Computing The Time Elements (hh, mm, ss)


There are slightly different procedures for computing the time elements (hh,mm,ss) depending on the starting argument and the type of time we are computing.  e.g. is it an actual time of day or a fraction of a day converted into equivalent time elements.

All times used here will be expressed in the universal standard 00h to 24h format.

There are three basic sources of fractions that will be converted into time elements.
  • If the starting argument is a general Julian Day number ((JD), to compute the time elements from its decimal part, Algorithm 2a applies.

  • If the starting argument is a time interval expressed as a fraction of a day (DayFrac), then Algorithm 2b applies.

  • If the starting argument is a time interval expressed in decimal (hours), then Algorithm 2c applies.



Algorithm 2a:

Given any general JD number, compute the time elements (hh,mm,ss) from its decimal part.  These time elements are will all equate to integer values with the seconds value (ss) rounded-off to the nearest second.

     uu = JD + 0.5
  hours = 24*(uu - floor(uu))
     hh = floor(hours)
minutes = 60*(hours - hh)
     mm = floor(minutes)
seconds = 60*(minutes - mm)
     ss = floor(seconds + 0.5)

RANDOM EXAMPLE 1:
Given:
JD = 2382183.478384494466

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number:
     JD = 2382183.478384494466
     uu = JD + 0.5 = 2382183.978384494466
  hours = 24*(uu - floor(uu)) = 23.4812278636

     hh = floor(hours) = 23
minutes = 60*(hours - hh) = 28.8736718148
     mm = floor(minutes) = 28
seconds = 60*(minutes - mm) = 52.420
     ss = floor(seconds + 0.5) = 52
So the time of day elements, in this case, work out to:
hh:mm:ss = 23:28:52 = 23h 28m 52s
resolved to the nearest second.


Algorithm 2b:

Given a (±DayFrac) value, compute the corresponding time elements (TimeSignVal, hh, mm, ss)

 if DayFrac < 0 then TimeSignVal = -1 else TimeSignVal = 1

  hours = TimeSignVal * 24 * DayFrac
     hh = floor(hours)
minutes = 60*(hours - hh)
     mm = floor(minutes)
seconds = 60*(minutes - mm)
     ss = floor(seconds + 0.5)
or
 TimeSignVal = (DayFrac < 0)? -1:1

  hours = TimeSignVal * 24 * DayFrac
     hh = floor(hours)
minutes = 60*(hours - hh)
     mm = floor(minutes)
seconds = 60*(minutes - mm)
     ss = floor(seconds + 0.5)

RANDOM EXAMPLE 2:
Given:
DayFrac = 0.7787634592011828

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac):
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 18.6903230208
          hh = floor(hours) = 18
     minutes = 60*(hours - hh) = 41.4193812497
          mm = floor(minutes) = 41
     seconds = 60*(minutes - mm) = 25.163
          ss = floor(seconds + 0.5) = 25
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 18:41:25 = 18h 41m 25s
resolved to the nearest second.


Algorithm 2c:

Given an (±hours) value, compute the corresponding time elements (TimeSignVal, hh,mm,ss).

 if hours < 0 then TimeSignVal = -1 else TimeSignVal = 1

 uu = TimeSignVal * hours
 hh = floor(uu)
 ww = 60*(uu - hh)
 mm = floor(ww)
 ss = 60*(ww - mm)
or
 TimeSignVal = (hours < 0)? -1:1

 uu = TimeSignVal * hours
 hh = floor(uu)
 ww = 60*(uu - hh)
 mm = floor(ww)
 ss = 60*(ww - mm)

RANDOM EXAMPLE 3:
Given:
hours = 16.09722379818072

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value:
 TimeSign = (16.09722379818072 < 0)? -1:1 = 1
    hours = 16.09722379818072
       hh = floor(hours) = 16
       ww = 60*(hours - hh) = 5.83342789084
       mm = floor(ww) = 05
       ss = 60*(ww - mm) = 50.006
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 16:05:50.006 = 16h 05m 50.006s
resolved to the nearest millisecond.


© Jay Tanner - 2017