Jim Heckman wrote: >John Baez wrote: >> Answer: The period of the precession is 26,000 years. This is easy to >> guess if you remember that Christ was born in the age of Pisces >Uh, yeah... That's a handy fact I always keep close at hand. ;-)So you never wondered why the symbol for Christ is a fish? Even if you're not an expert on this stuff, you may have seen that fish on bumper stickers - they're pretty popular these days.
Actually, there are lots of reasons why a fish was chosen as the symbol of Christ - see
http://udel.edu/stu-org/war4christ/fish.html
for a good discussion. The fact that his birth coincided roughly with the beginning of the age of Pisces may simply be a red herring. But at least it's a good mnemonic.
>> and right now we're getting close to the age of Aquarius. >Yowza! So that's what that means!Yeah! Here's something from Compton's Encyclopedia:
Aquarius was originally the tenth constellation of the zodiac. It is now variously listed as the 11th or 12th sign of the zodiac because of a phenomenon known as precession, the slow change of orientation of the Earth's axis with respect to the stars. The sun is in the astrological zodiacal sign from January 20 through February 18 each year; however, because of precession, it is actually in the astronomical constellation Aquarius from late February through early March. According to astrologers, approximately every 2,150 years Earth comes under the influence of a different sign of the zodiac. Presently in the astrological Age of Pisces, Earth is due to enter the Age of Aquarius next (some say as early as the 21st century).Why is it "some say"? Why is there disagreement about this issue? Is there disagreement on which day of the year the sun must enter a certain part of the zodiac for a new "age" to begin, or disagreement on how to seperate the zodiac into 12 parts, or are people interested in these things just woolly-headed? Probably all three.
Modern-day astrology is only for kooks, but once upon a time it was inseparable from astronomy, so lots of astronomical terms still have remnants of astrology attached to them. The reason I'm interested in this is that astronomy is the oldest quantitative science and the first precursor of what we now call "mathematical physics". The motion of the sun, moon and planets offers plenty of mathematical patterns to analyze. Some are simple, some are complicated, but even the simple ones usually require small "correction terms", so people were naturally led to develop more complicated models in the quest for accurate prediction. A nice example of how physics progresses!
For example, remember how Keith Ramsay and Phillip Helbig pointed out the existence of two kinds of day? There's the 24-hour "solar day" and the 23-hour, 56-minute and 4-second "sidereal day", depending on whether you watch the sun or the stars going around.
But that's nothing compared to the month! There are at least four kinds of month: the sidereal month, the anomalistic month, the synodic month, and the draconic month. Namely:
1) The SIDEREAL MONTH is the time it takes for the moon to orbit 360 degrees around the earth as viewed from the fixed stars. It's 27.321661 days long. (Don't ask me if these are solar or sidereal days - I assume the former, but the thing I'm reading doesn't say.)
2) The SYNODIC MONTH is the time it takes from new moon to new moon. This differs from the sidereal month because the earth is going around the sun. It varies quite a bit, but it's 29.530589 days long on average - technically this is the "mean synodic month".
3) The ANOMALISTIC MONTH is the time it takes for the moon to go from perigee to perigee. This differs slightly from the sidereal month because the moon's elliptical orbit gradually "regresses" - i.e., the ellipse slowly turns around. It's 27.554549 days long.
4) The DRACONIC MONTH is the time it takes the moon to go from one "node" to the other and back. What's a node? Well, the plane of the moon's orbit around the earth is not the same as the plane of the earth's orbit around the sun. These two planes intersect in a line, and we say the moon is at a "node" when it is on this line. For a picture, see:
http://www.hermit.org/Eclipse/why_cycles.html
The time it takes to go from one node to another and then back is the draconic month. It's 27.212220 days long.
In short, the month is quite a subtle concept! And this matters a lot when you want to predict eclipses - which is one of the things that kept astrologers in business!
To get a solar eclipse you have to have a new moon. But that's not sufficient: you also have to have the nodes lined up correctly, so the moon comes right between the earth and sun.
This means that eclipses occur in a pattern which depends on how the synodic and draconic months drift in and out of phase.
And this means that to predict eclipses, you need to find a number which gives you something close to an integer when you divide it by 27.321661 and also when you divide it by 27.212220.
It turns out that a good choice is the number 6585 + 1/3:
(6585 + 1/3)/27.321661 = 241.029758
(6585 + 1/3)/27.212220 = 241.999121
This means that the pattern of eclipses comes close to repeating every 6585 and 1/3 days. Or in other words: 18 years, 10 or 11 days depending on how the leap years work, and 1/3 of a day.
Q: Guess when this fact was discovered!
A: About 2500 years ago, by Babylonian astronomers/astrologers.
Q: Guess what it's called!
A: The Saros cycle!
Q: Right. What does "Saros" mean?
A: It means "cycle" - in Babylonian! (Or whatever you call the language Babylonians spoke.)
To complicated matters further, note that a solar eclipse will look different depending on whether the moon is at perigee, apogee or somewhere in between. To understand these subtler "anomalies", we also need to take into account the anomalistic month.
Q: Okay, so we've talked about two kinds of day and four kinds of month. How many kinds of years are there?
A: At least two: the tropical year and sidereal year!
Q: What's the difference?
A: Guess!
Q: Hmm, I'll have to think about it. But here's another question: why do they call it the "draconic month"? Is this an allusion to the Athenian lawmaker Draco or to the dragon-shaped constellation of the same name?
A: Hmm, good question - I don't know.
Q: Okay. Here's another thing that's been puzzling me. Though there are officially 12 months in a year, there are about 12.36 synodic months in a year - i.e., 12.36 new moons per year. Doesn't this make life even more complicated?
A: Sure! It means that the phases of the moon keep drifting out of synch with the passage of the seasons. They loop around back about once every 19 years - this is called the Metonic cycle.
Q: Why's it called that?
A: It was discovered by the Greek astronomer Meton in the 5th century BC. The Babylonians may have discovered it earlier - I don't really know - but he got his name on it.
Q: Hey! The Metonic cycle is pretty close to the Saros cycle: 19 years versus 18 years plus a bit. And these are both close to the period of the nutation of the earth - 18.6 years. Is there something interesting going on here?
A: Hmm, that's a very good question.
Q: Okay, one final question: what terrible error did John Baez make in his calculation above?
A: I know, but I'm not telling - for that you'll have to read Bill Jeffrey's comments on the next page. In the meantime, check these out for more info:
Different kinds of month:
http://www.hermit.org/Eclipse/why_months.html
Babylonian planetary theory and the development of heliocentrism:
http://www.spirasolaris.ca/sbb2c.html
Saros cycle versus Metonic cycle:
http://www.arval.org/metonic.htm