I am reading about the algorithms to convert from date and time format to Julian Date from the Fundamentals of Astrodynamics and Applications by Vallado (4th Edition) p183.

My question is specifically regarding the differences in converting UT1 vs UTC to JD(UT1) and JD(UTC) respectively. The formula provided has term which needs to be changed depending on if the day contains a leap second or not. Would I be correct in thinking that UT1 => JD(UT1) requires no accounting for leap seconds in contrast to UTC which does?

I guess my confusion is arising from the language in some literature I have read referring to both UTC and UT1 as "non-uniform" time systems. I understand UTC is discontinuous due to insertion of leap seconds and suppose that UT1 is continuous but non-uniform in the sense that the definition of a second is not constant.

Just wanted to get some confirmation/clarification, thanks.

  • $\begingroup$ Please check Consolidated Errata for editions 1-4. There is an entry that applies to pages 182-184 that involves time conversion. Also when you say "The formula provided" is it possible to edit your question and include the formula here? Some people may be able to answer your question but not have this specific book handy. Thanks! (MathJax tutorial if you need it) $\endgroup$
    – uhoh
    Jul 9, 2019 at 22:44

1 Answer 1


Would I be correct in thinking that UT1 => JD(UT1) requires no accounting for leap seconds in contrast to UTC which does?

Yes, that's correct. However, UT1 is neither predictable nor uniform either. It depends on polar motion, nutation, and precession of the Earth. UTC is a close approximation to UT1, and the IERS ensures that UTC stays within 0.9 seconds of UT1 by adding leap seconds every now and then. Here is the list of leap seconds: https://www.ietf.org/timezones/data/leap-seconds.list . The general rule is that a leap second may be added either on 01 January or 01 July.

Unless you need extremely precise times, like for astronomical measurements, then UTC fits perfectly. Otherwise, you can keep all of your time in TAI (International Atomic Time), and convert that time to UTC or UT1 when you need such a representation.

TAI is fixed in time and does not account for any leap second, but that also means it will drift with the time system used by the general population (which is based on UTC).


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