Re: [LEAPSECS] What problems do leap seconds *really* create?

From: Mark Calabretta <Mark.Calabretta_at_ATNF.CSIRO.AU>
Date: Thu, 30 Jan 2003 14:00:22 +1100

On Wed 2003/01/29 15:43:24 PDT, Rob Seaman wrote
in a message to: LEAPSECS_at_ROM.USNO.NAVY.MIL

>Basically we don't have leap seconds because the Earth's rotation is
>slowing down (by transfering angular momentum to the Moon). Rather,
>we have leap seconds because the Earth has *already* slowed down since
>1900. See the rather consistent slope of about 7 seconds per decade
>on the plot of UT1-UTC (with leap seconds removed) versus date:
>The current dynamical effects are the subtle wiggles imposed on this
>trend. This is actually a fairly useful bias since it guarantees (short
>of asteroid impact or armageddon) that there will be no negative leap
>Again, please note how consistent the divergence is between atomic
>and Earth timescales over decade long periods. Where precisely is the
>urgency to adopt a quick fix?

I agree with you that there is plenty of time to make an informed
decision, that nothing need be done on a timescale of decades, and
also that the process to date appears, at least to some of us, to have
bordered on Machiavellian, though I'm sure it was not.

It's also true that the leap-seconds we have now do come from the
slowdown since 1900. However, your "consistent slope of about
7 seconds per decade" obscures the basic point about the long term
future of UTC. Your graph shows a linear approximation to what is
actually a parabola.

The graph in the "GPS World" article shows the long term trend much
better. Though its fit to a parabola is not much more convincing - we
do know that it is a parabola because the physics of the Earth-Moon
dynamical system tells us so. The wiggles are caused by the motion of
dense material in the Earth's mantle which cause the Earth's moment of
inertia to vary unpredictably, thus causing it to spin up as well as
down. They are what leap-seconds were originally designed to handle,
not the predictable, long-term secular deceleration of the Earth's

Thus, what is 7 seconds per decade now will become 35 seconds per
decade in another two hundred years time. When you add up all those
so-many-seconds per decade over the next 20 decades the cumulative
error runs to many minutes - already nearly 60s by 2050 according to
the GPS World article, not 35s by a linear extrapolation, and more
than 140s by 2100, double the linear-extrapolated value.

The cumulative error grows quadratically; that is the problem.

Mark Calabretta
Received on Wed Jan 29 2003 - 19:00:43 PST

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