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CALENDARS

Explore the complexities of calendars, from lunar phases to year definitions, and learn how different civilizations tackled calendar reform over time. Discover the challenges and solutions in tracking days, months, and years across cultures.

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CALENDARS

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  1. CALENDARS Chapter 3

  2. The YEAR 2000 WAS

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

  4. LUNAR PHASES

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

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

  7. Definition of a Year

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

  9. 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. FLASHCARD

  10. DEFINITIONS • Mean Solar Day: 24h 00m 00s • Tropical Year: 365 d 05h 48m 46s • Defining calendar now looks easy

  11. PROBLEM with CALENDARS • 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. 1

  12. 1 PROBLEM with CALENDARS • 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. 91

  13. 1 PROBLEM with CALENDARS • 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. 182

  14. 1 PROBLEM with CALENDARS • 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. 274 1

  15. 1 PROBLEM with CALENDARS • 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. 365

  16. 1 PROBLEM with CALENDARS • 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. 366 1

  17. What do you do with the excess? PROBLEM with CALENDARS • 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.

  18. Day: 4 7 10 14 2022 26 ROMAN CALENDARS • Each month begins with the new Moon • Moon’s period is 29.5 days • Months have 29 and 30 days alternatively Lunar Based

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

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

  21. WESTERN CALENDAR REFORM • Julius Caesar 46 BC • 12 approximately equal months (average of 30.5 days) • Lunar month abandoned • 12 month total of 365 days • Based upon Tropical Year • A leap year of 366 days every 4 years • Does this completely solve the problem? • No - 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?

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

  23. EASTER 2004 • Vernal Equinox: March 21 • Full Moons: • March 6 (Saturday) • April 5 (Monday) • Easter: April 11 (Sunday)

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

  25. 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. FLASHCARD

  26. 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 FLASHCARD

  27. What do you do with the excess? PROBLEM with CALENDARS • 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.

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

  29. GREGORIAN CALENDAR • Pope Gregory XIII, 1582 • 10 days dropped from the calendar • Oct 15, 1582 followed Oct 4, 1582

  30. ASTRONOMICAL CALENDAR for OCTOBER, 1582

  31. GREGORIAN CALENDAR • Pope Gregory XIII, 1582 • 10 days dropped from the calendar • Oct 15, 1582 followed Oct 4, 1852 • In the Julian Calendar, Leap Year (LY) occurs every year divisible by 4 • Thus 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. • Need to remove 1 LY every 128 years. Cumbersome • New Reform in Gregorian Calendars • Only 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.

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

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