Time and Calendars

Time

What is time?

How do you know the passage of time?

What then is time?

What then is time?  If no one asks me, I know what it is.  If I wish to explain it to

him who asks, I do not know. 

~Saint Augustine

Day, n.  A period of twenty-four hours, mostly misspent. 

~Ambrose Bierce

Astronomical Cycles

Time Unit Approx Length Origin

Day 24 hours Earth’s rotation

Month 30 days Moon’s revolution (phases)

Year 365 days Earth’s revolution

“Great Year”

26,000 years Earth’s precession

Sun and Stars

• Solar-time by the sun

• Sidereal-time by the stars

• Days, months, years

Solar & Sidereal Day

• Earth’s rotation

• Solar day: 24 hours

• Sidereal day: 23h, 56m, 4s– 4 minute difference– Causes stars to change with the seasons

Sidereal and Solar Day [Animation]

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit2/Images/sidereal.gif

“Fixed stars”

Solar & Mean Times

• Local Apparent Time (LAT):– Time read from a sundial– Before time zones, every town had its own time

• Local Mean Time (LMT):– Average time, read from a wall clock

• Local Standard Time (LST):– “Time Zone” time, for example, Eastern Standard– LDT: Local Daylight Time

• Equation of time: – Difference between LAT and LMT – LAT sometimes ahead, behind LMT– Due to earth’s elliptical orbit

Synodic and Sidereal Months

• Moon’s revolution

• Synodic month: Lunar phases repeat– 29.5 days– e.g., one full moon to the next

• Sidereal month: Time for moon to pass a star again– 27.33 days

[Animation]

Tropical & Sidereal Year

• Earth’s revolution• Tropical Year: Time between successive spring

equinoxes– 365.242 days

• Sidereal Year: Time for the sun to return to the same point compared to background stars– 365.256 days– 20 minute difference due to earth’s precession

(wobble)

Earth’s Revolution

Earth’s revolution causes the constellations to appear to change with the seasons

Time Units

Time Unit

Length Origin

Day 24 hours (solar)

23.93 (sidereal)

Earth’s rotation

Month 29.5 days (synodic)

27.33 days (sidereal)

Moon’s revolution (phases)

Year 365.242 days (tropical)

365.256 (sidereal)

Earth’s revolution

Day Names

• Named for sun, moon, and the planets

• Latin names, Roman gods

• Some Norse names substituted

Modern Latin Meaning

Sunday Dies Solis Day of the sun

Monday Dies Lunae Day of the moon

Tuesday1 Dies Martis Day of Mars

Wednesday2 Dies Mercurii Day of Mercury

Thursday3 Dies Jovis Day of Jupiter

Friday4 Dies Veneris Day of Venus

Saturday Dies Saturni Day of Saturn

Day Names Table

Four of the Day Names are derived from the Norse names of the planet gods.

1Norse: “Tiw’s day”2Norse: “Woden’s day”3Norse: “Thor’s day”4Norse: “Frig’s day”

The Month

• Originally lunar phases

• i.e. one new moon to next

• Why 12 months? There are 12.4 cycles of lunar phases during a year.

• Moon = “Moonth”

The Week

• Traditional 7 days• Not a natural cycle• Bible, planets• 7 moving bodies ("planets") visible without

telescope• Sun, Moon, Mercury, Venus, Mars,

Jupiter, and Saturn• Cultural: 10 day weeks were used in

ancient Egypt and the French Revolution

Dividing the Year

• Solstices & Equinoxes:– Seasons– Divide the year into quarters

• "Quarter Days" – March equinox– June solstice– September equinox– Winter solstice

Quarter Days: Solstices and Equinoxes

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit2/Images/QuarterDays.gif

Quarter Day Table

Event Date SeasonSun Transit

(latitude) Tradition

MarchEquinox 21-Mar Spring

Equator,0° Easter

JuneSolstice 21-Jun Summer

Cancer, +23.5° July 4th

September Equinox 23-Sep Autumn

Equator,0°

First Day of School

December Solstice 21-Dec Winter

Capricorn, -23.5 ° Christmas

Traditional Quarter Days

• Vernal Equinox: Easter, Passover, Eoestre (Saxon goddess)

• Summer Solstice: Midsummer (A Midsummer Night's Dream), St. John's Eve, Fourth of July

• Autumnal Equinox: Mabon (Celtic/Welsh), Michaelmas (Feast of St. Michael the Archangel)

• Winter Solstice: Christmas, Advent, Saturnalia

Dividing the Year

• Cross-Quarter Days: Mid-way points between the Solstices and Equinoxes.

