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 = 2448103.872299210834

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2448103.872299210834
     uu = JD + 0.5 = 2448104.372299210834
  hours = 24*(uu - floor(uu)) = 8.93518105522

     hh = floor(hours) = 08
minutes = 60*(hours - hh) = 56.1108633131
     mm = floor(minutes) = 56
seconds = 60*(minutes - mm) = 06.652
     ss = floor(seconds + 0.5) = 07
So the time of day elements, in this case, work out to:
hh:mm:ss = 08:56:07 = 08h 56m 07s
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 = 0.4039646880429179

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 9.69515251303
          hh = floor(hours) = 09
     minutes = 60*(hours - hh) = 41.7091507818
          mm = floor(minutes) = 41
     seconds = 60*(minutes - mm) = 42.549
          ss = floor(seconds + 0.5) = 43
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 09:41:43 = 09h 41m 43s
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 = 1.40803817175960

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (1.40803817175960 < 0)? -1:1 = 1
    hours = 1.40803817175960
       hh = floor(hours) = 01
       ww = 60*(hours - hh) = 24.4822903056
       mm = floor(ww) = 24
       ss = 60*(ww - mm) = 28.937
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 01:24:28.937 = 01h 24m 28.937s
resolved to the nearest millisecond.

© Jay Tanner - 2017