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THE DAILY ASTRONOMER
Monday, February 29, 2016
Leap Day Astronomy

Ask a planetarium audience  what aspect of astronomy is most
compelling and every person will invariably shout, "calendar
reckoning!"  Unlike the tedious, boring topics such as 'black holes,'
'exploding stars,' 'extraterrestrial intelligence,' or 'parallel
universes,'  calendar reckoning ignites the imagination beyond
constraint and has inspired generations of children to select
lucrative, groupie-accumulating astronomy careers.   (And we've never
regretted it.)

Now, in a tidy Universe, calendar reckoning would be a complete
non-event.   Our planet would describe a perfect circle and its
constant rotation period would be a pleasant integer multiple of the
orbital period.  For instance, an ideal Earth would spin on its axis
exactly 300 times during each orbit, so every year would be precisely
300 days long, down to the picosecond.      Once established, the
calendar would retain its integrity forever.



Well, in our untidy, troublesome Universe, the situation is a complete
mess.     Earth's orbit is not a circle, but an ellipse (more on this
issue later); and the amount of time our planet requires to complete a
circuit about the Sun is hardly a well-behaved integer, but
approximately equals 365.24219265 days.*     (365 days, 5 hours, 48
minutes, 45.5 seconds, or thereabouts.)



Let's pretend we go back in time to a few thousand years ago, and we
don't have the convenience of knowing the value we just introduced.
However, we've been hired to construct a calendar that everybody can
use for sowing, harvesting, and festivals.    We have to keep in mind
the four seasonal points: the first day of spring, summer, fall and
winter.   Fortunately, we already conned some other unsuspecting time
travelers into ascertaining these points.**  Our calendar must
maintain these seasonal points:  so, to take a wild example out of our
hats, the Vernal (spring) Equinox must be on March 21, or very close.



Well, we're going to be completely lazy and decide that each year has
365 days.  Everybody will abide by it and all will be well.  At least
it will be for us, because our work is done and we can now spend the
rest of our lives engaged in ancient world amusements, such as playing
the Wii Sports Resort.      Initially, all seems well.    The calendar
and the seasons are in lovely sync.



A few years elapse and we notice a slight problem.   The seasonal
points are shifting, albeit slightly.   We're reaching the Vernal
Equinox and the other points later than we should.    "Hmmm," we
think, "why is our calendar off?"



We reluctantly tear ourselves away from our amusements and
investigate.     We discover that Earth's year, which we regard as the
time the Sun requires to move around us, is a bit longer than we
thought.      Calculations performed on our watches (remember, we're
time travelers) indicate that this discrepancy equals about one day
every four years.     Mind you, such a discovery would require a damn
long time, but we're compressing  the scenario.



Our calendar is wrong.



Fortunately, we don't have to make any changes because we fled back to
the modern world before anybody really noticed.    Many years later
after our cowardly departure, a Roman dictator named Julius decides to
take matters into his own divine hands.    Exactly 708 years after
Rome's mythical founding by Romulus and Remus (46 BCE or 46 BC to us),
Julius imposes a new calendar system to compensate for the older one's
deficiencies.      His year still consists of 365 days.   However,
every four years, a leap day is inserted.     This extra day accounts
for the extra time the Sun needs to complete its orbit around Earth.



As Julius was the only vain leader in Roman history, he names this
system the Julian calendar.    A little while later, Julius dies
because he chose the wrong friends, but the calendar survives.



Centuries elapse!

And, now, in the beautiful, mythological, age of castles, dragons and
hobbits, people find that the calendar is showing other errors.   The
Vernal Equinox is now happening EARLIER than March 21st.    Much
earlier.   In fact, spring is beginning around March 11th.    The
calendar had shown this "creep effect" ever since the Roman era, but
only after hundreds of years has this error accumulated enough to be
troublesome.   The Vernal  Equinox now precedes the actual Vernal
Equinox date by more than a week and a half.      Now, we know where
this is leading:  if left uncorrected, the  Vernal Equinox (and other
seasonal points) will migrate farther away from their established
dates.     The equinox will move toward the solstice date and the
solstice dates toward the equinoxes.   Eventually, the Vernal Equinox
will occur around December 21st, the date once reserved for the
solstice; and we'll reach the summer solstice in March and, well, what
a mess! The real trouble, ecclesiastically, is the Easter date, the
calculation of which involves the Vernal Equinox.***



We reach 1582, and Pope Gregory XII (Ugo Boncompagni to his friends)
takes it on himself to set things right.   He issues new calendar
rules designed to account for the smaller, but still significant,
errors inherent in the Julian calendar.   Along with Christopher
Clavius, the astronomer who does the real heavy lifting, Pope Gregory
XII introduces a dramatic calendar reform.  First, he removes 11 days
from the calendar so set the Vernal Equinox back in place.   He
essentially gives the calendar a swift kick..   He then modifies the
leap year rules that Julius developed:



Every four years will have a leap day; except for those years equally
divisible by 100, unless those years are  also divisible by 400.



Let's take a few examples:



1900 was not a leap year; but 1896 and 1904 were

2000 WAS a leap year, but 2100 will not be.

1600 WAS a leap year, but 1700 was not.



By imposing these extra rules, the calendar will match the seasonal
year much more closely.



Now, in a neat world, everybody would embrace these changes at once.

Instead, various countries take their sweet time adopting them.
(Religious strife, communication issues and sometimes stubbornness
impedes the calendar's promulgation and adoption.)      England waits
until the 18th century; and Greece waits until 1923, to cite a few
examples.



The Gregorian calendar is now widely accepted because it is so
beautifully accurate!

Mind you, the Vernal Equinox is not always on March 21st because our
orbit not circular and date variations are inherent in our orbit.
However, with this new reform, our calendar remains in sync with the
seasons and will for centuries to come.    These leap days do come in
handy.









*We could really tangle the knots with information about the different
types of years.  The value cited in the article's main body is the
"tropical year," defined as the time related to the seasonal changes.
    We will cheerfully neglect the other definitions.



**How would one make these determinations?    An easy  method would
involve sighting the sunrise-sunset points along the horizon.
Provided one maintains the same observation point, one could insert
posts to mark the various rise/set points.    The Sun rises due east
and sets due west on the equinoxes, John, and these points proceed
southward throughout the autumn, until reaching the
southeastern/southwestern most points on the winter solstice.
Conversely, they proceed progressively northward through the spring,
until reaching their northeastern/northwestern points on the summer
solstice.     One could designate posts specific to the seasonal
points.   (Granted, such determinations require more than one year.



***The First Council of Nicaea (325 AD) established the Easter date as
being the first Sunday after the Full Moon following the Vernal
Equinox.