Planetary orbital elements

    \[\begin{array}{|l|l|l|l|l|l|l|l|l|}\hline Name& a&\epsilon&i&\omega&\Omega&d_0&t_0$&$T_{days}\\ \hline     Mars&1.52371&0.09339&1.850&286.5&49.6&2018:9:16& 07:20&686.92971\\ \hline Merc&0.3870993&0.20564&7.005&29.13&48.3&2017:3:23& 10:33& 87.969257\\ \hline Venus& 0.723336&0.00678&3.3947&54.9& 76.7&2017:2:20& 05:19&224.700799\\ \hline Earth& 1.000003& 0.01671& 0.0& 102.9& 0.0&2017:01:04& 00:30& 365.25636\\ \hline Jup&5.2029&0.0484&1.304&274.3&100.4&2011:3:13& 05:19&4330.67043\\ \hline Sat&9.537&0.0539&2.486&338.9&113.7&2003:7:11& 13:30&10747.12745\\ \hline Uran&19.189&0.04726&0.773&96.9&74.02&1966:9:9&00:00&30589.273040\\ \hline Nept&30.0699&0.00859&1.7700&273.2&131.784&2046:11:13&00:00&59800.943732\\ \hline Pluto&39.4821&0.24883&17.14001&113.76&110.30&1990:1:13&00:00&90591.174612 \\ \hline\end{array}\]

d_0 (date of perihelion passage) is (Y:M:D), t_0 (time of perihelion passage) is (H:Min).
a is in AU, all anomalies i,\omega,\Omega are in degrees. d_0 is date of perihelion passage, t_0 is time of perihelion passage UTC. T_{days} is orbital period in days.

    \[1.0\, AU=1.495978707\times 10^{11}m=92.956\times 10^6 \, mi, \qquad 1.0\, day=86400\, s\]

Julian time

    \[1.0 \, JD=86400 \, s, \qquad 1.0 \, JY=365.25 \, JD\]

and a zero-point, taken to be 12^{h} \, UT for January 1, 4713 \, BC. The Montenbruck algorithm lets us transform a calendar day to Julian.
Let Y,M,D, UT be year, month, day and UT time according to your calendar and watch. Compute

    \[\begin{array}{lllll} y=Y-1 & \mbox{and} & m=M+12 & \mbox{if} & M\le 2\\ y=Y & \mbox{and} & m=M & \mbox{if} & M>  2\end{array}\]

and

    \[\begin{array}{ll} B=-2 & \mbox{up to/including 4 Oct 1582}\\ B=floor(y/400)-floor(y/100) & \mbox{from and including 15 Oct 1582}\end{array}\]

since those are days/years in which Europe played fiddles with the calendar system. Then

    \[JD=floor(365.25 \, y)+floor(30.6001 (m+1))+B\]

    \[+1720996.5 +D +UT/24\]

For example, today’s date and current time of loading this page is the Julian time

Note that you also need the universal time (UT). For us that’s local time plus 5 hrs.

Convert this  to UT in the formula above via (Hr+min/60+sec/3600). In the formula for Julian date/time the result is expressed in Julia days, hence the penultimate division by 24.0.

You can  run this application to compute Julian date/time for (semi) arbitrary dates:

Yr : Mon:
Day: Hrs:
min: sec:

Julian date=

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