3. Sidereal time 4. Polar motion The rotation matrix for sidereal time rs is The previous computations yield the instantaneous CEP. R=R36 The cep must still be rotated into the cio The computation of the apparent Greenwich sidereal This is achieved by means of the pole coordinates xp, yp time eo which define the position of the CEp with respect to the CIO. The pole coordinates are determined by the IErS is shown in the section on time systems. and are available upon request. The rotation matrix for R=R2(-XPiRi(-yp)=0 y R=RR 3. Time Systems The rotation matrices R andr are often combined to a single matrix for earth rotation What is Time? 3. 1 A Group of Time System Definition of time criterion must be motion object Several time systems are in current use. They are based on various periodic processes such as earth rotation Periodie process Earth rotation Greenwich Sidereal Time(00) 1. Earth rotation by itself( Sidereal time, Solar time Earth revolution Terrestrial Dynamic Time(DT) 2. Earth rotation around Sun(Calendar time Barycentric Dynamic Time(BDT) Atomic oscillations nternational 3. Oscillation frequency of atomie motion(AtomIc UT Coordinated (UTC)4 3. Sidereal time The rotation matrix for sidereal time RS is The computation of the apparent Greenwich sidereal time is shown in the section on time systems. { } R = R3 Θ0 S Θ0 The previous computations yield the instantaneous CEP. The CEP must still be rotated into the CIO. This is achieved by means of the pole coordinates xp, yp which define the position of the CEP with respect to the CIO. The pole coordinates are determined by the IERS and are available upon request. The rotation matrix for polar motion is given by 4. Polar motion           − = − − = − 1 0 1 1 0 2{ } 1{ } P P P P P P S x y y x R R x R y The rotation matrices and are often combined to a single matrix for earth rotation: R M S R = R R S R M R 3. Time Systems What is Time? Definition of time criterion must be motion object • Periodic • Stable • Observable 1. Earth rotation by itself (Sidereal time, Solar time 2. Earth rotation around Sun (Calendar time 3. Oscillation frequency of atomic motion (Atomic time) 3.1 A Group of Time System International Atomic Time (IAT) UT Coordinated (UTC) Atomic oscillations Terrestrial Dynamic Time (TDT) Barycentric Dynamic Time (BDT) Earth revolution Universal Time (UT) Greenwich Sidereal Time (00) Earth rotation Periodic Process Time System Several time systems are in current use. They are based on various periodic processes such as earth rotation