Clavius's Bull's-eye
The Calendar--Julius Caesar to Pope Gregory XIII
Introduction: In this short discussion, I will spare readers most of the arithmetic. There is no mathematics--just arithmetic. And I will be referring to 'fast' calendars. About that, keep some things in mind, for it can get confusing. Not difficult, just confusing. You can read books about calendars, find all sorts of 'stuff' on the internet, or even get a Ph.D. in the history and future (Ha, as you will see) of calendars. Keep the following things in mind always: A 'fast' calendar says it is earlier than it really is. Or, it's later than the calendar says. And note that 'calendar' and 'clocks' will at times be used interchangeably.
Late in his life, 100BC - 44BC, Julius Caesar decided a new calendar was necessary to keep track of where we were in our path around the Sun (the 'ecliptic.') This was for agrarian and general purposes like what to expect the weather to be like and all sorts of other reasons, --birthdays and holidays, etc. The calendars in use were put together for other reasons like religious events, customs, and sometimes just whimsy. They were all very inaccurate and crazy, with 5-day weeks, 6-week months, 8-month years. None served well, and adjustments had to be made continually.
So Caesar's astronomers set up a calendar based on the revolutions of Earth around the Sun. At first they counted 365. Then they realized it was more like 365 1/4. The quick fix for this was to have one 366-day year every four years. Thus leap year, with the addition of February 29, the only place on the calendar the additional day would work out. It worked well--almost. But the true tropical year, one revolution around and relative to the Sun, was actually 365.2422 tropical days. So there was an overstatement of 365.25 - 365.2422 = .0078 days per year. In 400 years, this amounted to a 3.12-day overstatement. The Julian calendar was fast, saying it was 3.12 days earlier than it really was. Or it was later than the calendar said. When it indicated the vernal equinox, it was really 3.12 days later than that. So the calendar equinox crept backwards in the ecliptic path around the Sun. (A 'sidereal year,' a revolution around the Sun as observed by a distant star, shows the true Earth day--one revolution on its axis--to be 23 hours and 56 minutes. A fix for that was pretty irrelevant and not persued, even if it was understood.)
By 1582, there was a 10-day error--when the calendar equinox (March 21) arrived, (set to March 21 in the fourth century, by the true equinox) it was really 10 days after the true equinox. The calendar said it was earlier than it was. Enter Pope Gregory XIII and his astronomers Clavius and colleagues. Gregory realized farmers would soon be planting, if they used the calendar equinox as a guide, way before the true equinox.
In an ingenious scheme, Clavius proposed and Gregory agreed: 'Suppress' 10 days, the 11th to 20th of March, then make only century years divisible by 4, leap years. This corrected the calendar and subtracted 3 days in 400 years, thereby reducing the error to .12 days in 400 years. That's a day in 3333 and 1/3 years. Trying to improve this accuracy is academic folderol. But isn't academe rife with folderol anyhow?
Now to beat the horse a couple more times--just to make sure he's dead:
Your grandfather rose about 1/2 hour earlier than you do. You sleep in. If he got up at 6 AM, your getting up at 6 AM is really getting up 32.4 minutes later: 75 x 25.92 seconds = 32.4 minutes.
If you're crazy enough to go to Times Square on New Year's Eve, know that: At clock 12M it's really 12:00:25.9; and at true 12M, the ball says 11:59:34.08. Jump up and down and kiss everybody at 11:59:34.08.
That's all.
Introduction: In this short discussion, I will spare readers most of the arithmetic. There is no mathematics--just arithmetic. And I will be referring to 'fast' calendars. About that, keep some things in mind, for it can get confusing. Not difficult, just confusing. You can read books about calendars, find all sorts of 'stuff' on the internet, or even get a Ph.D. in the history and future (Ha, as you will see) of calendars. Keep the following things in mind always: A 'fast' calendar says it is earlier than it really is. Or, it's later than the calendar says. And note that 'calendar' and 'clocks' will at times be used interchangeably.
Late in his life, 100BC - 44BC, Julius Caesar decided a new calendar was necessary to keep track of where we were in our path around the Sun (the 'ecliptic.') This was for agrarian and general purposes like what to expect the weather to be like and all sorts of other reasons, --birthdays and holidays, etc. The calendars in use were put together for other reasons like religious events, customs, and sometimes just whimsy. They were all very inaccurate and crazy, with 5-day weeks, 6-week months, 8-month years. None served well, and adjustments had to be made continually.
So Caesar's astronomers set up a calendar based on the revolutions of Earth around the Sun. At first they counted 365. Then they realized it was more like 365 1/4. The quick fix for this was to have one 366-day year every four years. Thus leap year, with the addition of February 29, the only place on the calendar the additional day would work out. It worked well--almost. But the true tropical year, one revolution around and relative to the Sun, was actually 365.2422 tropical days. So there was an overstatement of 365.25 - 365.2422 = .0078 days per year. In 400 years, this amounted to a 3.12-day overstatement. The Julian calendar was fast, saying it was 3.12 days earlier than it really was. Or it was later than the calendar said. When it indicated the vernal equinox, it was really 3.12 days later than that. So the calendar equinox crept backwards in the ecliptic path around the Sun. (A 'sidereal year,' a revolution around the Sun as observed by a distant star, shows the true Earth day--one revolution on its axis--to be 23 hours and 56 minutes. A fix for that was pretty irrelevant and not persued, even if it was understood.)
By 1582, there was a 10-day error--when the calendar equinox (March 21) arrived, (set to March 21 in the fourth century, by the true equinox) it was really 10 days after the true equinox. The calendar said it was earlier than it was. Enter Pope Gregory XIII and his astronomers Clavius and colleagues. Gregory realized farmers would soon be planting, if they used the calendar equinox as a guide, way before the true equinox.
In an ingenious scheme, Clavius proposed and Gregory agreed: 'Suppress' 10 days, the 11th to 20th of March, then make only century years divisible by 4, leap years. This corrected the calendar and subtracted 3 days in 400 years, thereby reducing the error to .12 days in 400 years. That's a day in 3333 and 1/3 years. Trying to improve this accuracy is academic folderol. But isn't academe rife with folderol anyhow?
Now to beat the horse a couple more times--just to make sure he's dead:
Your grandfather rose about 1/2 hour earlier than you do. You sleep in. If he got up at 6 AM, your getting up at 6 AM is really getting up 32.4 minutes later: 75 x 25.92 seconds = 32.4 minutes.
If you're crazy enough to go to Times Square on New Year's Eve, know that: At clock 12M it's really 12:00:25.9; and at true 12M, the ball says 11:59:34.08. Jump up and down and kiss everybody at 11:59:34.08.
That's all.
posted by Tom at 9:21 AM
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