calendarscalendars chapter 3. the year 2000 was yearaccording to: 1997christ’s actual birth circa...
TRANSCRIPT
CALENDARSCALENDARSCALENDARSCALENDARSChapter 3Chapter 3
The YEAR 2000 WASThe YEAR 2000 WASThe YEAR 2000 WASThe YEAR 2000 WASYear According to:
1997 Christ’s actual birth circa 4 BC
2753 Old Roman calendar
2749 Ancient Babylonian calendar
6236 First Egyptian calendar
5760 Jewish calendar
1420 Moslem calendar
1378 Persian calendar
1716 Coptic calendar
2544 Buddhist calendar
5119 Current Maya great cycle
208 French Revolution calendar
Dragon Chinese calendar
DEFINITION of a DAYDEFINITION of a DAYDEFINITION of a DAYDEFINITION of a DAY
(stars) Siderial Day: (stars) Siderial Day: 23 h 56 m 04s 23 h 56 m 04s
(sun) Mean Solar (sun) Mean Solar Day: 24 h 00 m 00sDay: 24 h 00 m 00s
We use Mean Solar We use Mean Solar DayDay
LUNAR PHASESLUNAR PHASESLUNAR PHASESLUNAR PHASES
DEFINITION of a MONTHDEFINITION of a MONTHDEFINITION of a MONTHDEFINITION of a MONTH
Siderial Month 27.3 daysSiderial Month 27.3 days Synodic Month 29.5 daysSynodic Month 29.5 days
DEFINITION of a YEARDEFINITION of a YEARDEFINITION of a YEARDEFINITION of a YEAR
(stars) Siderial Year: 365 (stars) Siderial Year: 365 d 06h 09m 10sd 06h 09m 10s
(vernal equinox) (vernal equinox) Tropical Year: 365 d 05h Tropical Year: 365 d 05h 48m 46s48m 46s
Which do we use?Which do we use?
Definition of a YearDefinition of a YearDefinition of a YearDefinition of a Year
DEFINITION of a YEARDEFINITION of a YEARDEFINITION of a YEARDEFINITION of a YEAR (stars) Siderial Year: 365 (stars) Siderial Year: 365
d 06h 09m 10sd 06h 09m 10s (vernal equinox) (vernal equinox)
Tropical Year: 365 d 05h Tropical Year: 365 d 05h 48m 46s48m 46s
Which do we use?Which do we use? We use Tropical YearWe use Tropical Year The 20 minute difference The 20 minute difference
is due to precession, is due to precession, Days/week arbitrary, Days/week arbitrary,
human invention human invention (wanderers)(wanderers)
FLASHCARDFLASHCARDFLASHCARDFLASHCARD
WHY DO WE USE THE TROPICAL YEAR FOR WHY DO WE USE THE TROPICAL YEAR FOR OUR DEFINITION OF A YEAR?OUR DEFINITION OF A YEAR?
A)A) It is easiest to measure.It is easiest to measure.
B)B) It is closest to an even number of years. (days?) It is closest to an even number of years. (days?)
C)C) It naturally accounts for precession. It naturally accounts for precession.
D)D) Measuring the length of the siderial year Measuring the length of the siderial year requires clear skies. requires clear skies.
DEFINITIONSDEFINITIONSDEFINITIONSDEFINITIONS
Mean Solar Day: 24h Mean Solar Day: 24h 00m 00s 00m 00s
Tropical Year: 365 d 05h Tropical Year: 365 d 05h 48m 46s48m 46s
Defining calendar now Defining calendar now looks easylooks easy
11
Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS
9911
11
Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS
Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS
11
182182
11
274274
Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS
11
11
Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS
365365
11
Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS
11366366
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in
a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
What do you do with the excess?What do you do with the excess?
