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 ) roundedoff 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) = 52So 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) = 25So 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) = 50.006So 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
