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