2. CALENDARSCALENDARS Chapter 3

3. The YEAR 2000 WAS YearAccording to: 1997Christ’s actual birth circa 4 BC 2753Old Roman calendar 2749Ancient Babylonian calendar 6236First Egyptian calendar 5760Jewish calendar 1420Moslem calendar 1378Persian calendar 1716Coptic calendar 2544Buddhist calendar 5119Current Maya great cycle 208French Revolution calendar DragonChinese calendar Huge number of calendars Which do we use? Which is correct? Why do we use the one that has been adopted?

4. DEFINITION of a DAY l (stars) Siderial Day: 23 h 56 m 04s l (sun) Mean Solar Day: 24 h 00 m 00s l We use Mean Solar Day

5. LUNAR PHASES

6. DEFINITION of a MONTH Siderial Month 27.3 days Synodic Month 29.5 days

7. DEFINITION of a YEAR l (stars) Siderial Year: 365 d 06h 09m 10s l (vernal equinox) Tropical Year: 365 d 05h 48m 46s l Which do we use?

8. Definition of a Year l

9. DEFINITION of a YEAR l (stars) Siderial Year: 365 d 06h 09m 10s l (vernal equinox) Tropical Year: 365 d 05h 48m 46s l Which do we use? l We use Tropical Year l The 20 minute difference is due to precession, l Days/week arbitrary, human invention (wanderers)

10. FLASHCARDFLASHCARD WHY DO WE USE THE TROPICAL YEAR FOR OUR DEFINITION OF A YEAR? A) It is easiest to measure. B) It is closest to an even number of years. (days?) C) It naturally accounts for precession. D) Measuring the length of the siderial year requires clear skies. requires clear skies.

11. DEFINITIONSDEFINITIONS l Mean Solar Day: 24h 00m 00s l Tropical Year: 365 d 05h 48m 46s l Defining calendar now looks easy

12. 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Year consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS

13. 91 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS

14. l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 1 182

15. 1 274 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 1

16. 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 365

17. 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 1 366

18. l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. l What do you do with the excess?

19. ROMAN CALENDARS l Each month begins with the new Moon l Moon’s period is 29.5 days l Months have 29 and 30 days alternatively Day: 4 7 10 14 20 22 26 Lunar Based Lunar Based

20. ROMAN CALENDARS l This leads to following problem:  12 lunar months have (6 x 29) + (6 x 30) = 354 days l Solution:  Tropical year is about 365.25 days  Add a 13 th month of 30 days 7 times in 19 years (year 3, 6, 8, 11, 14, 17 & 19)! (Babylonian solution)  After 3 years, there is a difference of more than 1 month between solar time and the calendar l The Jewish calendar still uses this 19 year cycle. The Muslim lunar-based calendar does not add the 13 th month.

21. OTHER ANCIENT CALENDARS l Chinese calendar:  60 day (double lunar) month  12 year cycle based upon Jupiter’s position in the Zodiac l Egyptian Calendar:  Solar calendar consisting of 12 thirty-day months plus 5 lucky days

22. WESTERN CALENDAR REFORM l Julius Caesar 46 BC l Does this completely solve the problem? ä äNo - The Julian Year is exactly 365.25 days (365d 6h 00m 00s) the Tropical Year is 365d 05h 48m 46s – Julian Year is 11m 14s longer than the Tropical year – what do you do with this 11m 14s difference? l 12 approximately equal months (average of 30.5 days) l Lunar month abandoned l 12 month total of 365 days l Based upon Tropical Year l A leap year of 366 days every 4 years

23. RELIGIOUS HOLIDAYS l Easter and other Christian religious holidays were fixed in 325 AD l Easter: 1 st Sunday after the first full Moon that occurs after March 21 (the Vernal Equinox)

24. EASTER 2004 l Vernal Equinox: March 21 l Full Moons: äMarch 6 (Saturday) äApril 5 (Monday) l Easter: April 11 (Sunday)

25. FLASHCARDFLASHCARD What was the date of Easter in 2001? What was the date of Easter in 2001? l Data: Vernal Equinox: March 20 (Tuesday) Full Moons: March 9 (Friday) Full Moons: March 9 (Friday) April 8 (Sunday) April 8 (Sunday) A) March 11. B) March 25. C) April 8. D) April 15.

26. FLASHCARDFLASHCARD IF THE VERNAL EQUINOX IS MARCH 21, WHAT IS THE EARLIEST THAT EASTER CAN BE? A) March 21. B) March 22. C) March 23. D) March 24.

27. FLASHCARDFLASHCARD IF THE VERNAL EQUINOX IS MARCH 21, WHAT IS THE LATEST THAT EASTER CAN BE? A) April 21 B) April 23 C) April 26 D) April 28

28. DEFINITIONSDEFINITIONS l Mean Solar Day: 24h 00m 00s l Tropical Year: 365 d 05h 48m 46s l Defining calendar now looks easy

29. 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Year consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS

30. 91 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS

31. l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 1 182

32. 1 274 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 1

33. 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 365

34. 1 l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. PROBLEM with CALENDARS 1 366

35. l Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT 365 days. l What do you do with the excess?

36. CALENDAR REFORM l Julius Caesar 46 BC l Did not completely solve the problem ä äThe Julian Year of 365.25 days is 11m 14s longer than the Tropical year ä äBy 1582, the difference between “sun” time and calendar time was 10 days ä äEventually, Easter would be in WINTER l 12 approximately equal months (average of 30.5 days) l Lunar month abandoned l 12 month total of 365 days l Based upon Tropical Year l A leap year of 366 days every 4 years

37. GREGORIAN CALENDAR l 10 days dropped from the calendar ä äOct 15, 1582 followed Oct 4, 1582 l Pope Gregory XIII, 1582

38. ASTRONOMICAL CALENDAR for OCTOBER, 1582

39. GREGORIAN CALENDAR l 10 days dropped from the calendar l In the Julian Calendar, Leap Year (LY) occurs every year divisible by 4 l New Reform in Gregorian Calendars ä äOct 15, 1582 followed Oct 4, 1852 äThus the Julian average year was 365.25 days whereas the Tropical Year is 365.242199 days. This results in a difference of 1 day in 128 years. äNeed to remove 1 LY every 128 years. Cumbersome äOnly century years divisible by 400 are LYs. Eg. 1700, 1800 & 1900 are NOT Lys. 1600, & 2000 are LYs. Correct to 1 day in 3300 years. l Pope Gregory XIII, 1582

42. CALENDAR REFORM l Modern modification: 4000, 8000, 12000 now are NOT Leap Years. l Calendar is now accurate to 1 day in 20,000 years.