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projectswinners solstice
Personal note: My family began celebrating (if only through cheeky verbal acknowledgement) the winter solstice around the time I became old enough to protest the vague attempts my parents briefly and occasionally made at actual religious observance.
But in 2004, my mother thoughtfully sent me a bouquet of flowers from a Brooklyn florist to amp up the holiday spirit a notch. The card said:
Dear Laurin,
Enjoy the beuty of the winners solstice.
Love, Mom, Dad, and Mickel
Since then, every December 21st has been an opportunity to bask in the beutiful glow of the winners solstice instead.
Last year on the 21st I brought you a wikipedia-summarizing description of lesser-known winter festivals, from HumanLight to Soyal to Karachun.
This year, enjoy the above-provided peak into my family's endless capacity to derive humor from an unintentionally hilarious florist's card, and a brief explanation of the movement of the "official" date to celebrate this fine holiday.
This graph, courtesy of, well, you know, apparently shows how the Gregorian calendar gradually falls behind the seasons, despite making a notable correction (the frequent spikes on the chart) each leap year. But biggest corrections (marking the beginning and end of each chunk of the chart) happen on the centennial years, which are never leap years unless they're divisible by 400—like the year 2000, in which there was no realignment between the Gregorian calendar and the seasons.
Why these seismic shifts happen in years that aren't correcting for the disparity between our 24 hour day and the variable amount of time the planet actually takes to rotate on its axis 365-day calendar and the 365.2424 days over which we experience the change in seasons [thanks, Michael!] has now joined the fact that the universe is expanding (despite being infinite! how is that possible?), in the ranks astronomical/physical/mathematical facts that just hurt to think about. Hopefully my brother will offer up some help in the comments.
Happy winners solstice!
update: Michael sez:
It takes the Earth about 365.26 days to revolve around the Sun, but […] Earth's rotational axis is not perpendicular with the radius of Earth's orbit, […] which is why we have seasons in the first place. This axis, however, does not stay still. Polaris, a well-known nautical guide, is currently directly above the Earth's northern axis, but in a few thousand years this will not be so. This wobble accounts for the difference between a sidereal year [the time it takes for the sun to return to the same position (as viewed from earth) of alignment with the stars of the celestial sphere] and a tropical year [the time it takes to pass through a full year's worth of seasons], but in this case it subtracts from the time because the axis is wobbling in a clockwise direction. Finally, we arrive with the fact that a tropical year is about 365.2424 days.
Because the tropical year is longer than the calendar year, the Earth will be 0.9696 days behind the calendar every four years. That means that once the leap year comes, the Earth will actually be 0.0304 days ahead of the calendar. Multiply this number by 25 to arrive [at] 0.76, the number of days ahead that this error will [accumulate] to every 100 years. (There are 25 sets of 4 years in 100 years.) To account for THIS error, we have common years on centurial years, but, oops, now the Earth is 0.24 days behind. Multiply this number by 4 to arrive with 0.96, the number of days behind that this error will [accumulate] to every 400 years. To account for THIS error, we have a leap year on centurial years divisible by 400 (remember that normally centurial years WOULDN'T be leap years), reducing the error down to 0.04 days every 400 years. You'll recall that we had a leap year in 2000 despite the fact that it was a centurial year. We still have some error, but at this point it's so small that we'll let the people deal with it 10,000 years from now when the equinoxes are finally off by a whole day.
Mike said,
I wouldn't call myself an authority on this issue, but just for you I've done a fair amount of research. I hope that I can "shed some light" on this issue. Get it?
It turns out that the leap year has nothing to do with the fact that the Earth's rotational period is less than 24 hours. Though its rotational period is only 23 hours, 56 minutes, and 4 seconds, a solar day is slightly longer than that. Because the Earth is also revolving around the Sun, it must make slightly more than one rotation before any given point on the Earth faces the Sun again. (Note that the Earth's revolution has an adding effect because the Earth rotates in the same direction that it revolves; that is to say that if you viewed the Earth from above the North Pole, it would be both rotating and revolving in a counter-clockwise direction. If either of these motions were to be reversed, then the solar day would be shorter than the sidereal day.) It turns out that the solar day is almost exactly 24 hours: It is 24 hours and 0.002 seconds to be exact. This small error is corrected by those atomic clocks that Dad follows obsessively. (Worthy of noting is that the solar day is growing longer at a rate of about 0.0014 seconds per century, which probably indicates that the Sun is pulling the Earth in closer to it, which the Earth is in turn doing to the Moon.)
Anyway, the real issue with the leap day is the discrepancy between the calendar year and the orbital period of the Earth. It takes the Earth about 365.26 days to revolve around the Sun, but again, things are not quite what they seem. You may be aware that Earth's rotational axis is not perpendicular with the radius of Earth's orbit. In fact, this axis is tilted, which is why we have seasons in the first place. This axis, however, does not stay still. Polaris, a well-known nautical guide, is currently directly above the Earth's northern axis, but in a few thousand years this will not be so. This wobble accounts for the difference between a sidereal year and a tropical year, but in this case it subtracts from the time because the axis is wobbling in a clockwise direction. Finally, we arrive with the fact that a tropical year is about 365.2424 days.
Because the tropical year is longer than the calendar year, the Earth will be 0.9696 days behind the calendar every four years. That means that once the leap year comes, the Earth will actually be 0.0304 days ahead of the calendar. Multiply this number by 25 to arrive with 0.76, the number of days ahead that this error will accumumlate to every 100 years. (There are 25 sets of 4 years in 100 years.) To account for THIS error, we have common years on centurial years, but, oops, now the Earth is 0.24 days behind. Multiply this number by 4 to arrive with 0.96, the number of days behind that this error will accumumlate to every 400 years. To account for THIS error, we have a leap year on centurial years divisible by 400 (remember that normally centurial years WOULDN'T be leap years), reducing the error down to 0.04 days every 400 years. You'll recall that we had a leap year in 2000 despite the fact that it was a centurial year. We still have some error, but at this point it's so small that we'll let the people deal with it 10,000 years from now when the equinoxes are finally off by a whole day.
