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 = 2428455.736324462777
To find the time of day elements ( hh,mm,ss ) from the decimal part of any general JD number:
JD = 2428455.736324462777 uu = JD + 0.5 = 2428456.236324462777 hours = 24*(uu  floor(uu)) = 5.67178710178 hh = floor(hours) = 05 minutes = 60*(hours  hh) = 40.3072261065 mm = floor(minutes) = 40 seconds = 60*(minutes  mm) = 18.434 ss = floor(seconds + 0.5) = 18So the time of day elements, in this case, work out to: hh:mm:ss = 05:40:18 = 05h 40m 18s 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 = 0.2564080683314449
To find the time elements ( TimeSignVal, hh,mm,ss ) corresponding to day fraction (±DayFrac ):
TimeSignVal = (DayFrac < 0)? 1:1 = 1 hours = TimeSignVal * 24 * DayFrac = 6.15379363995 hh = floor(hours) = 06 minutes = 60*(hours  hh) = 9.22761839728 mm = floor(minutes) = 09 seconds = 60*(minutes  mm) = 13.657 ss = floor(seconds + 0.5) = 14So the time elements corresponding to the fraction of a day, in this case, work out to: hh:mm:ss = 06:09:14 = 06h 09m 14s 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 = 9.12520543933800
To find the time elements ( hh,mm,ss ) corresponding to the decimal (hours ) value:
TimeSign = (9.12520543933800 < 0)? 1:1 = 1 hours = 9.12520543933800 hh = floor(hours) = 09 ww = 60*(hours  hh) = 7.51232636028 mm = floor(ww) = 07 ss = 60*(ww  mm) = 30.740So the time elements, corresponding to the hours value, in this case, work out to: hh:mm:ss = 09:07:30.740 = 09h 07m 30.740s resolved to the nearest millisecond. © Jay Tanner  2017
