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I'm using https://github.com/Bill-Gray/jpl_eph for a personal project to read JPL DE files, namely DE430 and the more recent DE440. This generally works great and when tested against a reference implementation the output shows the correct vectors for location and velocity.

I am puzzled as to what time scale I should use for the DE files or more specifically, how I can convert the time scale that I have available (UTC) to the required TDB.

I read SOFA, explanations in the docs of Skyfield and https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems and have built a beginner's understanding of the time scales and their differences.

Question 1: My understanding is that DE430 and later version require TDB as input variable. Is my current working assumption correct that I can therefore take a time in UTC, add the appropriate number of leap-seconds that have been inserted since 1972 to arrive at TAI, add 32.184s to arrive at TT and use the approximate formula shown here to arrive at an approximation of TDB?
I would then convert this to Julian days and use as input to DE430?

Question 2: How do I do this for dates before 1972? I should mention that like any beginner, I have stumbled over $${\Delta}T = TT - UT$$ and historical records of it, but this seems to be the difference between UT (or UT1) rather than UTC. I think this is where I have the biggest confusion. Can I use records of ${\Delta}T$ available at the IERS to arrive at the correct TT (and use that to calculate TDB)? If so, how?

Question 3: Setting JPL DE aside for a moment, I've also came across other ephemeris like Brown's theory of the motion of the Moon, VSOP87 (and newer) or Newcombe's table of the sun and was wondering what time scale they require as input? I read an explanation given for VSOP87 and it seems to require TT, but what about the Improved Lunar Ephemeris?

zero0cool
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    You need a "leap second kernel", https://naif.jpl.nasa.gov/pub/naif/generic_kernels/lsk/ – Barry Carter Aug 20 '22 at 16:48
  • What sort of accuracy are you needing ? In general, unless you are doing ultra-precise work, you can use TT~TDB as close enough as per the SLALIB (precursor to SOFA). If you want the full precision, look at DE440t which has the TT-TDB transformation in it and you can iterate until convergence (start with just TT, see what TT-TDB that gives you for the date, add to your date and feed back in to get a refined TT-TDB value). This then only needs a leapsecond table for the UTC-TT part – astrosnapper Aug 20 '22 at 21:30
  • The only thing I understood of this question is that time is way more complicated that I ever imagined XD. This reminds me of https://xkcd.com/1882/ – Prallax Aug 20 '22 at 22:47
  • Also the fact that you call it "beginners question" makes me shiver – Prallax Aug 20 '22 at 22:52
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    You're assumptions are correct about the conversions, SOFA has a more extensive TDB estimate, and as mentioned above some of the DE have an even more extensive conversion. Additionally, some systems are now using Barycentric Coordinate Time (TCB) to be even more accurate than TDB. For what to use with each one, you should consult the publication accompanying each. Generally, JPL DE use TDB, and VSOP87 isn't accurate enough to warrant a conversion from TT. – Greg Miller Aug 20 '22 at 23:14
  • For the exact conversion of UTC to JPL's $T_{eph}$, see pages 2 to 4 of The JPL Planetary and Lunar Ephemerides DE440 and DE441, Ryan S. Park et al. Warning: that equation is seriously scary. ;) – PM 2Ring Aug 21 '22 at 07:24
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    Here's the IETF leap seconds list (human & machine readable). Here's my Python code to read it. – PM 2Ring Aug 21 '22 at 07:41
  • @Prallax See https://physics.stackexchange.com/a/402062/123208 Steve has a lot more info about time scales on https://www.ucolick.org/~sla/leapsecs/ – PM 2Ring Aug 21 '22 at 07:48
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    @GregMiller - thank you. What about any dates before 1972? Ignoring the small difference between TDB and TT, is the difference between UTC and TT constant for any date before 1972? – zero0cool Aug 21 '22 at 09:50
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    @PM2Ring - thanks! Fully agree on the scariness of the equation :) – zero0cool Aug 21 '22 at 09:54
  • Before 1972? It's a bit messy... See https://hpiers.obspm.fr/iers/bul/bulc/TimeSteps.history Steve Allen gives the gory details in https://www.ucolick.org/~sla/leapsecs/timescales.html – PM 2Ring Aug 21 '22 at 10:10
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    I strongly recommend the Python astropy module, which is quickly becoming the standard used by working astronomers. It provides a Time class for working with all sorts of time standards and an interface for JPL ephemerides. – Paul T. Aug 29 '22 at 16:28

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