Lecture Notes on Astrometry Time X Newtonian Viewpoint X Absolute Time X Time Transformation: 1-to-1 X Ordering: Chronology X Precision X Accuracy???

Lecture Notes on Astrometry Integrated Time Scale X Assumption: Same Time Interval of Repeating Phenomenon X Counted Numbers to Expr. of Time X Examples –Month, Day –Mechanical Clock –Quartz, Atomic Time

Lecture Notes on Astrometry Atomic Time X Definition of SI Second (CGPM, 1967) – Periods, Certain Radiation, Cs133 X International Atomic Time (TAI) X BIPM (Paris) X ~ 200 Cs + some H Masers X Relative Precision: digits

Lecture Notes on Astrometry Dynamical Time X Argument of Eq. of Motion X Inverse Function of some Observable X Example: –Mean Longitude of Sun –L(T) = –Ephemeris Time, ET = T(L)

Lecture Notes on Astrometry Universal Time X Dynamical Time of Earth Rotation X UT (= Greenwich Mean Time) X UT0, UT1, UT2 X International Earth Rotation Service (IERS) X Coordinated Universal Time (UTC) X Leap Seconds

Lecture Notes on Astrometry Barycentric Dynamical Time X IAU( ) X General Relativistic Effects X Adjustment of Unit of Time X Solar System Barycentric Dyn. Time: TDB X Terrestrial Dynamical Time: TDT X TDT = TAI s X =

Lecture Notes on Astrometry Barycentric Coordinate Time X IAU(1991-) X No More Adjustment of Unit of Time X SS Barycentric Coordinate Time: TCB X Geocentric Coordinate Time: TCG X Terrestrial Time: TT X TT = TDT = TAI s

Lecture Notes on Astrometry Broadcast Time X Standard Time, Time Zone: 15deg = 1 h X Japan Standard Time (JST) X JST = UTC + 9 h X Radio/Wired Time: JJY, TV, NTT X Time on Computer Network: NTP X Time from Satellites: GPS

Lecture Notes on Astrometry Time Units X 1 day = 24 h = 1440 m = s X Julian Century: jc, Julian Year: jy X 1 jc = 100 jy = days X Besselian Year = Mean Solar Year X 1 mean solar year = … days  ms, ms, ns, ps, fs, … X c = m/s

Lecture Notes on Astrometry Time Representations X Hour, Minute, Second X Year, Month, Day –Day of Year X Julian Dates (Day Number) –2000 Jan.1,12h = J = X Modified Julian Dates (MJD) –MJD = JD –

Lecture Notes on Astrometry Conversion to Julian Date X (Y,M,D,h,m,s) to JD X L=int((M-14)/12); X I=1461*(Y+4800+L); X J=367*(M-2-12*L); X K=int((Y+4900+L)/100); X N=int(I/4)+int(J/12)-int((3*K)/4)

Lecture Notes on Astrometry Conv. To JD (contd.) X JD0=N+D-32075; X JD1=JD0-0.5; X JD2=h/24.0+m/ s/ ; X JD=JD1+JD2 or JD = (JD1,JD2)

Lecture Notes on Astrometry Conversion from Julian Date X JD to (Y,M,D,h,m,s) X JD0=int(JD-0.5) or JD0=JD1-0.5; X L=JD ; X N=int((4*L)/146097); X K=L-int((146097*N+3)/4); X I=int(4000*(K+1))/ ); X P=K-int((1461*I)/4)+31;

Lecture Notes on Astrometry Conv. From JD (contd.) X J=int((80*P)/2447); X D=P-int((2447*J)/80); Q=int(J/11); X M=J+2-12*Q; Y=100*(N-49)+I+Q; X JD2=JD-JD1; X h=int(JD2*24); m=int(JD2*1440-h*60); X s=JD2*86400-h*3600-m*60;

Lecture Notes on Astrometry Day of Week from Julian Date X I=JD0-7*int((JD0+1)/7)+2; X I: 1,2,3,4,5,6,7 X I=1: Sunday