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# Julian Date

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Fundamentals
Title Julian Date
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Intermediate
Year of Publication 2011

In order to facilitate calculations for long time intervals, the Julian Date (JD) is used (from Julio Scalier).

The Julian Date defines the number of days [footnotes 1] elapsed since 4713 B.C., January $\displaystyle{ 1^d_{\cdot}5 }$ (i.e. 12$\displaystyle{ ^{h} }$ of January 1st). This day is the zero epoch for the Julian Date and, after that time, the days are counted without interruption. Every Julian day begins at the $\displaystyle{ 12 }$ hours UT of the civil day and ends at the $\displaystyle{ 12 }$ hours UT of the following. This kind of calendar does not use the hour:minute:second format, but it uses fractions of day.

The conversion between calendar year(Y)-month(M)-day(D)-UT and Julian dates is given by the following expressions [Hofmann-Wellenhof et al., 2008] [1], however this is a simplification of a general expression only valid for the time period from March 1900 to February 2100:

$\displaystyle{ JD=int[365.25\; y]+int[30.6001\; (m+1)]+D+\frac{UT\_hours}{24.0}+1\,720\,981.5 \qquad \mbox{(1)} }$

where:

$\displaystyle{ \begin{array}{lll} y=Y-1 &\mbox{ and } m=M+12; & M\leq2 \\ y=Y &\mbox{ and } m=M; & M\gt 2; \end{array} \qquad \mbox{(2)} }$

The JD relative to J2000 is obtained by subtracting $\displaystyle{ 2\,451\,545.0 }$ days to the JD (i.e., the number of days elapsed since 2000 January $\displaystyle{ 1.5 }$-st).

The inverse transformation is carried out computing the next values:

$\displaystyle{ \begin{array}{l} a=int[JD+0.5] \\[0.3cm] b=a+1537 \\[0.3cm] c=int[\displaystyle\frac{b-122.1}{365.25}] \\[0.3cm] d=int[365.25\; c] \\[0.3cm] e=int[\displaystyle\frac{b-d}{30.6001}] \end{array} \qquad \mbox{(3)} }$

Afterwards the civil date is obtained with the following expressions:

$\displaystyle{ \begin{array}{c} D=b-d-int[30.6001\; e]+frac[JD+0.5] \\[0.3cm] M=e-1-12\times int[\displaystyle\frac e{14}]\\[0.3cm] Y=c-4715-int[\displaystyle\frac{7+M}{10}] \end{array} \qquad \mbox{(4)} }$

where $\displaystyle{ int }$ and $\displaystyle{ frac }$ denote the integer and the fractional part of a real number.

## Notes

1. ^ Julian century is defined as $\displaystyle{ 36\,525 }$ days.

## References

1. ^ [Hofmann-Wellenhof et al., 2008] Hofmann-Wellenhof, B., Lichtenegger, H., K. and Wasle, E., 2008. GNSS - Global Navigation Satellite Systems.. Springer-Verlag, Wien, Austria.