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PORTSIDE  March 2012, Week 1

PORTSIDE March 2012, Week 1

Subject:

The Physics of Leap Day

From:

Portside Moderator <[log in to unmask]>

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Date:

Sun, 4 Mar 2012 22:23:40 -0500

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The Physics of Leap Day
by Ethan Siegel
Starts With A Bang
February 29, 2012
http://scienceblogs.com/startswithabang/2012/02/the_physics_of_leap_day.php

    "When in doubt, make a fool of yourself. There is a
    microscopically thin line between being brilliantly
    creative and acting like the most gigantic idiot on
    earth. So what the hell, leap." -Cynthia Heimel

[moderator: please use the link above to view this
post with accompanying graphics]


Once every four years, the elusive entity that is today
-- February 29th -- comes along. The historical origins
and urban legends associated with it are incredibly
interesting, but the reason there's any such thing as
Leap Day at all is because of the physics of planet
Earth.

The Earth, of course, is rotating on its axis while
simultaneously revolving around the Sun. Rotation, as we
all learn, is responsible for sunrise, sunset, moonrise,
moonset, the Coriolis effect, and the rotation of all
the stars in the night sky about the poles. Revolution,
on the other hand, is responsible for the seasons; when
your hemisphere tilted away from the Sun, that's when
you have your winter (and minimum daylight), and when
your hemisphere is tilted towards the Sun, that's when
you have your luminous summer.

And you probably learned that a day is 24 hours, due to
the rotation, while a year is 365 days (with an
occasional 366 for leap years), taking care of the
revolution. It turns out it's a little more complicated
than that, so let's dive in! 

The Earth completes a full rotation in less than 24
hours: 23 hours, 56 minutes and 4.09 seconds, to be more
precise. But even though we've spun around a full 360
degrees, we've progressed just a little bit in our orbit
around the Sun. If we insisted on using the 23:56:04.09
figure as our day, the Sun would be out at midnight for
half the year! To fix the motion of the Earth around the
Sun, we need those extra 3 minutes and 56 seconds to
orient ourselves correctly. That takes care of what a
day is, but what about a year? A revolution -- for the
Earth to return to the same position with respect to the
Sun -- might be an interesting astronomical thing to
mark, it isn't a useful definition for a year on Earth.

In order for the Earth to achieve the same seasonal
position in its orbit around the Sun -- and trust me, if
you live on Earth, you'll want to mark your calendars by
the seasons -- you'll need for the Earth to be oriented
the exact same way with respect to the Sun as it was
exactly one revolution ago. We could do this from winter
solstice to winter solstice, when the Earth's north pole
(for me) points maximally away from the Sun, or any
other arbitrary point in its orbit. This way of
measuring the year, known as the tropical year, is
actually a little shorter than the astronomical
measurement of a year we might be tempted to make.

Because the Earth only needs to revolve slightly less
than 360 degrees around the Sun to make one tropical
year. The difference is tiny -- 359.986 degrees instead
of 360 -- but enough to make the tropical year about 20
minutes shorter than the sidereal (or astronomical)
year. This difference is known as precession, and it
explains why the pole star in the night sky appears to
change very slowly over a period of about 26,000 years.
(25,771 years, for the sticklers.) 

Combine all three of those effects together -- rotation,
revolution, and precession -- and you can answer the
question of how many days will it take the Earth to make
a tropical year?

The answer, as precisely as we can figure for 2012, is
365.242188931 days. If we just had 365 days in the year
every year, we'd be off by nearly a month every century,
which is pretty lousy. Putting in a leap year (with an
extra day) every 4th year gets us closer, giving us
365.25 days in a year. (This was how we kept time with
the Julian Calendar, which we followed for 1,600 years!)
Still, this difference was significant enough that, by
1582, we had put in 10 too many days. For this reason,
October 5th through October 14th of 1582 never existed
in Italy, Poland, Spain and Portugal, with other
countries skipping 10 days at a later date. The
Gregorian calendar, which we now follow, is exactly the
same as the Julian calendar, except instead of having a
leap year if your year is divisible by 4 (as 2012 is),
you don't get a leap year on the turn-of-the-century
unless your year is also divisible by 400! So even
though 2,000 was a leap year, 1,900 wasn't and 2,100
won't be, but 2,400 will be again. When did your country
make the switch? 

The adoption of the Gregorian calendar gives us a
calendar of with -- over time -- 365.2425 days in the
year. In comparison with the present, actual figure of
365.242188931 days, it will take over 3,200 years for us
to be off by a single day, which is certainly good
enough for a little while.

But if we want to be planning for the long term, we
shouldn't simply be thinking about this difference. We
should be thinking about the fact that the Earth's
rotation rate is changing, and over long enough amounts
of time, so should our definition of what a "day" is!

What am I talking about? Two things happen that change
the Earth's rotation rate, and they push the day in
opposite directions. 

Every time we have an earthquake, that's mass inside the
Earth rearranging itself so that -- by the conservation
of angular momentum -- its rotation speeds up a little
bit. For instance, last year's Japanese earthquake
shortened the day by 1.8 microseconds, and the 9.1
Sumatra earthquake in 2004 shortened the day by 6.8
microseconds. On the other hand, there are two bodies
out there with large gravitational effects on the Earth!

The Sun and the Moon both exert gravitational pulls on
the Earth, all while the Earth itself rotates. If the
Earth were just a point in space, this wouldn't matter;
the Earth would make its elliptical orbit around the
Sun, the Earth-Moon system would orbit their center of
mass, and nothing would change. But because the Earth is
a sphere, both the Sun and the Moon exert greater
gravitational pulls on the side of Earth that's closer
to them than on the side that's farther away.

Throw in the Earth's rotation, and you not only get
tides, you also get tidal braking, which causes the
Earth's rotation to slow down! 

The slow-down is small but pretty consistent, at an
average of 14 microseconds per year, a much larger
effect than the speedup due to earthquakes. And over
geological times, this really adds up! If we go back to
the daily patterns left in the soil from the tides --
known as tidal rhythmites -- we can calculate what the
period of Earth's rotation was from it. 

If we look at the most ancient one we know of on Earth,
from 620 million years ago, we find that a day back then
was a little under 22 hours long!

If you extrapolate this tidal braking back to when the
Earth was first formed, 4.5 billion years ago, you'll
find that a day was originally only around 23,000
seconds, or six-and-a-half hours! 

And the best part about this is that the Earth continues
to slow down! Every 18 months or so, because of the
difference between 86,400 seconds and an actual day, we
add an extra leap second to our clocks (for now). Wait
around for around four million years or so, and the day
will lengthen by about 56 seconds, enough that we won't
even want leap year anymore; a year will have exactly
365 Earth days!

So appreciate this leap day and our attention to detail
to getting the Earth's seasons to remain constant from
year-to-year, but also be aware that our Earth, however
imperceptibly, means that these leap days, too, shall
pass.

___________________________________________

Portside aims to provide material of interest to people
on the left that will help them to interpret the world
and to change it.

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