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# Julian Date

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 [math]\displaystyle{ 1^d_{\cdot}5 }[/math] (i.e. 12[math]\displaystyle{ ^{h} }[/math] 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 [math]\displaystyle{ 12 }[/math] hours UT of the civil day and ends at the [math]\displaystyle{ 12 }[/math] 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:

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

where:

- [math]\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)} }[/math]

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

The inverse transformation is carried out computing the next values:

- [math]\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)} }[/math]

Afterwards the civil date is obtained with the following expressions:

- [math]\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)} }[/math]

where [math]\displaystyle{ int }[/math] and [math]\displaystyle{ frac }[/math] denote the integer and the fractional part of a real number.

## Notes

- ^ Julian century is defined as [math]\displaystyle{ 36\,525 }[/math] days.

## References

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