ROMAN CALENDARSROMAN CALENDARSROMAN CALENDARSROMAN CALENDARS
Each month begins Each month begins with the new Moonwith the new Moon
Moon’s period is Moon’s period is 29.5 days29.5 days
Months have 29 Months have 29 and 30 days and 30 days alternativelyalternatively
Day: 4 7 10
14 20 22 26
Lunar Lunar BasedBased
ROMAN CALENDARSROMAN CALENDARSROMAN CALENDARSROMAN CALENDARS This leads to following problem:This leads to following problem:
12 lunar months have (6 x 29) + (6 x 30) = 12 lunar months have (6 x 29) + (6 x 30) = 354 354 daysdays
Solution:Solution:
Tropical year is about Tropical year is about 365.25 days365.25 days
Add a 13Add a 13thth month of 30 days 7 times in 19 years month of 30 days 7 times in 19 years (year 3, 6, 8, 11, 14, 17 & 19)(year 3, 6, 8, 11, 14, 17 & 19)! ! (Babylonian solution)(Babylonian solution)
After 3 years, there is a difference of more than 1 After 3 years, there is a difference of more than 1 month between solar time and the calendar month between solar time and the calendar
The Jewish calendar still uses this 19 year cycle. The Jewish calendar still uses this 19 year cycle. The Muslim lunar-based calendar does not add the The Muslim lunar-based calendar does not add the 1313thth month. month.
OTHER ANCIENT CALENDARSOTHER ANCIENT CALENDARSOTHER ANCIENT CALENDARSOTHER ANCIENT CALENDARS Chinese calendar:Chinese calendar:
60 day (double lunar) month60 day (double lunar) month12 year cycle based upon Jupiter’s position in 12 year cycle based upon Jupiter’s position in the Zodiacthe Zodiac
Egyptian Calendar:Egyptian Calendar:Solar calendar consisting of 12 thirty-day Solar calendar consisting of 12 thirty-day months plus 5 lucky daysmonths plus 5 lucky days
WESTERN CALENDAR REFORMWESTERN CALENDAR REFORMWESTERN CALENDAR REFORMWESTERN CALENDAR REFORM
Julius Caesar 46 BCJulius Caesar 46 BC
Does this completely solve the problem?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?
12 approximately equal months (average of 30.5 days)12 approximately equal months (average of 30.5 days) Lunar month abandonedLunar month abandoned 12 month total of 365 days12 month total of 365 days Based upon Tropical YearBased upon Tropical Year A leap year of 366 days every 4 yearsA leap year of 366 days every 4 years
RELIGIOUS HOLIDAYSRELIGIOUS HOLIDAYSRELIGIOUS HOLIDAYSRELIGIOUS HOLIDAYS Easter and other Christian religious Easter and other Christian religious
holidays were fixed in 325 ADholidays were fixed in 325 AD Easter: 1Easter: 1stst Sunday after the first full Moon Sunday after the first full Moon
that occurs after March 21 (the Vernal that occurs after March 21 (the Vernal Equinox)Equinox)
EASTER 2004EASTER 2004EASTER 2004EASTER 2004
Vernal Equinox: March 21Vernal Equinox: March 21Full Moons: Full Moons:
March 6 (Saturday)April 5 (Monday)
Easter: April 11 (Sunday)Easter: April 11 (Sunday)
FLASHCARDFLASHCARDFLASHCARDFLASHCARD
What was the date of Easter in 2001?What was the date of Easter in 2001? Data: Vernal Equinox: March 20 (Tuesday)Data: Vernal Equinox: March 20 (Tuesday)
Full Moons: March 9 (Friday)Full Moons: March 9 (Friday) April 8 (Sunday)April 8 (Sunday)
A)A) March 11.March 11.
B)B) March 25. March 25.
C)C) April 8. April 8.
D)D) April 15. April 15.
FLASHCARDFLASHCARDFLASHCARDFLASHCARD
IF THE VERNAL EQUINOX IS MARCH 21, IF THE VERNAL EQUINOX IS MARCH 21, WHAT IS THE EARLIEST THAT EASTER CAN WHAT IS THE EARLIEST THAT EASTER CAN BE?BE?