• Once considered the start of the seasons (“midsummer” refers to the summer solstice)

Cross-Quarter Days

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit2/Images/CrossQuarter.gif

Cross-quarter days are indicated by the red plus signs:

1st: Feb 2

2nd: May 1

3rd: Aug 2

4th: Nov 1

Cross-Quarter DaysName Date Other Names

(season)

Groundhog Day

Feb 2 Candlemas (spring)

May Day May 1 Beltane (summer)

Lammas Aug 2 Lughnasadh (autumn)

Halloween Oct 31,

Nov 1

All Saints, Samhain

(winter)

Precession

• Earth’s other motion• Slow wobble of the earth’s axis• Once every 26,000 years• Moon’s gravitational pull on the earth

Effects of Precession

• “North Star” changes• Positions of solstices and equinoxes

(“precession of the equinoxes”)• Star coordinates (Right ascension,

declination) slowly change

Earth’s Wobble

• Each wobble takes 26,000 years

• The axis will point towards the bright star Vega in 12,000 years

Click: Precession Animation

Path of the Pole

Precession of the Equinoxes

The Hour

Dividing the Day

• 24 hours, beginning at midnight

• Traditionally, day started at sunrise, ended at sunset

• Day hours were longer in the summer, shorter in the winter

• Modern clock hours are equal in length regardless of the season

Day & Night Hours

http://odin.physastro.mnsu.edu/~eskridge/astr101/day_night.jpg

12 hours?

Solar & Mean Times

• Local Apparent Time (LAT):– Time read from a sundial– Before time zones, every town had its own time

• Local Mean Time (LMT):– Average time, read from a wall clock

• Local Standard Time (LST):– “Time Zone” time, for example, Eastern Standard– LDT: Local Daylight Time

• Equation of time: – Difference between LAT and LMT – LAT sometimes ahead, behind LMT– Due to earth’s elliptical orbit

Standard Time

• With railroads and telegraphs, small differences in LAT began to matter

• 1883: United States divided into four time zones • Each zone observed the LAT at the center of

each zone (standard meridian)• US Standard Meridians: 75º, 90º, 105º, 120º

(15º of longitude apart)• Entire globe has 24 zones (360º/24h = 15º/hour)

US Standard Times75°120° 105° 90°

Standard Meridians

EST Meridian

World Time Zones

http://www.infoplease.com/spot/daylight2.html

Indiana Time (before & after)

http://www.timetemperature.com/tzmaps/intz.gif

EST only

EST, EDT

CST, CDT

EST, EDTCST,

CDT

Eastern Standard Zone

• EST: Same LAT time as 75° west meridian (Philadelphia)

• Bremen: Latitude 86°W• Earth: 360°, 24 hours of time• 1 hour = 15° longitude• 1° longitude = 4 minutes• Bremen is 86°-75° = 11° of

longitude off our central meridian

• When our standard time clocks say 12:00 pm (noon), our LAT* is actual 11° x 4 min = 44 minutes off, or 11:16 am

*Without equation of time

Equation of Time

• Equation of time: – Difference between LAT and LMT – LAT sometimes ahead, behind LMT– Due to earth’s elliptical orbit (obliquity)

and 23-degree tilt (orientation)• Result: Sun appears fast or slow

depending upon the time of year• Graph of equation of time reveals

analemma

Plot of Equation of Time

Sun “fast”

Sun “slow”

Analemma Plot

Obliquity (elliptical orbit)

Orientation (23-degree tilt)

The Tropics

•Tropic of Cancer: Sun directly overhead June 21—Solstice

•Equator: Sun directly overhead Mar 21 and Sept 21—equinoxes

•Tropic of Capricorn: Sun directly overhead Dec 21--Solstice

http://www.math.nus.edu.sg/aslaksen/pictures/analemma.jpg

First Analemma Photo

Labeled Analemma

A

B

C

D

Animations

• Analemma from Earth

• APOD Dec 04, 2007

http://www.perseus.gr/Images/solar-analemma-060000-UTC.jpg

http://epod.usra.edu/archive/images/main_solar-analemma-102816-utc2.jpg

http://curious.astro.cornell.edu/images/analemma.jpg

Create an Analemma•Plot the shadow tip of the end of the post

•Use the same mechanical clock time each day for plotting

•Over the course of one year, an analemma will result

Castaway

Stranded on a deserted island in the South Pacific following the crash of his Fed Ex airplane, Chuck Noland (Tom Hanks) constructs an analemma on a cave wall to track the daily displacement in the shaft of sunlight through a small natural portal. He explains the science and the repetitive annual figure-8 cycle to his sanity companion, Wilson, the volleyball.

