Ch 02-03 Time

• Time
  • Meridian; meridian transit
    
    
    
  • Apparent solar day (Why is it different every day?)
    
    
    
  • Mean solar day (Defined to be 24 hours)
    
    
  • UTC (Coordinated Universal Time)
    = GMT (Greenwich Mean Time)
    
    
  • Sidereal time
    A sidereal day = 23^h56^m4^s.091 (This is the Earth's rotation period!)
    The R.A. of an object at meridian transit is the local sidereal time.
  
   
• Calendar
  • Sidereal year : the Sun returning to the same position in the background stars
    365.2564 day (365^d6^h9^m13^s)
    
    Tropical year : the Sun returning to the same equinox
    365.2422 day (365^d5^h48^m46^s)
    (Note that the Sun moves eastwards and the equinox moves westwards, so the tropical year is shorter than the sideral year.)
     
  • A calendar year is 365 days, but a tropical year is about one quarter day longer. In 46 BC, the Julian calendar was established, which has a leap year every 4 years.
    
    
  • The tropical year is not exactly 365.25 days. In fact,
    365^d.25 - 365^d.2422 = 11^m14^s, i.e., a difference of about 3 days per 400 years.
     
    In 1582, the Sun was at the vernal equinox on 3/11.
    Pope Greyory XIII :
       1) Leap every 4 yrs, but not at every 100 yrs, and still leap at every 400 yrs
       2) In 1582, 10/4 followed by 10/15
    We now use this Gregorian system, which has 1 day error per 3300 years.
  
   
• Julian Date
  • The Julian Date (JD) is referred to the noon at Greenwich on Jan. 1, 4713 B.C. (Julian calendar), which is Nov. 24, 4714 B.C. in Gregorian calendar.
    e.g.   UTC 12:00, Jan. 1, 2000 AD
       = JD 2451545.0
    
    
  • The Modified Julian Date (MJD)
    MJD = JD-2400000.5
     
    e.g. UTC 18:00, Sep. 9, 2024 AD
         = JD 2460563.25
         = MJD 60562.75