[MUSIC PLAYING] 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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