm orsten Mayer-Gürr 19
20 Polar motion orsten Mayer-Gürr 20
21 Polar motion orsten Mayer-Gürr 21
22 Polar motion Change of the Earth s rotation vector relative to the Earth s body Can not be described satisfactorily by mathematical models Dominated by the Chandler wobble(eriod ~432 d, cone angle ~0.2 arcsec) and annual wobble(cone angle <0.1 arcsec) Suerosition yields counter-clockwise revolution (eriod ~450 d) Periodic changes suerosed by secular drift of ~0.003 arcsec er year (olar wandering) and unredictable variations Exressed in terms of (left-handed) metric olar coordinates R y ( x ) R x ( y ) 1 0 x 0 1 y x y 1 orsten Mayer-Gürr 22
23 ransformation rue equatorial system at eoch t - z: true celestial ehemeris ole (CEP) - x: true vernal equinox Earth rotation R z (GS) rue terrestrial system at eoch t - z: true celestial ehemeris ole (CEP) - x: true Greenwich meridian Polar motion R y ( x ) R x ( y ) Conventional errestrial System (CRS) Mean terrestrial system - z: mean rotation ole - x: mean Greenwich meridian orsten Mayer-Gürr 23
24 ransformation between International Celestial Reference System (ICRS) and International errestrial Reference System (IRS) orsten Mayer-Gürr 24
25 Celestial Reference System (CRS) Mean equatorial system at reference eoch t 0 ransformation Precession & Nutation Q (t) rue (celestial) equatorial system at eoch t Earth rotation R (t) rue terrestrial system at eoch t Polar motion W (t) errestrial Reference System (RS) orsten Mayer-Gürr 25
26 ransformation Celestial Reference System (CRS) Mean equatorial system at reference eoch t 0 Precession & Nutation rue (celestial) equatorial system at eoch t Earth rotation rue terrestrial system at eoch t Polar motion R W Q (t) (t) (t) Mean equatorial system at reference eoch t 0 - z: mean celestial ehemeris ole, CEP(t 0 ) - x: mean vernal equinox, VE(t 0 ) R z ( za ) R y ( a ) R z ( a ) Mean equatorial system at eoch t - z: mean celestial ehemeris ole - x: mean vernal equinox, VE(t) R x ( s ) R z ( ) R x ( s ) rue equatorial system at eoch t - z: true celestial ehemeris ole, CEP(t) - x: true vernal equinox errestrial Reference System (RS) orsten Mayer-Gürr 26
27 Celestial Reference System (CRS) Mean equatorial system at reference eoch t 0 ransformation Q ( t) R x ( s Q ) R(t) z ( ) R x ( s ) R z ( za ) R y ( a ) R z ( a ) Precession & Nutation rue (celestial) equatorial system at eoch t Earth rotation R (t) rue terrestrial system at eoch t Polar motion W (t) errestrial Reference System (RS) orsten Mayer-Gürr 27
28 Celestial Reference System (CRS) Mean equatorial system at reference eoch t 0 ransformation Precession & Nutation Q (t) rue (celestial) equatorial system at eoch t Earth rotation R (t) R z (GS) rue terrestrial system at eoch t Polar motion W (t) R y ( x ) R x ( y ) errestrial Reference System (RS) orsten Mayer-Gürr 28
29 ransformation between RS and CRS Rotation matrix R CRS RS ( t) Q( t) R( t) W( t) Polar motion (wobble) W( t) R y ( x ) R x ( y ) Earth rotation R( t) R z ( GS ) Earth rotation cannot modelled erfectly. Corrections to the models are the 5 Earth Orientation Parameters (EOPs) x, y U1 Precession and nutation Q( t) N( t) P( t) P( t) R z ( a ) R y ( a ) R z ( za ) N( t) R ( ) R ( ) R ( ) x s z x s, Measured on daily basis. Published by the International Earth Rotation and Reference Systems Services (IERS) orsten Mayer-Gürr 29
30 International Earth Rotation and Reference Systems Service (IERS) x, y, U1,, INERNAIONAL EARH ROAION AND REFERENCE SYSEMS SERVICE EARH ORIENAION PARAMEERS EOP (IERS) 08 C04 FORMA(3(I4),I7,2(F11.6),2(F12.7),2(F11.6),2(F11.6),2(F11.7),2F12.6) ********************************************************************************** Date MJD x y U1-UC LOD dpsi des " " s s " (0h UC) orsten Mayer-Gürr 30
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