# Beginners question about time scales

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?

• You need a "leap second kernel", naif.jpl.nasa.gov/pub/naif/generic_kernels/lsk Commented Aug 20, 2022 at 16:48
• 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. Commented Aug 20, 2022 at 23:14
• Here's the IETF leap seconds list (human & machine readable). Here's my Python code to read it. Commented Aug 21, 2022 at 7:41
• @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? Commented Aug 21, 2022 at 9:50
• @PM2Ring - thanks! Fully agree on the scariness of the equation :) Commented Aug 21, 2022 at 9:54