It kills me to have made the Universe make that much more sense to you, so I'll leave you with something else to drive you crazy: The Earth actually rotates on its axis 366.26 times every time it revolves around the Sun, though in this time we only experience 365.26 days.
comment posted on December 23, 2007 at 2:50
Mike said,
After much additional digging on Wikipedia, I must offer a correction:
The Earth is, in fact, not being pulled in closer to the Sun, and in turn the Earth is, in fact, not pulling in the Moon closer. It turns out that the reason that the solar day is getting longer is that the Earth's rotation is decelerating. As you may be aware, the gravitational force of the Moon upon the Earth causes the tides that we experience. Since the Earth is rotating on its axis faster that the Moon is revolving around the Earth, however, the tides are pushed slightly ahead of the Moon as they rotate around the Earth. The tides themselves in turn exert a torque on the Moon, adding to its angular velocity. Because of the law of conservation of angular momentum, this slows down the rotation of the Earth. This is why the solar day is getting longer. So after all is said and done, the Moon is actually getting farther from Earth, not closer as I said. (Artificial satellites are much closer to the Earth than is the Moon, and their orbits decay because of friction with Earth's atmosphere. The Moon is too far from the Earth and the Earth is too far from the Sun for this phenomenon to affect either's orbit.) Earth's rotation will continue to slow down, and the Moons revolution will continue to accelerate until the Earth makes one rotation in the same amount of time that the Moon makes one revolution around the Earth . . . well, actually that WOULD happen, but the Sun will have turned into a red giant and consumed both the Earth and the Moon well before that will ever happen.
It appears to me that the moral of both stories is that the Moon's gravity has a huge effect on us. It causes tides and seasons, it moves the Earth's axis around the celestial sphere, and it is slowing down the Earth's rotation. Not bad for a little pipsqueak like the Moon.
Also, I realize that you hinted that you want me to explain how the Universe is expanding. Unlike the topic I just covered, scientists don't all agree on that issue, so I can't offer a definitive answer. It's very difficult for anyone to even wrap their head around. Rest assured, however, that I will do some more research on prevailing theories for you, and Cosmology 101 will be back in session before you know it!
comment posted on December 23, 2007 at 6:14
lauren said,
Ah-ha! Well, now the larger correction on non-leap centennial years makes sense mathematically (if not quite physically).
As for the earth rotating 366.26 times for every year it rotates the earth, I'm going to guess that it's caused by the fact you mentioned previously: That any given point on the earth make more than one full rotation on the earth's axis before facing the sun again, since we're orbiting in the same direction as we're rotating.
Anyway, I actually wasn't meaning to hint that you should explain the universe's expansion right here in these comments—that one's a doozy. But of course I'd love to hear your thoughts.
My personal way of reconciling it to myself, which has no basis in astronomical research, goes like this: The universe is completely limitless with no outer bounds. However, all things within it do have a specific distance from each other. This distance is gradually expanding, meaning that every object in the universe is moving farther away from every other object towards the outer reaches of the universe. But since the universe has no outer limits, this will continue indefinitely and the distance between astronomical objects will gradually approach infinity.
Whaddya think?
comment posted on December 23, 2007 at 12:00
Mike said,
Okay, so this allegory is courtesy of Stephen Hawking:
Imagine that the Universe is a giant balloon. Similar to how a balloon expands when it inflates, the Universe is expanding due to inertia retained from the Big Bang. This means that, similar to how two points on a balloon's surface become farther apart as the balloon expands, two objects with no relative motion still are constantly becoming farther apart. This explains why the Universe has a radius greater than 13.7 billion light years, which would otherwise be unexplainable without allowing objects to travel faster than light. Note that the Universe is not of homogenous density, so one theory is that the Universe is constantly seeking to reach the lowest possible density, leading some scientists to posit that the expansion of the Universe will accelerate until all objects are infintely far apart, as you presumed. This possibility has been termed the "Big Rip," as everything would be literally ripped apart if this happened.
There is some evidence that the Universe may indeed be expanding at an accelerating rate, so to account for this oddity (the Universe should be expanding at a slowing rate because of gravity, even if the rate of expansion would never reach zero) many scientists hypothesize the existence of dark energy. You can imagine dark energy as pressurized air in the balloon, which occupies all space evenly and causes the balloon to expand.
So if the Universe is in a balloon, so to speak, what is there beyond the Universe? It's possible that spacetime streches infinitely so that it takes an increasing amount of time to travel the same distance at the same speed as you approach the outer bounds of the Universe. It's also possible that the Universe is simply expanding into empty space free of dark energy. Probably the craziest theory that I came across posited that the Universe contains everything that does NOT exist in addition to everthing that does exist, claiming that "even unrealized possibilities contribute to the probability amplitudes of events in the Universe."
comment posted on December 24, 2007 at 1:51
lauren said,
Sweet! Who can I quote on that last one?
comment posted on December 24, 2007 at 8:24
Mike said,
Wikipedia, duh. So many people have been getting in trouble for plagiarizing Wikipedia these days that I wanted to be sure not to fall into that trap.
comment posted on December 24, 2007 at 15:38
Sean said,
Dear Sperbers,
Thanks for making my brain hurt. That is actually a better explanation of the Big Rip than the one I caught on the History Channel's Universe show. Props to Stephen Hawking. Carl Sagan, RIP.
Sincerely,
Sean
comment posted on December 28, 2007 at 20:18