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Time

Time. Newtonian Viewpoint Absolute Time Time Transformation: 1-to-1 Ordering: Chronology Precision Accuracy???. Integrated Time Scale. Assumption: Same Time Interval of Repeating Phenomenon Counted Numbers to Expr. of Time Examples Month, Day Mechanical Clock Quartz, Atomic Time.

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Time

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

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

  3. Atomic Time • Definition of SI Second (CGPM, 1967) • 9162631770 Periods, Certain Radiation, Cs133 • International Atomic Time (TAI) • BIPM (Paris) • ~ 200 Cs + some H Masers • Relative Precision: 15-16 digits Lecture Notes on Astrometry

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

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

  6. Barycentric Dynamical Time • IAU(1984-1991) • General Relativistic Effects • Adjustment of Unit of Time • Solar System Barycentric Dyn. Time: TDB • Terrestrial Dynamical Time: TDT • TDT = TAI+32.184s • <TDB> = <TDT> Lecture Notes on Astrometry

  7. Barycentric Coordinate Time • IAU(1991-) • No More Adjustment of Unit of Time • SS Barycentric Coordinate Time: TCB • Geocentric Coordinate Time: TCG • Terrestrial Time: TT • TT = TDT = TAI+32.184s Lecture Notes on Astrometry

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

  9. Time Units • 1 day = 24 h = 1440 m = 86400 s • Julian Century: jc, Julian Year: jy • 1 jc = 100 jy = 36525 days • Besselian Year = Mean Solar Year • 1 mean solar year = 365.2421897… days • ms, ms, ns, ps, fs, … • c = 299792458 m/s Lecture Notes on Astrometry

  10. Time Representations • Hour, Minute, Second • Year, Month, Day • Day of Year • Julian Dates (Day Number) • 2000 Jan.1,12h = J2000.0 = 2451545.0 • Modified Julian Dates (MJD) • MJD = JD – 2400000.5 Lecture Notes on Astrometry

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

  12. Conv. To JD (contd.) • JD0=N+D-32075; • JD1=JD0-0.5; • JD2=h/24.0+m/1440.0+s/86400.0; • JD=JD1+JD2 or JD = (JD1,JD2) Lecture Notes on Astrometry

  13. Conversion from Julian Date • JD to (Y,M,D,h,m,s) • JD0=int(JD-0.5) or JD0=JD1-0.5; • L=JD0+68569; • N=int((4*L)/146097); • K=L-int((146097*N+3)/4); • I=int(4000*(K+1))/1461001); • P=K-int((1461*I)/4)+31; Lecture Notes on Astrometry

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

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

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