A)A) March 21.March 21.
B)B) March 22. March 22.
C)C) March 23. March 23.
D)D) March 24. March 24.
FLASHCARDFLASHCARDFLASHCARDFLASHCARD
IF THE VERNAL EQUINOX IS MARCH 21, IF THE VERNAL EQUINOX IS MARCH 21, WHAT IS THE LATEST THAT EASTER CAN WHAT IS THE LATEST THAT EASTER CAN BE?BE?
A)A) April 21April 21
B)B) April 23 April 23
C)C) April 26 April 26
D)D) April 28 April 28
PROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARSPROBLEM with CALENDARS Basic problem: the number of Mean Solar days in Basic problem: the number of Mean Solar days in
a Tropical Year is not an integer number. A a Tropical Year is not an integer number. A Tropical Years consists of 365d 05h 48m 46s NOT Tropical Years consists of 365d 05h 48m 46s NOT 365 days.365 days.
What do you do with the excess?What do you do with the excess?
CALENDAR REFORMCALENDAR REFORMCALENDAR REFORMCALENDAR REFORM
Julius Caesar 46 BCJulius Caesar 46 BC
Did not completely solve the problemDid 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
12 approximately equal months (average of 30.5 days)12 approximately equal months (average of 30.5 days) Lunar month abandonedLunar month abandoned 12 month total of 365 days12 month total of 365 days Based upon Tropical YearBased upon Tropical Year A leap year of 366 days every 4 yearsA leap year of 366 days every 4 years
GREGORIAN CALENDARGREGORIAN CALENDARGREGORIAN CALENDARGREGORIAN CALENDAR
10 days dropped from the calendar10 days dropped from the calendarOct 15, 1582 followed Oct 4, 1582
Pope Gregory XIII, 1582Pope Gregory XIII, 1582
ASTRONOMICAL CALENDAR ASTRONOMICAL CALENDAR for OCTOBER, 1582for OCTOBER, 1582
ASTRONOMICAL CALENDAR ASTRONOMICAL CALENDAR for OCTOBER, 1582for OCTOBER, 1582
GREGORIAN CALENDARGREGORIAN CALENDARGREGORIAN CALENDARGREGORIAN CALENDAR
10 days dropped from the calendar10 days dropped from the calendar
In the Julian Calendar, Leap Year (LY) occurs every In the Julian Calendar, Leap Year (LY) occurs every year divisible by 4year divisible by 4
New Reform in Gregorian CalendarsNew Reform in Gregorian Calendars
Oct 15, 1582 followed Oct 4, 1852
Thus the Julian average year was 365.25 days Thus the Julian average year was 365.25 days whereas the Tropical Year is 365.242199 days. This whereas the Tropical Year is 365.242199 days. This results in a difference of 1 day in 128 years.results in a difference of 1 day in 128 years.Need to remove 1 LY every 128 years. Need to remove 1 LY every 128 years. CumbersomeCumbersome
Only century years divisible by 400 are LYs. Eg. Only century years divisible by 400 are LYs. Eg. 1700, 1800 & 1900 are NOT Lys. 1600, & 2000 are 1700, 1800 & 1900 are NOT Lys. 1600, & 2000 are LYs. Correct to 1 day in 3300 years.LYs. Correct to 1 day in 3300 years.
Pope Gregory XIII, 1582Pope Gregory XIII, 1582
CALENDAR REFORMCALENDAR REFORMCALENDAR REFORMCALENDAR REFORM Modern modification: 4000, 8000, 12000 Modern modification: 4000, 8000, 12000
now are NOT Leap Years.now are NOT Leap Years. Calendar is now accurate to 1 day in 20,000 Calendar is now accurate to 1 day in 20,000
years.years.