Re: Watch out for Y2K
Message #65 Posted by James M. Prange (Michigan) on 6 Oct 2005, 5:14 p.m.,
in response to message #63 by Dave Shaffer
My attempt to explain the "precession of the equinoxes",
Milankovitch cycles, leap years...
But I'm not anastronomer; I wouldn't even consider myself an
"amateur astronomer" (I don't even have a telescope). But I do
find astronomy, calendars, and time-keeping interesting. Maybe I'm
an "armchair astronomer"? Anyway, take the following with a few
grains of salt.
First off, we have at least three major definitions of a year
based on astronomy, in addition to the various calendar years.
A "tropical" year, the period of the seasons. For example, from
vernal equinox to vernal equinox; our Gregorian calendar year is
based on this.
A "sidereal" year, the period of the earth's revolution around the
sun in relation to the "fixed stars", or equivalently, the
apparent position of the sun against the starry background. Of
course, the stars, galaxies, quasars, and so on are actually
moving, but due to their immense distance from us, except for the
nearest stars, any change in their apparent angular relationships
as viewed from the earth is negligible. A sidereal year is about
20 minutes longer that a tropical year. Note that even the length
of the sidereal year is changing, presumably due to transfers of
angular momentum among the bodies of the solar system, "friction"
with interplanetary gas and "dust", the affects of the solar wind,
and so on. Everything in the universe affects everything else.
An "anomalistic" year, the period from the earth's perihelion
(closest approach to the sun in its elliptical orbit) to its next
perihelion. An anomalistic year is about 25 minutes longer that a
tropical year, or 5 minutes longer than a sidereal year. This
precession is due (at least mostly) to perturbations of our orbit
from the major planets, particularly Jupiter and Saturn. The
period of this precession (in relation to the fixed stars) seems
to be about 114000 years. The eccentricity (how nearly a true
circle the orbit is) is thought to vary too, with a period of
about 95000 years.
The ecliptic is the plane of earth's orbit, so called because an
eclipse of the sun or moon occurs when the moon crosses this plane
very nearly at the new or full moon. Of course the sun, as viewed
from the earth, always appears to be on the ecliptic. The
constellations that appear to be on the ecliptic are called the
zodiac. The sun, as viewed from the earth, appears to move through
the zodiac once per sidereal year. As noted in another post, the
ecliptic is very stable (at least in terms of human history), and
except perhaps for some relatively nearby stars, so is the zodiac.
Of course, when the sun evolves into a red giant, that will effect
Earth's orbit, to put it mildly, but no one on Earth will be
concerned with that. The moon's orbital plane around the earth is
at an angle of about 5.1 degrees to the ecliptic. The orbital
planes of the other planets, except Pluto, are near the ecliptic,
ranging from about 0.8 degrees from the ecliptic for the orbital
plane of Uranus to 7.0 degrees for Mercury's, so the planets also
appear to be near the ecliptic. Even Pluto's orbital plane is only
about 17.2 degrees from the ecliptic.
The celestial equator is the earth's equator projected into the
sky. Of course the plane of the celestial equator is perpendicular
to the earth's axis of rotation.
The celestial poles are the earth's axis of rotation projected
into the sky. Currently, the north celestial pole is near Polaris
(the North Star).
Currently, the planes of the ecliptic and celestial equator are at
an angle of about 23.5 degrees, though that's thought to vary a
few degrees with a period of about 41000 years.
An equinox occurs when the earth passes through the line of
intersection of the planes of the ecliptic and the celestial
equator.
Because the earth spins, it has an equatorial bulge. The sun's and
moon's gravity pull on this bulge, one might say trying to pull it
into alignment with a line from the sun to the moon, in effect,
applying a torque to the earth's rotational axis. As anyone who's
played with a gyroscope should recognize, the affect is to cause a
precession of the earth's axis, causing it to sweep out a (more or
less) cone in the sky, relative to the fixed stars. This
precession has a period of about 26000 years, relative to the
fixed stars. One effect is that Polaris is near the axis only
periodically; the stars (as viewed from the northern hemisphere)
won't always appear to revolve around it. The celestial poles move
in (more or less) circles in the sky. Since the plane of the
celestial equator is perpendicular to the axis, as the axis
precesses, this plane "wobbles" (for lack of a better term) in
synch with it, and of course, this causes its line of intersection
with the ecliptic plane to rotate one full turn for every period
of the precession, and thus the equinoxes to move relative to the
fixed stars, so the apparent position of the sun at the time of
the vernal equinox moves through the zodiac once for every period
of precession. Note that there are also smaller. faster,
oscillations of the axis, known as nutations.
As noted above, the point of perihelion is precessing, and the
combined effect of this precession with the precession of the
equinoxes in the opposite direction is that the period of Earth's
perihelion coinciding with the vernal equinox is about 21000
years.
Because the earth's orbital speed (like a comet's) is fastest at
perihelion (currently about January 3rd) and slowest at aphelion
(currently about July 5th) the length of the seasons vary too;
currently shortest for (northern hemisphere) winter, with autumn
longer, then spring, and summer longest.
We all know that the sun appears to revolve around the earth due
to the earth's rotation, but actually, the sun's apparent daily
motion across the sky is a combination of both the earth's
rotation and its revolution around the sun.
After all, if the earth didn't rotate at all in relation to the
fixed stars, the sun would appear to revolve around us once per
sidereal year, in the direction opposite to what we're familiar
with. As the earth is both closest to the sun and at its highest
orbital speed at its perihelion, the sun's apparent motion from
the earth's revolution around the sun would be fastest at
perihelion.
