Decimal Time - Fractional Days

Fractional Days

The most common use of decimal time of day is as fractional days used by scientists and computer programmers. Standard 24-hour time is converted into a fractional day simply by dividing the number of hours elapsed since midnight by 24 to make a decimal fraction. Thus, midnight is 0.0 day, noon is 0.5 d, etc., which can be added to any type of date, including (all of which refer to the same moment):

• Gregorian dates: 2000 January 1.5
• Two-line elements: 00001.5
• Julian dates: 2451545.0
• Excel serial dates: 36526.5

As many decimal places may be used as required for precision, so 0.5 d = 0.500000 d. Fractional days are often reckoned in UTC or TT, although Julian Dates use pre-1925 astronomical date/time (each date began at 0h thus ".0" = noon) and Microsoft Excel uses the local time zone of the computer. Using fractional days reduces the number of units in time calculations from four (days, hours, minutes, seconds) to just one (days).

Fractional days are often used by astronomers to record observations, and were expressed in relation to Paris Mean Time by the 18th century French mathematician and astronomer Pierre-Simon Laplace, as in these examples:

... et la distance périhélie, égale à 1,053095 ; ce qui a donné pour l'instant du passage au périhélie, sept.29j,10239, temps moyen compté de minuit à Paris.

Les valeurs précédentes de a, b, h, l, relatives à trois observations, ont donné la distance périhélie égale à 1,053650; et pour l'instant du passage, sept.29j,04587; ce qui diffère peu des résultats fondés sur cinq observations. — Pierre-Simon Laplace, Traité de Mécanique Céleste

Fractional days have been used by astronomers ever since. For instance, the 19th century British astronomer John Herschel gave these examples:

Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 0d·286003, or at 6h 51m 50s·66 Greenwich Mean Time ... For example, at 12h 0m 0s Greenwich Mean Time, or 0d·500000... — John Herschel, Outlines of Astronomy

Fractional days are commonly used to express epochs of orbital elements. The decimal fraction is usually added to the calendar date or Julian day for natural objects, or to the ordinal date for artificial satellites in two-line elements.