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I'm confused by the ust of the term "UT" in the description of time scales used by the JPL HORIZONS system.

Their manual states that

UT is Universal Time This can mean one of two non-uniform time-scales based on the rotation of the Earth. For this program, prior to 1962, UT means UT1. After 1962, UT means UTC or "Coordinated Universal Time".

and the key attached to the tool's output says

Prior to 1962, times are UT1. Dates thereafter are UTC.

My understanding is that UTC has leap seconds, so that there should be an extra second at the end of a day on which a leap second was added, but the intervals reported by HORIZONS lacks these, and look more like UT1:

 2012-Jun-30 23:59:58.000 2456109.499976852 
 2012-Jun-30 23:59:58.667 2456109.499984568 
 2012-Jun-30 23:59:59.333 2456109.499992284 
 2012-Jul-01 00:00:00.000 2456109.500000000
 2012-Jul-01 00:00:00.667 2456109.500007716 
 2012-Jul-01 00:00:01.333 2456109.500015432 
 2012-Jul-01 00:00:02.000 2456109.500023148

Even more confusingly, the data reported do in fact behave as if the times are UTC. For example the reported azimuth of Pluto at Greenwich for the times above changes by 0.0028° for each of the intervals but the third, where it changes by 0.0069°, a factor of 2.5 times the change in each of the other intervals, which is exactly what would be expected ((1 + 2/3)/(2/3)) if there were an extra second between 2012-Jun-30 23:59:59.333 and 2012-Jul-01 00:00:00.000. This, despite the fact that the difference in JD over that interval is the same as each of the other intervals, meaning that one can't expect differences between JD that span any leap seconds to line up with changes in data!

If the times and data are UTC, how can the differences between JD be uniform? If they're UT1 how can the data "jump" at the leap second?

Note also that the form for entering queries describes "Delta T" as CC-UT

enter image description here

which means that if "UT" can mean UTC, this means that after 1962, $\Delta T$ is a discontinuous function, but my understanding is that $\Delta T$ is that a continuous function, TT-UT, where UT is not UTC (see note 1 here).

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Good question, but I don't think it's a reference-request. –  David Z Nov 28 '12 at 20:14
@DavidZaslavsky: Correct. I'm not seeing a tag for something like "data sources" though. –  raxacoricofallapatorius Nov 28 '12 at 20:15
True... I don't think we get enough questions of that nature to justify a tag for it. (But still, that doesn't mean you should use a tag that doesn't fit the question! You only technically need one.) –  David Z Nov 28 '12 at 20:19
The difference between UT1 and UTC is always kept to less than a second, the precise value being -0.9s < dUT1 < +0.9s. It's value is encoded in the WWV time signals. The leap seconds in the UTC scale are inserted or deleted to keep dUT1 within its specified range. The JPL ephemerides use a smoothly flowing form of dynamical time they name T_eph. It is mathematically related to the terrestrial and barycentric dynamical timescales,all of which are relativistic in nature. –  user11266 Nov 28 '12 at 20:23
The whole issue of time in the JPL ephemerides is far too complicated to explain here. I strongly suggest you get a copy of the new edition of The Explanatory Supplement to the Astronomical Almanac, which was just published last month. It, along with internal JPL memos, is the definitive documentation for the ephemerides that Horizons uses. –  user11266 Nov 28 '12 at 20:25

2 Answers 2

You raise two issues: ΔT, and the HORIZONS timescales. Let us tackle each in turn.

1. What is Delta-T?

You are correct that HORIZONS is using a confusing term here.

What the HORIZONS menu calls Delta-T is an entirely different quantity than the ΔT you will see defined and used in many other references on astronomy. Briefly:

  • What HORIZONS calls Delta-T tallies the diverging difference between how time behaves down at the bottom of the (fairly) temporally stable environment of the solar system barycenter, and how time behaves up here on Earth as we speed up and slow down each year as our orbit takes us close to and then away from the Sun. Their idea of CT is a clock at the solar system barycenter, their UT means UTC, and — absent any leap second events — the difference CT - UTC will slowly grow smaller as the stationary clock CT runs more quickly than the accelerating clock UT stationed on the Earth (per relativity). But because our rotation is slowing down, leap seconds are being added to UTC faster than CT can outrun it, so over the foreseeable future the different CT-UT will get gradually larger.

  • The traditional measure ΔT is defined as ∆T = TT – UT1, as you can confirm in the United States Naval Observatory PDF linked below. This quantity has nothing to do with the solar system barycenter at all, as both TT and UT1 are Earth time scales. TT is, conceptually, the time scale of an Earth atomic clock that runs forever without interruption or leap seconds, gradually going in and out of sync with actual Earth days and nights as the Earth's rotation speed changes through geologic ages. UT1 is the complete opposite: it is a sun-dial time defined by the direction the Earth is really genuinely pointing at any given moment with respect to the Sun. The difference, therefore, tells someone with an atomic clock “how far off” real Earth day and night are going to be from their atomic clock when they look out the window. The quantity, since the invention of TT fairly recently, has grown to more than 60 seconds — there is more than a minute difference, already, between strict atomic clock time and where the Earth is really pointing.


Thus the HORIZONS Delta-T and traditional ∆T, strictly speaking, have literally nothing in common! They measure the difference between completely different time scales. But, more loosely, they do have a resemblance: they tend to stay within a second of each other because their first terms, CT and TT, are defined such that they are very close together now and for the foreseeable future, and their second terms, UTC and UT1, are kept within 1s of each other thanks to the leap-second system. But their small day-to-day differences are tied to different astronomical effects.

2. What Is The HORIZONS Timescale?

When doing normal Observer tables, it is UTC, as you carefully and correctly observed by the fact that objects travel farther during the minute, hour, and day that contains a leap second.

When doing vector tables, it is CT, and no leap seconds are present in the time scale.

Finally, you are correct that it seems a bit daft to use JD floating-point values for a timescale like UTC that has leap seconds — how would you represent them? Invent an extra digit beyond 9 (maybe a?) and have it appear after the decimal point after .99999 has been exceeded but you cannot yet increment the day integer because you are in the leap second? Would you repeat the fraction for the second :59 again? Or just have the date hang at .99999 or the .00000 moment for a full second? You are right: the result is a bit odd whatever they choose to do, and as a result I always express UTC as dates and times, and reserve JD numbers for uniform timescales like TAI, TT, and TDB.

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The JPL ephemerides use a timescale called T_eph which is the best possible approximation to Newton's concept of a freely flowing universal time that appears in dynamical equations of motion. T_eph is related mathematically to other important relativistic timescales used in astronomical and astrometric calculations, and their relationships are rather complicated as they depend on gravitational potential. The best reference for this topic is the new Explanatory Supplement to the Astronomical Almanac published by University Science Books. In practice, one usually begins with UTC (Coordinated Universal Time), which is available internationally via standard time signals, and expresses the desired UTC as T_eph for extracting ephemeris data.

I'll edit this for clarity later.

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I think the answer here is simply that the times are indeed UTC. The question about JD is a separate, more general one. –  raxacoricofallapatorius Dec 2 '12 at 22:26

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