Calendars Calendars from different cultures

Keeping Time Today you probably think of a year as 365 days, but why do we have 365 days? The 365 day year is based on how long it takes the earth to revolve around the sun. Venus’s year is earth years, Jupiter’s is 11.9 earth years, and Pluto’s is earth years.

Other Calendars Not all calendars are 365 days! We do not know exactly how long the Inca calendar was. The Aztec and Mayan had two calendars: one was 260 days long and the other 365 days. The Jewish Year is 354 days long. Both the Jewish and Incan calendars are based on lunar cycles.

The Lunar Cycle A calendar based on the lunar cycle has months are usually 30 days long These months mark a full cycle of the moon. A full cycle of the moon is the time it takes for the moon to go from new moon to new moon again.

Is Our Calendar Right? Is a year exactly 365 days? No! A year is slightly longer than 365 days ( days is the more exact duration of one earth orbit around the sun). If we do not compensate for this underestimation, we would lose days a year. While this may not seem like a big deal, we would lose 484 days every 2000 years!

Leap Years Their have been many different ways to compensate for the loss of days in our calendar. Today we have leap years every four years. Since we have a leap year every year, one year is equal to days.

Reviewing Decimals When we write we are using decimal places. The numbers to the right of the decimal hold places just as the positions to the left of the decimal spot do Hundreds Ones Tenths TensDecimal Hundredths

Interpreting Decimals The number 0.25 means 25 hundredths. This can be written as. So if we gain 0.25 days per year, how many days would we gain in a 1,000 years? If there are really ( = 0.242) days per year, how many days would we lose in 1,000 years with only years that are 365 day long? ,000

Leap Year Problems Because of leap years, we gain 0.25 days ever year or 250 days every 1,000 years as we learned on the last slide. We also learned that we lose 242 days every 1,000 years by the exact number of days in a year. So how many days ahead are we after 1,000 years?

Compensating for Leap Years Every four years, we gain ONE whole day on February 29 th. This means that we average a gain of 0.25 or 1/4 th day for the past four years. However, earth’s orbit is days, not days. Leap years are overestimating the time we actually lose! How do we lose the days that we gain annually due to leap years?

Our Best Answer So Far … Skip some leap years! –Specifically, skip leap years every so often so that our calendar becomes synchronized to Earth’s orbit again. –But how many leap years should be skipped??

Determine the Leap Years If a year were days how many leap years should there be in 1,000 years? What if there were days in a year? Using the two above answers how many leap years would have to be skipped in that 1,000 years if there is one every four years?

Incas, Mayans, and Aztecs The Mayans, Aztecs, and Incas all had 12 months every year in their calendar. The Mayan and Aztec months were 30 days in length exactly. The Incas based their months on the lunar cycle so most of their months were 30 days. If their years had 12 months with 30 days each, how many days would there be in each year?

How Would You Fix the Problem? If their year had 360 days per year and we know a year is really 365 days long, how many days would they lose each year? If you were an Inca how would you propose to fix this problem?

What the Incas Did The Incan calendar, like the Jewish calendar, was based on the lunar cycle. So even though we do not know the exact length of an Incan year, let’s assume that it was 355 days long. It was probably not 360 days long, because that would not have coincided with the lunar cycle. How many days short of a full year was the Incan year if it was 355 days long?

How the Incas Compensated If their year was 355 days long, the Incas would have lost 10 days a year. How could they make up those 10 days and still have each month start on the new moon?