Why Do We Keep a Calendar?

1. Why Do We Keep a Calendar? • Although useful for counting the passage of days, the calendar has deeper roots. • What we really care about is when the Seasons start and end. • Planting and survival were at stake....

2. What Are We Trying to Accomplish? • Ancient civilizations tracked the position of the Sun throughout the year. Interested? Consider taking Astr 3410 – Archeoastronomy (which also counts for non-western perspective credit)

3. What Are We Trying to Accomplish? • Simply put, the calendar attempts to register/relate two completely independent (and changing) quantities. • The rotating Earth (the day) – we're counting days after all... • The Earth's orbit around the Sun (the year). • The primary goal – have Spring happen on about the same day each year.

4. Why is it so Difficult? • The number of days in a year is 365.2422 • Therein lies the problem.... a calendar can't have a fraction of a day. • Before looking at the solution, consider some subtle aspects of the definition of the year. • The time it takes the Earth to complete an orbit around the Sun is 365.2564 days – a Sidereal Year

5. Sidereal vs. Tropical Year • The time it takes the Earth to complete an orbit around the Sun is 365.2564 days – a Sidereal Year • During that year, however, precession moves the location of “Spring” a little ways along the orbit. • The Tropical Year, the time from Spring to Spring, is 365.2422 days. • The crossing point on the celestial sphere between the ecliptic and celestial equator – the Vernal Equinox – shifts 1/26000th of the way around the sky each year. • This shift is the difference between the Tropical and Sidereal year. • Now the crossing point lies in the zodiac constellation of Pisces. • It will cross the formal constellation boundary into Aquarius around the year 2600 - the “Age of Aquarius”

6. How do you fix the calendar? • Each year the calendar misses accounting for the full year by ¼ of a day...almost: one year = 365.2422 days. • After four years the calendar is running ahead by one full day – 4 x 0.2422 = 0.9688 – close enough... • Insert a “leap day” into the calendar every four years (roughly) and you can make up the difference. • What if you lived on a planet that has a year that is 397.10 days long?

7. How much trouble can you cause? • If your name is Julius Caesar, quite a bit... • In 46 B.C Caesar instituted the first formal calendar that included a leap year to keep it in sync. • Good idea... however, the “Julian” calendar included a leap year every four years without fail • The calendar's average year was 365.25 days, not quite 365.2422 days. • 0.0078 days per year doesn't sound like a lot, but it adds up. • By the 1500's the calendar was 11 days out of sync with the Seasons • People began to notice....

8. How do you fix it? • With the calendar increasingly out of sync with the seasons the Catholic church became concerned. • Certain church holidays, Easter for example, are tied to astronomical events. • Pope Gregory XIII instituted a slightly revised calendar that was better matched to the Tropical Year – the Gregorian calendar. • Skip leap year if it is a century year (1700, 1800, 1900), but not if that century year is divisible by 400. • So the year 2000 was a once in 400 year special occasion • This calendar, with 97 leap days ever 400 years, has an average year length of 365.2425 days compare with the 365.2422 day year • It falls out of sync one day every 3300 years – easy to fix/adjust with an extra leap day every few thousand years.

9. Did this change make people happy? • Not entirely • The seasonal shift was corrected by making the day after October 4, 1582 .... October 15, 1582. • Landlords got to collect rent nearly 2 weeks early.... renters were not so happy. • The initiative came from the Catholic church in Rome • The Protestants, for example, refused to adopt the new calendar. • It took 350 years before the world all agreed to the same calendar. • The US (colonies) and England did not switch until 1752... • George Washington was born on Feb 11 by his calendar, but his official birthday is Feb 22 • Greece (the Orthodox Church) didn't switch until 1923

10. Can you improve the calendar further? • What people don't like is that 365 factors very poorly – 5 x 73 • so there is no easy way to break up the year into constant sized months, weeks • 7 is a pretty lousy number as well – although note that 7*52 = 364. • What constitutes “better”? • No more leap years – every year is the same • Every month the same length • Every month starts on the same day of the week • The 3rd of the month, for example, is the same day of the week every month every year.... forever. • How can you accomplish this • Days “outside” the calendar – they are just days, but not days of the week. • Fiddle with the length of the week – 5 or 6 day weeks help. • 360 factors very nicely: 2*2*2*3*3*5 – lots of options

11. Another way to fix it • Wait a while.... • As we will learn in detail later, the Moon's tug on the Earth is gradually slowing down Earth's rotation. • The day gets about 1 second longer every 50 thousand years. • Over time, given longer days, fewer days will fit into a year. • The year itself is not changing nearly as much, but that, too, is variable. • Specifically, in about 50 million years there will be exactly 360 days in a year and the calender will be quite simple. • It is unlikely that a 7-day week would survive • 360 = 2 * 2 * 2 * 3 * 3 * 5 • Lots of options for weeks and months, but 7 isn't one of them. • Why the fascination with seven?? – Moon + Sun + 5 planets • Sunday, Monday, Tuesday (mardi), Wednesday (mercredi), Thursday (jeudi), Friday (venredi), Saturday