A sidereal day, the period of Earth's rotation relative to the
fixed stars, is about 3 minutes 56 seconds shorter than a mean
solar day. The earth really rotates, relative to the stars, about
366-1/4 times per year, but Earth's revolution around the sun
makes the sun appear to revolve around the earth only about
365-1/4 times per year, that is, the earth's revolution around the
sun slows down the apparent motion of the sun around the earth.
Because the earth's orbital speed is fastest at perihelion, and
the distance to the sun is shortest, the sun's overall apparent
motion is slowest at perihelion, so a solar day (as from high noon
to high noon) is longest near perihelion.
No doubt Earth's actual orbit is much more complicated than I've
mentioned, but I think that I've covered the most important
points.
The relationships of the above periodic motions are the bases of
Milankovitch cycles, which may well have an affect on our climate,
though they don't totally account for the apparent climatological
record.
To simplify timekeeping, we use a "mean solar day".
Of course now we no longer define a second as 1/86400 mean solar
day, but rather define a second by atomic clocks, and a day as
86400 seconds, adding (or potentially dropping) a second
occasionally as needed to keep UTC close to astronomical time.
As noted in another post, earth's rotation varies, and it's
difficult to predict exactly how long a solar day will be. Before
accurate timekeeping was available, a day was a solar day. Exactly
how long was a solar day in Caesar's or Pope Gregory's time? At
first glance, that would seem to be a good question for
geophysicists, but maybe astronomers can have an important role in
this. Because the earth's and moon's orbits are known, astronomers
can determine when an eclipse occurred in the past. By looking at
records of eclipses, some answers as to the exact date of some
events can be found, even though various calendars were used.
Astronomy can also tell us where a solar eclipse should have been
visible from; comparing this with the historical record could give
us information on the rotation of the earth. Of course, an
astronomer may well respond "been there, done that".
Regarding leap years, to be pedantic, they're used simply because
a tropical year, rather inconveniently, doesn't happen to be a
whole number of days long.
Before Julius Caesar's reform, Roman years varied in length,
typically with 355 days, with an extra month added to the year as
needed to bring the calendar back close to the seasons. Sometimes,
as in times of war, they neglected to add the extra month. Besides
the rather irregular length of year, exactly when to add the extra
month was subject to political/financial pressures, a rather
unsatisfactory situation for many.
Of course now we change the dates of the "fiscal year" instead,
and Michigan's government is currently shifting the dates of its
"property tax year". Of course, they're not increasing the taxes,
they're just having the counties collect taxes earlier every year
for the next few years. Yeah, right....
Anyway, a fixed-length year would be an obvious solution the
Romans' problems with the calendar, but a 366-day calendar year is
too long, and a 365-day calendar year is too short. Having a
"partial day" in every calendar year would seem rather
inconvenient.
Julius Caesar's calendar reform came fairly close. The idea is to
keep the average calendar year very nearly the same length as the
average tropical year, while also keeping each calendar year a
whole number of days long, and varying the length of the calendar
year by only 1 day. Three calendar years of 365 days followed by
one of 366 days, and repeating this cycle indefinitely, was an
elegant solution.
Unfortunately, with Julius Caesar already dead, his reform was
apparently misunderstood to mean a leap year every three years,
and this error was finally corrected by Caesar Augustus after 36
years.
Of course it would've been more "elegant" to distribute the days
of the months something like the following:
Month normal year leap year
number length length
1 30 30
2 31 31
3 30 30
4 31 31
5 30 30
6 31 31
7 30 30
8 31 31
9 30 30
10 31 31
11 30 30
12 30 31
___ ___
total 365 366
and for that matter, start both month #1 and the year on (okay,
near) the day of the vernal equinox.
Why the vernal equinox? Well, it's the beginning of spring, a
season that seems to me symbolic of renewal (birds, bees, eggs,
flowers, bunnies, etc.), and an equinox is fairly easily
verifiable by rather simple astronomical observation, and thus a
good time to start a new year. On the other hand, the solstices
seem to me even more obvious (sunrise and sunset farthest south or
north, sun at "high noon" farthest south or north relative to the
zenith), so wouldn't be bad choices, although the changes in
sunrise/sunset direction and the daily highest point of the sun
are smallest near the solstices and greatest near the equinoxes.
Of course the year has actually started on various dates in
various cultures.
But the Julian calendar was certainly a huge improvement from the
previous Roman system. Besides, February is such a depressing
month around here that I'm rather glad that it's the shortest of
all.
Notably, under the Julian calendar, the vernal equinox was
considered to be on the 21st of March, regardless of the actual
astronomical date, and for the purpose of calculating the date of
Easter, it still is by most western Christian churches, even with
the Gregorian calendar. By Pope Gregory's time, it was evident
that the average calendar year was too long, with an all too
noticeable accumulated error of about 10 days in the date of the
vernal equinox. Rather than totally discarding the existing leap
year rules and starting over, they chose to modify them, dropping
3 out of every 100 leap years.
Of course they also dropped 10 calendar days, so 1582 had only 355
days, at least in the Vatican's reckoning.
In my opinion, it might've been simpler to just acknowledge that
the vernal equinox was actually on a different date, and settle
for the leap year modifications to keep it from drifting much
farther. Maybe it would've been easier to get the rest of the
world to go along with this? But this still would've changed the
date of Easter, giving the Protestant churches yet another reason
to condemn the Pope.
Of course other leap year rules, some arguably better, can be (and
have been) devised, but for now, most of the world has adopted the
Gregorian calendar, at least for most secular purposes.
Regards,
James
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