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In an earlier episode, we mentioned the Earth's rotation
is slowing down.
On average, the day gets longer by about two milliseconds
every 100 years.
Supposedly, leap seconds are related
to this slowing rotation, but the math seems to be way off.
In the past 40 years, we've had over 20 leap seconds,
but the day should only have gotten
around one millisecond longer.
What's going on?
Here's the deal.
Back in the day, the second was defined as exactly 1/86,400
of a solar day.
But Earth's rotation slows, so that's a bad definition.
Thus, in 1960, the second was redefined to be whatever
would make the motions of multiple objects
in the solar system fit Newton's laws of motion.
This was called the ephemeris second.
In 1967, we redefined the SI second again
based on atomic clocks since they're more stable,
but the atomic clock second was calibrated
to agree with the ephemeris second.
So SI, ephemeris second, the same.
Now, here's the thing.
The astronomical observations that
were used to define the ephemeris second
were made in the 18th and 19th centuries
using the old definition of a second to keep time.
Thus, those two definitions would have actually
agreed exactly back in 1820.
Since then, though, Earth's actual day
has gotten about 2 and 1/2 milliseconds longer so
that by the 1960s, one solar day was now
86,400.0025 new seconds.
The atomic clock second just inherited this discrepancy.
As a result of all this unit shifting,
the current solar day right now is already
2 and 1/2 official milliseconds longer than 24 hours.
That means right now, we're measuring the day
and keeping actual time on our clocks using slightly
different concepts of a second.
Thus, 12:00 PM on our clocks is continually
getting ahead of when the sun is directly over us.
Every year or so, the discrepancy
accumulates and grows to around one second
and we insert leap seconds to force our clocks back
into sync with the sun.
Of course, Earth's rotation has irregularities
due to earthquakes and other effects.
Ergo, why we don't do leap seconds
on a precise yearly schedule.
Now, over time, Earth's rotation will
keep slowing and leap seconds will become more frequent.
But the current frequency right now of leap seconds,
that arises because of a preexisting difference
in the size of an SI second and the size of 1/86,400 of a day.
Earth is spinning down, yeah, but not that quickly.
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