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Let’s say that you were an alien and you were transported to Earth well before humankind existed. (Don’t you love how serious physics discussions usually start with a completely ridiculous supposition?)

Since we want to be able to measure everything around us, it makes sense that we should be able to quantify the amount of time that passes between events. But how?

For one thing, there’s an enormous change in one’s environment every once in a while. Namely, the Sun appears in the sky and then goes away. This happens fairly frequently. Let’s say you call this unit of time a “day”.

Being an astute observer, you then notice this other celestial body hanging up in the sky, which you call the “Moon”. The Moon appears variously as some fraction of a complete circle. Sometimes it completely goes away, and other times it is virtually a perfect circle. In between, it looks something like a crescent-shape. You call these shapes “phases” of the Moon. A Moon that’s 100% visible is called a “Full Moon”, while a Moon that’s completely gone is a “New Moon”.

Now you’ve been on Earth a while, and you’ve seen these patterns occur. And it dawns on you that maybe there’s some regularity to the Moon’s phases. Between two full moons you note that there are between 29 and 30 days. Perfect. Let’s call this unit of time, based on the moon, a “Moonth” (but we’ll shorten it to “Month” just because).

So, let’s start measuring time. You deem today to be an important day, since the moon is full, and so you call it “1/1″ — the first day of the first month. On “1/30″, the thirtieth day of the first month, there’s a full moon about halfway through the day. So the next day will be “2/1″, the first day of the second month. But now, since we’re already “ahead” by half a day, the moon will be full as of the end of “2/29″. (Remember, the last full moon actually occurred about halfway through “1/30″, not at the start of “2/1″.) There’s no need for a “2/30″ (since the moon is already full), and so the day after “2/29″ is “3/1″.

We can keep this up for a while, alternating 30-day and 29-day months. After twelve of these months, we’ll notice that the weather’s about the same, the crops are about in the same place of their development, and the Sun is about in the same point in the sky at the middle of each day. This is also a convenient marker, so we’ll call this amount of time a “Year”.

So to sum up, the year has six months of 30 days and six months of 29 days, which we add up to be 354 days. Days are a lot easier to keep track of than months anyway, so we’ll call 354 days our year and be done with it. Great, now we have our system of time!

Not so fast.

First of all, we would notice after a couple years that the date we call “1/1″ each year will have a slightly different climate. The Sun is not exactly at the same point in the sky each “1/1″. If “1/1″ is during the hot summer one year, then sixteen years later “1/1″ will fall on a cold winter day.

This might not bother some people. After all, dates are essentially just numbers. But now that you’ve been on Earth a while, you and your offspring and others’ offspring have begun to have governments and other civil structures such that it might be convenient to have the months line up with the same season each year.

So let’s take a step back and figure out how we need to add or subtract days to make the months match the seasons. After a little trial-and-error and a little astronomical surveying, we realize that there is an eleven day difference between our year and the astronomical year.

We have a couple of options at this point.

We have a twelve-month calendar, and we need to add eleven days. So, let’s add a day to every month but one. Instead of having months of alternating 30 and 29 days, we’ll have eleven months of alternating 31 and 30 days, and a month of 29 days. That makes for 365 days in a year, and that makes our months match our seasons (pretty closely, anyhow).

Another option could be to take those 11 days and make a new month out of them. It would be annoying to have months of 30, 29, 30, 29, 11, 30, 29, et cetera, but we could handle it. It might be less of a headache to instead make a 33-day month every third year. That way months are more-or-less the same length, and our months will match our seasons for quite a while. This extra, occasional month is called an “Intercalary Month”.

We’re off by a bit, but our error is slowly decreasing. I could go on, but this little example more-or-less demonstrates the evolution of our modern calendar systems. Leap years (and more recently leap seconds) are continued attempts at making sure our system of measuring time matches the motions of the Earth in its orbit around the Sun.

What does this have to do with Easter?

Religious institutions tend to prefer a lunar month. The Muslim calendar is purely lunar — the holy fasting month of Ramadan falls at a different time each year. My Muslim friends during my freshman year of college (1992-1993) celebrated Ramadan during the months of March and April. In 2008 the first day of the lunar month of Ramadan will be on September 2. It’s been almost sixteen years, and so the month of Ramadan has migrated across half the calendar in that time.

The Hebrew calendar is based on the intercalary month calendar described above. The calendar is essentially lunar, but an extra month is added seven times each nineteen years. The extra month is added as the twelfth month of the calendar and called “Adar I”; the usual twelfth month (just “Adar”) becomes the thirteenth month and is named “Adar II”.

The Christian calendar was pegged to the solar calendar due to the influence of Rome. The Julian calendar, the leading political calendar at the time of the spread of Christianity, became the Christian calendar.

Easter is the only Christian holiday to be based on a lunar standard. (There are other so-called “moveable feasts” in the Christian calendar, but they’re all based off of Easter’s date so that doesn’t count.) In order to guarantee that Easter falls in the springtime, its date was set to be the date of the first full moon after the vernal equinox, March 21.

Easter was not always a Sunday. In about the second or third century AD, the festival was moved to a Sunday, so the official definition of Easter became “the first Sunday after the first full moon after the vernal equinox.”

If you’re up to a challenge, you can see the “real” rules for dealing with Easter calculations on Wikipedia. The rules are called the computus and are really tough to follow. (I have a couple degrees in physics and started to zone out around the third paragraph. So read at your own risk.)

This means that Easter can fall as early as March 22 (if the full moon occurs on the vernal equinox which is a Saturday) or as late as April 25 (if the moon is one-day past full on the equinox and that happens to fall on a Sunday).

Why is Easter so early this year? Because we’re lucky, that’s why.

Tags: calendar, dates, easter, history, months, religion

This entry was posted on Saturday, March 22nd, 2008 at 4:34 pm and is filed under Physics Is Phun. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.