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AbsoluteTime supposedly reports the "total number of seconds" between two dates, but it does not. For example, because of the leap second applied at 2012-06-30T23:59:60Z,

AbsoluteTime[{2012, 7, 1}] - AbsoluteTime[{2012, 6, 29}]

should be 172,801, but it returns 172,800. In fact, Mathematica seems to ignore leap seconds altogether:

DateList[{2012, 6, 30, 23, 59, 60.5}, TimeZone -> 0]

produces {2012, 7, 1, 5, 0, 0.5} when it should produce {2012, 6, 30, 23, 59, 60.5}.

Am I missing something here? How are calculations and functions, such as AstronomicalData, that depend on accurate time specifications supposed to work?


Update: This remains the case in version 9.0 and 10.0.2.

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    $\begingroup$ Note that I'd be happy (well, a bit unhappy actually) with an answer that simply clarified Mathematica's concept of a "time". For example, it seems that by "time", it really means "calendar date including hours, minutes, and seconds", so that AbsoluteTime is a bit of a misnomer: it's really "DifferenceBetweenCalendarDatesConvertedToSeconds". $\endgroup$ – orome Nov 22 '12 at 18:30
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    $\begingroup$ This is known to be a deficiency for a lot of years. I think it will not be changed. $\endgroup$ – Rolf Mertig Nov 22 '12 at 20:08
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    $\begingroup$ @RolfMertig: So it's easy enough then (I think) to see one implication of this for AstronomicalData: leap seconds are ignored and time is just ticking away according to a uniform clock, but not UTC, so that the data reported by AstronomicalData for a given (*Mathematica) "date" will actually be the data for a different UTC date (what the world outside *Mathematica *means by "date") some seconds away. But that leaves the question: which date? $\endgroup$ – orome Nov 22 '12 at 20:53
  • $\begingroup$ @RolfMertig, got a Uncompress::corrupt error on your hashed email. Can you fix? $\endgroup$ – alancalvitti Dec 11 '14 at 17:40
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    $\begingroup$ @alancalvitti: I've tried. They got defensive and angry. Very unpleasant experience. $\endgroup$ – orome Dec 11 '14 at 17:49
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The U.S. Naval Observatory keeps a list of when leap seconds have been added and I think it has been at a stable URL for a while: http://maia.usno.navy.mil/ser7/tai-utc.dat

You could use this if you need to know when seconds were added. I wrote a solar position routine, and used this for a while, but I changed it to use an output file from their MICA software, which has a closer interpolation routine for a better approximation to solar time for the present and immediate future. Their algorithm and data are upgraded regularly, if you don't need the interpolation for current estimate, the data set above should be adequate to give you the history of when leap seconds were added.

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  • $\begingroup$ The question is how to get AstronomicalData to report the "total number of seconds" between two dates, as claimed; not how to calculate them on one's own. $\endgroup$ – orome Dec 11 '14 at 16:48
  • $\begingroup$ How to interpret the several gaps between regular intervals? years in tai-utc (year only, ignoring month) Import["http://maia.usno.navy.mil/ser7/tai-utc.dat"][[All, 1]] // NumberLinePlot $\endgroup$ – alancalvitti Dec 11 '14 at 18:05
  • $\begingroup$ I think they add the leap second at 0:00:00 UTC on the date. They add them based on astronomical observations; the earth's rotation is not constant so the gaps vary. $\endgroup$ – Bob R Dec 12 '14 at 19:31
  • $\begingroup$ Markus Roellig provides a Mathematica routine for $\Delta T$ here. $\endgroup$ – J. M. will be back soon Aug 2 '16 at 8:24

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