# What is a leap second

Paul Millar paulm at astro.gla.ac.uk
Tue Oct 29 16:03:55 CST 2002

```Hmmm, probably drifting OT here, but ...

> On Tue, Oct 29, 2002 at 06:45:42PM -0000, György 'Nog' Jeney wrote:
> > While I was looking through dlls/ntdll/time.c I came across the following
> > two comments: "FIXME: Compute the number of leap second corrections here"
> > and "FIXME: get the GMT offset here" What do these this mean?

I took this to be a coding question, rather than an astronomical one, so
kept quite, but ...

On Tue, 29 Oct 2002, Steve Langasek wrote:
> Just as there are leap years which have an extra day, from time to time
> it's necessary to adjust the clock by adding leap seconds because IIRC, a
> siderial day is not *exactly* 24 hours -- there's a little bit of drift
> which adds up over time and needs to be corrected for.

which is both right and wrong, so I thought I'd (hopefully ;) clear up any
confusion.  You're right, sidereal day != solar day.  But, that's not what
leap seconds are for.

A solar day is the time it takes from sun-transit (== "high noon") to
sun-transit and is exactly 24 solar-hours.  A solar-hour is what most
people think of as an hour.

A sidereal day is the time between Betelgeuse-transit and
Betelgeuse-transit (choosing a star at random ;)  It isn't 24 solar-hours,
but rather a smidgen over 23 hours, 56 minutes and 4 seconds (I calculated
it as 4.1, but the web page I just check said 4.09 ...).

The two aren't the same because over the course of a year, the Earth
"gains" an extra day.  Nothing magical, just that even if the Earth didn't
spin (on its axis) you'd still have a day/night period as the Earth goes
around the sun.  Try it with a grapefruit and a satsuma to see what I
mean.  Keep the label saying "satsuma" pointing in the same direction and
rotate it around the grapefruit.  Over "one year", all around the satsuma
has faced the grapefruit, indicating a "day" has passed.

Ok, so what about leap seconds?  It turns out the Earth is slowing down.
Not by much, but atomic clocks are sufficiently accurate to measure this.
GMT measure time by the Sun (e.g. solar dials), whereas UTC is time
measured by atomic clocks.  Mostly the difference is just names, but when
as Earth starts to slow down, a discrepancy develops and the atomic clocks
start to tell the "wrong" time.

So, to compensate for this, there are leap seconds. This just "jumps" UTC
back whenever the difference between GMT and UTC is around a second.
They're introduced in a somewhat ad hoc fashion because the exact rate the
Earth is slowing down isn't 100% predictable.

HTH

...

(Now returning you to your normal program :)

----
Paul Millar

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