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 = 2385846.718225129023

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2385846.718225129023
     uu = JD + 0.5 = 2385847.218225129023
  hours = 24*(uu - floor(uu)) = 5.2374030947685

     hh = floor(hours) = 05
minutes = 60*(hours - hh) = 14.244185686111
     mm = floor(minutes) = 14
seconds = 60*(minutes - mm) = 14.651
     ss = floor(seconds + 0.5) = 15
So the time of day elements, in this case, work out to:
hh:mm:ss = 05:14:15 = 05h 14m 15s
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 = 0.8919341836502859

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 21.406420407607
          hh = floor(hours) = 21
     minutes = 60*(hours - hh) = 24.385224456412
          mm = floor(minutes) = 24
     seconds = 60*(minutes - mm) = 23.113
          ss = floor(seconds + 0.5) = 23
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 21:24:23 = 21h 24m 23s
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 = 6.72558444920784

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (6.72558444920784 < 0)? -1:1 = 1
    hours = 6.72558444920784
       hh = floor(hours) = 06
       ww = 60*(hours - hh) = 43.53506695247
       mm = floor(ww) = 43
       ss = 60*(ww - mm) = 32.104
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 06:43:32.104 = 06h 43m 32.104s
resolved to the nearest millisecond.

© Jay Tanner - 2024