Fraction of the day

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The day fraction is the time that has elapsed since the beginning of the day and is expressed in days. It is used in some natural sciences , especially astronomy , instead of the usual time for time information. The time 6 o'clock corresponds to the fraction of the day 0.25. This has several advantages:

  1. The spaces or special characters between hours, minutes and seconds are omitted;
  2. the numbers are shorter with the same accuracy;
  3. only one unit of time (the day ) is necessary;
  4. Time differences can be calculated more easily without calculating in the sexagesimal system .

Conversion between time and fraction of the day

In order to calculate the fraction of the day τ from a time HH : MM : SS ( SS also with decimal places), the time elapsed since the beginning of the day can first be converted into seconds and then converted into days: 

  τ = ((HH·60 + MM)·60 + SS)/86.400

For the opposite direction (τ → HH : MM : SS ), τ can first be converted into seconds and then determined by dividing twice with remainder SS , MM and HH : 

  s = ⌊τ·86.400⌋
  s/60 = m,  Rest SS;  SS = SS + frac(τ·86.400)
  m/60 = HH, Rest MM

Here ⌊… ⌋ is the integer part, frac (…) the fraction of the decimal point of the product. When specifying the result of a conversion, the accuracy should be rounded accordingly.

Decimal places of τ 1 2 3 4th 5
accuracy 2.4 h 14 min 1.4 min 9 s 0.9 s

The following examples show how the fraction of the day can be combined with the calendar day: 

  10. Januar  6 Uhr         wird zu   Jan. 10,25
  10. Januar  06:06         wird zu   Jan. 10,254
  10. Januar  06:06:03      wird zu   Jan. 10,25420
  10. Januar  06:06:03,456  wird zu   Jan. 10,25420667
  10. Januar  06:06:03,457  wird zu   Jan. 10,25420668

Benefits to astronomy

The calculation in fractions of a day is particularly common in astronomy , for example for specifying asterisk words in yearbooks - where the table interval often counts in sidereal days - or in other ephemeris .

Example (astronomical yearbook 2013) with year jump: 

 z. B. für Sternkoordinaten im 10-Tage-Intervall (Sternzeit):
... Dez 14,50273     lautet herkömmlich    ... 14. Dez., 12:03:56 
... Dez 24,50000         -- " --           ... 24. Dez., 12:00:00
... Dez 34,49727         -- " --           ... 03. Jan. (2014), 11:56:04

As the above example shows, the interpolation of the star locations is facilitated by fractions of a day at the turn of the year . At the beginning of the year, at 10-day intervals, e.g. E.g. before Jan 17 and Jan 7 there is the strange time Jan -3 (for December 28, 2012).

See also