Wolfgang,
Thanks very much -- I was ignoring real-world details.
Roger
-----Original Message-----
From: sundial [mailto:[email protected]] On Behalf Of Wolfgang R.
Dick
Sent: Monday, November 30, 2015 11:14 AM
To: Sundial Mailing List
Subject: RE: No decision on future of leap seconds
Dear Rudolf and Roger,
The leap second comes from the fact that the Earth's rotation rate has
decreased since the definition of the second. Currently each day is 1
millisecond longer than 24 hours in the mean. One has to regard the Earth as a
clock, which is too slow compared to a precise clock (= UTC running in parallel
to atomic time TAI).
After one day the difference in time which the two clocks display is 1 ms,
after two days 2 ms, ..., after 1000 days 1 second. This is the leap second.
UTC clocks are stopped for one second, so that after this the two clocks (Earth
= UT1 and precise clock = UTC) are showing the same time again. 1000 days is
about 3 years - currently a leap second is introduced each 3 years in the mean.
When the mean "length of day" (LoD, one day = 24 h + LoD)) was 2 ms in 1990s,
we had a leap second each 1 1/2 years in the mean (= 500 days). Since then the
Earth rotation has speeded up due to decadal fluctuations (core-mantle coupling
in Earth). But it will decrease again due to the Moon.
After the next 100 years, LoD will be about 3 ms in the mean. Then a leap
second will be needed every 333 days. And so on. This is a quadratic function
with time, i.e. the frequency of leap seconds increases quadratically with
time. This will be a big problem for our grandgrandgrand...children.
Best regards,
Wolfgang
Gesendet: Montag, 30. November 2015 um 12:18 Uhr
Von: "Roger W. Sinnott" <[email protected]>
An: [email protected]
Betreff: RE: No decision on future of leap seconds
Rudolf,
If the day length starts at 86400 seconds and grows by 0.000017 second each
year, it would indeed reach 86401 seconds in about 60000 years. But if this
rate is uniform, the tiny fractional increases would accumulate to 1 second in
just 343 years, so I think that's when the first leap second would be needed.
Roger
From: sundial [mailto:[email protected]] On Behalf Of Rudolf
Hooijenga
Sent: Monday, November 23, 2015 5:18 PM
To: 'Brooke Clarke'; [email protected]
Subject: RE: No decision on future of leap seconds
. . . 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.
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