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 = 2433582.677121548513
To find the time of day elements ( hh,mm,ss ) from the decimal part of any general JD number:
JD = 2433582.677121548513 uu = JD + 0.5 = 2433583.177121548513 hours = 24*(uu - floor(uu)) = 4.2509171627462 hh = floor(hours) = 04 minutes = 60*(hours - hh) = 15.055029764771 mm = floor(minutes) = 15 seconds = 60*(minutes - mm) = 03.302 ss = floor(seconds + 0.5) = 03So the time of day elements, in this case, work out to: hh:mm:ss = 04:15:03 = 04h 15m 03s 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 = 0.8296340055836929
To find the time elements ( TimeSignVal, hh,mm,ss ) corresponding to day fraction (±DayFrac ):
TimeSignVal = (DayFrac < 0)? -1:1 = 1 hours = TimeSignVal * 24 * DayFrac = 19.911216134009 hh = floor(hours) = 19 minutes = 60*(hours - hh) = 54.672968040518 mm = floor(minutes) = 54 seconds = 60*(minutes - mm) = 40.378 ss = floor(seconds + 0.5) = 40So the time elements corresponding to the fraction of a day, in this case, work out to: hh:mm:ss = 19:54:40 = 19h 54m 40s 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 = 18.00626265240864
To find the time elements ( hh,mm,ss ) corresponding to the decimal (hours ) value:
TimeSign = (18.00626265240864 < 0)? -1:1 = 1 hours = 18.00626265240864 hh = floor(hours) = 18 ww = 60*(hours - hh) = 0.37575914451843 mm = floor(ww) = 00 ss = 60*(ww - mm) = 22.546So the time elements, corresponding to the hours value, in this case, work out to: hh:mm:ss = 18:00:22.546 = 18h 00m 22.546s resolved to the nearest millisecond. © Jay Tanner - 2025
|