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.