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CALENDARS

CALENDARS. Chapter 3. The YEAR 2000 WAS. 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. LUNAR PHASES. DEFINITION of a MONTH. Siderial Month 27.3 days. Synodic Month 29.5 days. DEFINITION of a YEAR.

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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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