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 00 h to 24 h format.
There are three basic sources of fractions that will be converted into time elements.
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 = 2396774.077223306832
To find the time of day elements ( hh,mm,ss ) from the decimal part of any general JD number:
JD = 2396774.077223306832 uu = JD + 0.5 = 2396774.577223306832 hours = 24*(uu - floor(uu)) = 13.853359367698 hh = floor(hours) = 13 minutes = 60*(hours - hh) = 51.201562061906 mm = floor(minutes) = 51 seconds = 60*(minutes - mm) = 12.094 ss = floor(seconds + 0.5) = 12So the time of day elements, in this case, work out to: hh:mm:ss = 13:51:12 = 13h 51m 12s 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 = 0.5867308278212032
To find the time elements ( TimeSignVal, hh,mm,ss ) corresponding to day fraction (±DayFrac ):
TimeSignVal = (DayFrac < 0)? -1:1 = 1 hours = TimeSignVal * 24 * DayFrac = 14.081539867709 hh = floor(hours) = 14 minutes = 60*(hours - hh) = 4.8923920625326 mm = floor(minutes) = 04 seconds = 60*(minutes - mm) = 53.544 ss = floor(seconds + 0.5) = 54So the time elements corresponding to the fraction of a day, in this case, work out to: hh:mm:ss = 14:04:54 = 14h 04m 54s 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 = 2.05373416980024
To find the time elements ( hh,mm,ss ) corresponding to the decimal (hours ) value:
TimeSign = (2.05373416980024 < 0)? -1:1 = 1 hours = 2.05373416980024 hh = floor(hours) = 02 ww = 60*(hours - hh) = 3.2240501880144 mm = floor(ww) = 03 ss = 60*(ww - mm) = 13.443So the time elements, corresponding to the hours value, in this case, work out to: hh:mm:ss = 02:03:13.443 = 02h 03m 13.443s resolved to the nearest millisecond. © Jay Tanner - 2025
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