Sept. 2, 2011: 10am Class

1. Sept. 2, 2011: 10am Class • On-line Quiz #2 on d2l, available after class today • Please complete before class on Friday, Sept. 9 • HW 2 on line (d2l and boojum): Create a Constellation • Turn in next Wednesday, Sept. 7, in class. • 21inch Telescope will open for telescope lab Sept. 19. • Honors Section 3H: Please complete doodle poll • (see Megan’s email and class web site) • Today: Astronomical Basis for Calendars

2. The Astronomical Basis for Calendars (1) The Earth rotates on its axis once a day. A day is exactly 24 hours. (2) The Earth orbits the Sun with a period of about 365 days, 5 hours, 48 minutes and 46 seconds, or 365.242190 days (3) The Moon orbits the Earth, such that the period between new moon and new moon is 29.5305 days These periods vary a little bit because of the gravitational forces exerted by the other planets and other factors.

3. If you are a farmer, you want to base your calendar on the solar cycle, so you are in sync with the seasons: You want to plant your crops when the Earth is at the same part of its orbit around the Sun every year If you are just walking around, you might want to base your calendar on the Moon, since the phases of the moon are easy to see If you are a sailor, you might want to base your calendar on the Moon, since the Moon determines the tides

4. The problem is that 12x 29.5305 days = 354 1/3 days 13x 29.5305 days = 383.9 days So it’s not obvious how to have a calendar that is synchronized with both the lunar orbit and the Earth’s orbit around the Sun. If you define your year to be 12 months and 354 days (lunar calendar) you slip 11 days every year. The Babylonians figured out however that 254 lunar months is almost exactly 19 solar years that is, 254 x 29.53 = 19 x 265.24 This is called the Metonic Cycle, and so you could have a calendar where one “year” is 19 solar years, and 254 lunar months.

5. The Gregorian Calendar(the one we use) is based on the motion of the Earth around the Sun.  The length and number of months have no connection to the motion of the Moon It is based on the Julian Calendar, which was introduced by Julius Caesar in 45 BC.  He made Jan. 1 the start of the Year. During the middle ages, different groups in Europe adopted different start dates for the new years. In 1582, Pope Gregory reformed the calendar, which is basically what we use today.  The French recognized a different pope for a while and had a different calendar. A Solar Calendar

6. The Islamic Calendar is based on the motion of the Moon, with no connection to the motion of the Earth around the Sun. Hijri Calendar, Based on the Qur'an.   Used in many countries around the Gulf, e.g. Saudi Arabia. Purely lunar: 12 months, each with 29.53 days. Therefore the Islamic year has 12x29.53 = 354.36 days The Islamic year is shorter than the time it takes the Earth to go around the Sun.  Thus, a particular Islamic month falls during different times of the year , e.g. Ramadan. Years are counted since the Hijra, which is is the time that Mohammed emigrated to Medina in AD 622.  So AD 2009 is Islamic year 1430. A Lunar Calendar

7. The Jewish and Chinese Calendars combine both, using the Metonic Cycle so years are linked to the period of the orbit of the Earth around the Sun, AND months are linked to the motion of the Moon around the Earth. 19 x365.24 = an integral number of 29.53 day months. Jewish Year:  A "ordinary" year has 355 days, and 12 months. A "leap" year has 385 days and 13 months.  The length of a particular month varies from year to year by a day, so that if  New Year's Day (Rosh HaShannah) is, say, a new moon, then the first day of every month is a new moon. Years are counted since the creation of the world, taken to be 3761 BC.  Thus 1998 is Jewish year 5759. The Chinese have two calendars: one is Lunar and one is solar.

8. Leap Year The orbit of the Earth takes 365 days + about a quarter of a day. So every 4 years, we add a day to our calendar year (Feb. 29), so we don’t keep slipping That’s why sometimes the summer solstice is June 21, sometimes June 22, etc. In fact we have to be a little more clever because the year is 365 + a little less than ¼ of a day • The system we used was devised by an Italian physician, Luigi Lilio, in 1582 as part of • Pope Gregory’s calendar reformation: • Every year divisible by 4 is a leap year • Exception is any century year is NOT a leap year unless it is divisible • by 400 • 2000 is a leap year, but 1700, 1800, 1900, are not • So this removes 3 days of slippage every 400 years • Still have about 3 hours of slippage every 400 years

9. Mayan Calendar The ancient Mayans developed a complex and accurate calendar, which was adopted by other people in meso-america – Aztecs, Tolmec . Actually had THREE calendars, which they used at the same time: The Haab Civilian calendar 18 months, 20 days each + 5 days to make 365 day years The 5 extra days were considered unlucky, days of mourning Did not count YEARS in the Haab calendar however The Tzolkin Devine calendar, used for divinations two types of weeks, one with 13 days, the other with 20 days Each year was 260 days Years were not counted Aztec Calendar

10. Mayan Calendars, continued: The Long Count Instead of years, the Mayan used the Long Count calendar system to keep track of historical events kin = 1 day uinal (1 uinal = 20 kin = 20 days) Tun (1 tun = 18 uinal = 360 days = approx. 1 year) katun (1 katun = 20 tun = 7,200 days = approx. 20 years) baktun (1 baktun = 20 katun = 144,000 days = approx. 394 years) pictun = 20 baktun = 2,880,000 days = approx. 7885 years calabtun = 20 pictun = 57,600,000 days = approx. 158,000 years kinchiltun = 20 calabtun = 1,152,000,000 days = approx. 3 million years alautun = 20 kinchiltun = 23,040,000,000 days = approx. 63 million years The Mayan calendar started on our August 11, 3114 BC. With Date: 0.0.0.0.0. Then date 13.0.0.0.0 is our December 21, 2012, or 12/21/2012.

11. This coincidence has caused some people to claim that the Mayan Calendar predicts the end of the world on December 21, 2012. But the Long Count calendar doesn’t end on 13.0.0.0.

12. Harvest Moon: The full moon which occurs closest to the autumnal equinox Blue Moon: Third full moon to occur in a season with 4 full moons Each solar year contains 11 days more than 12x29.5 days So every 2 or 3 years, you get an “extra” month: the blue moon

13. Planets Known in Ancient Times • Mercury • difficult to see; always close to Sun in sky • Venus • very bright when visible; morning or evening “star” • Mars • noticeably red • Jupiter • very bright • Saturn • moderately bright

14. Aristotle • 4th century BC, Greece • First to give reasons why the Earth is spherical

15. Aristotle’s 1st reason: Gravity pulls matter to center of Earth, compressing the Earth into as compact a shape as possible. …a sphere Thanks to Barbara Ryden for this discussion

16. 2nd reason: Big Dipper You see different stars from the south than from the north. Southern Cross

17. If the Earth were flat: Southern Cross Big Dipper

18. 3rd reason: The shape of the Earth’s shadow. During a lunar eclipse, Earth’s shadow is always circular. Only object whose shadow is always circular is a sphere.