Rudolf Hooijenga wrote:
> You need, on average, to add more leap seconds than subtract because the
> earth is on average a little slower than the atomic reference. But that in
> itself does not mean Earth is slowing down.
>
> Suppose that the Earth kept absolutely constant speed, without slowing down
> at all, then there would be a fixed speed difference with a corresponding
> number of leap seconds each year to be added or subtracted ? just as when,
> when a clock needs to be adjusted by a minute each and every month, it means
> that its speed is constant ? although slow (or fast).
>
> In fact, the Earth does slow down ? and not just lately ?, but this effect
> amounts to about 17 microseconds each year on average, and would only
> necessitate an extra leap second every sixty thousand years or so. The
> day-to-day fluctuations are much larger than this.
>
> Brooke Clarke wrote:
>
>> [?] In order to keep the UTC1 correction below a second leap seconds can be
>> added or subtracted as needed, but since the Earth is slowing down lately
>> they seem to all be adding a second. [?]
Indeed, we have leap seconds not because the Earth is slowing down, but because
it has already slowed down (a little) from the effective zero-point in 1820.
Variations on the time scale of decades and centuries, let alone months and
years, are quite unpredictable; the slowest value for the sidereal rotation of
the Earth (that is, the longest value for the length of the mean solar day) was
at the beginning of the 20th century. The Earth (or, at least, its crust) has
actually sped up by a few milliseconds in the past century. It is only on the
order of millennia that clear patterns begin to emerge, see:
http://ucolick.org/~sla/leapsecs/dutc.html
<http://ucolick.org/~sla/leapsecs/dutc.html>
Tidal transfer of angular momentum from the spinning Earth to the Moon’s orbit
does increase length-of-day by about one SI-second every fifty or sixty
thousand years; each second corresponds to the Moon receding about one U.S.
mile (a kilometer or two), as confirmed by laser ranging of retroreflectors
left on the Moon’s surface by the Apollo astronauts. This day of 86,401
SI-seconds would correspond to one leap second per day to compensate – assuming
humans are still around to care. The continuing long-term tidal slowing of the
Earth will mean a quadratic acceleration in the rate of leap seconds.
Much more about leap seconds (and a little about sundials) is available from
the preprints and presentations of two workshops held in 2011 and 2013:
http://futureofutc.org <http://futureofutc.org/>
Readers on this list may be particularly interested in the contributions from
Denis Savoie:
http://www.cacr.caltech.edu/futureofutc/2011/program/presentations/AAS_11-670_Savoie.ppt.pdf
<http://www.cacr.caltech.edu/futureofutc/2011/program/presentations/AAS_11-670_Savoie.ppt.pdf>
http://www.cacr.caltech.edu/futureofutc/2011/preprints/22_AAS_11-670_Savoie.pdf
<http://www.cacr.caltech.edu/futureofutc/2011/preprints/22_AAS_11-670_Savoie.pdf>
and Ken Seidelmann:
http://www.cacr.caltech.edu/futureofutc/2011/program/presentations/AAS_11-682_Seidelmann.ppt.pdf
<http://www.cacr.caltech.edu/futureofutc/2011/program/presentations/AAS_11-682_Seidelmann.ppt.pdf>
http://www.cacr.caltech.edu/futureofutc/2011/preprints/48_AAS_11-682_Seidelmann.pdf
<http://www.cacr.caltech.edu/futureofutc/2011/preprints/48_AAS_11-682_Seidelmann.pdf>
Danny Hillis’s paper on the 10,000-year clock discusses various aspects of
building a timepiece to accommodate these long-term quirks of Mother Earth:
http://www.cacr.caltech.edu/futureofutc/2011/preprints/10_AAS_11-665_Hillis.pdf
<http://www.cacr.caltech.edu/futureofutc/2011/preprints/10_AAS_11-665_Hillis.pdf>
The resulting discussion was one of the more interesting of the meeting:
http://www.cacr.caltech.edu/futureofutc/2011/preprints/11_AAS_11-665_discuss_3.pdf
<http://www.cacr.caltech.edu/futureofutc/2011/preprints/11_AAS_11-665_discuss_3.pdf>
Rob Seaman
Network Time Foundation
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