[LEAPSECS] What is a day?

Rob Seaman seaman at noao.edu
Sun Nov 2 07:55:29 EST 2014

Dennis Ferguson wondered:

> I see Terrestrial Time being expressed as a Julian Date quite
> a lot.  What is the unit of that number if not "Day"?

We may refer to 86400 seconds in a time scale like TT as being its "day" precisely because TT, TAI and other time scales were calibrated against the length of the mean solar day in the first place.  A day is not a free parameter.  You can't call 13.5 hours of 3600 SI-seconds a day, at least, not successfully for the purpose of civil timekeeping on Earth.

I had written:

> "Day" is a fundamental physical fact about a planet or moon.

For more details, see:


 ...and the presentation from which my paper originated:


(The discussion following that talk may also be of interest:  http://futureofutc.org/preprints/files/29_AAS%2013-515discussion.pdf)

I recommend the Moon Phase and Libration series from the NASA Goddard Scientific Visualization Studio.  For instance try the version with Brazilian Samba:


The point of opening my talk with this movie was to show the mean solar time clock that is hanging high in our sky every night.  A month on the Moon is the same as its day - its mean solar day.  It is also true that language is flexible.  As has been pointed out in other messages, including a private exchange below, the vocabulary word "day" can have numerous meanings.  Also see Kevin Birth's talks from the Charlottesville meeting.  But the mean solar day is special on every planet, not only Earth.  It sets the diurnal cadence for everything else.

A day is a unit of time.  An SI-second is an inverse unit of frequency.  They are not the same thing and civil timekeeping relies on both kinds of time scale.  As Steve Allen has pointed out, Universal Time meant mean solar time before there were leap seconds.  It is not a revolutionary concept to suggest that Universal Time should continue to mean what it always has, and if TAI is somehow deficient that another time scale be defined with its own new name.  This was the position at the Torino colloquium in 2003.

Rob Seaman

Steve Allen wrote:

> On Thu 2014-10-30T12:18:39 -0700, Rob Seaman hath writ:
>> Do you have any comments on this question, on or offline?
> The explanatory note from the 1964 IAU GA makes it clear that
> the dilemma for radio broadcasts was the need for atomic time
> interval and also the need for universal time.
> Those were the motivating factors for the leap second.
> From the other events during that era I read that "the second" without
> any other context is currently defined as the SI second using the
> cesium hyperfine transition, and "the day" without any other context
> is currently defined as one rotation of the earth according to UT1.
> There exists a "mean solar second", a "sidereal second", a "TCB second",
> etc., but those require a context saying so.
> There exists an "atomic day", an "ephemeris day", a "sidereal day", a
> "TT day", etc., but those require a context saying so.

Arnold Rots  wrote:

> I think one needs to distinguish between the unit of duration and
> the token in an ISO-8601 expression. Oh, and then there is the
> concept of "day" as a measure of rotation of the earth.
> In terms of units of time duration (i.e., in the context of a chronometer)
> we have:
> - s: SI second
> - h = 3600 s
> - d = 86400 s
> - a = 365.25 d  - the Julian year
> - cy = 36525 d - the Julian century
> And nothing will change that.
> When we look at the tokens in an ISO-8601 (or equivalent) expression,
> it is really no more than a way of saying where you are in time. Like
> decimal numbers, each token increases monotonically and triggers
> the next higher token to increment when it rolls over, but to some extent
> it is immaterial where the roll-over point is.

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