Earth’s Revolution

• At perihelion, earth revolves faster in its orbit, slower at aphelion

• Sun’s apparent size changes slightly as a result

Close and Far

What Time is It?

• Click: http://www.time.gov/timezone.cgi?Eastern/d/-5/java

Sundials

Sundials

• Sundials are the earliest form of clocks

• Read local apparent time (LAT) directly from the sun

• Times can be converted from LAT to LMT

• Main Types– Horizontal– Equatorial

Horizontal ‘Dials

• Designed for a single latitude ()

• Parts:– Gnomon– Style– Hour lines– Furniture

Polaris (North)

Latitude

The Style points toward the North Celestial Pole

(Polaris)

Identify: style, gnomon, hour lines, furniture

Horizontal

Equatorial ‘Dials

• Can be adjusted to work in any latitude by tilting gnomon to latitude value ()

• Seasonal: Sun shines on top of dial plate after the March equinox, below the dial plate after the september equinox

• Parts:– Gnomon– Hour lines– Dial plate (disk)

Gnomon

Dial plate

Equatorial

Polaris

Latitude

Identify: gnomon, hour lines, dial plate (equator)

Seasonal ‘Dial

Adler Planetarium Equatorial ‘Dial, Chicago

Wood Equatorial Dial

Human Sundial

Calendars

The “Modern” Calendar

• Our modern calendar is the same as the Gregorian Calendar introduced in 1582

• Gregorian Calendar reformed the older Julian Calendar

Astronomical Basis of the Year

• Equinoxes and solstices are anchors

• Calendar measures a “tropical year,” the time between two vernal equinoxes

• Tropical year = 365.2425 days

• Leap years used to correct the extra six hours (0.2425 day) per year

Julian Calendar

• Reform of 10 month Roman Calendar

• Julius Caesar, 45 BC

• Inserted leap day every 4 years

• Resulted in 10-day error between starts of seasons by 1500s

• Gregorian calendar removed the extra days, changed the leap day procedure

Gregorian Calendar

• Every year divisible by 4 is a leap year• Every century year (multiple of 100) is

NOT a leap year, unless it is divisible by 400

• The tropical year equals 365.2425, equal to an error of one day 3300 years

• Our modern calendar• 2000 was a century year. Was it also a

leap year?

Western Calendars

Calendar Used Founder Features

Roman

(355 days)

< 45 BC Romulus & Remus*

10 months initially

Julian

(365.25 days)

45 BC Julius Caesar

Leap day

Gregorian

(365.2425 days)

1582 AD to present

Pope Gregory XIII

Leap day (refined)

*legendary founders of Rome

Gregorian Month Names

Our months are named for numbers, gods, festivals, and Roman emperors

1. January: Januarius, the god Janus

2. February: Februarius, the festival of Februa

3. March: Martius, the god Mars

4. April: Aprilis, the goddess Aphrodite

5. May: Maius, the goddess Maia

6. June: Junius, the goddess Juno

Month Names, Cont.

7. July: Julius, after Julius Caesar

8. August: Augustus, after emperor Augustus

9. September: The seventh month (septem)

10.October: The eighth month (octo)

11.November: The ninth month (novem)

12.December: The tenth month (decem)

Gregorian Months

http://www.spirit-of-yggdrasil.com/images/Gregorian%20-%2012%20months.jpg

Dog Days

• Caesar based his new calendar on one used in Egypt• The Egyptians counted days from the first appearance of

the Dog Star Sirius in the morning sky before sunrise• Sirius is the brightest star in the sky (other than the sun)• This heliacal rising of Sirius was the beginning of the

Egyptian year, today it occurs in July• The heliacal rising of Sirius also coincided with the

annual flooding of the Nile river upon which life in Egypt depended

• We still call mid-July the Dog Days because some of the Greeks believed that the heat of summer came from the combined energy of the sun and Sirius

http://www.astropix.com/IMAGES/B_WINTER/SIRIUS.JPG

?Calendar Changes

• This change was (from Julian to Gregorian) observed in Catholic countries such as Italy, Poland, Portugal, and Spain.

• Protestant countries were reluctant to change. For example, Great Britain and America eventually changed in 1752.

• Washington’s Birthday was originally Feb 11, 1732 in the Julian Calendar, today we say it was Feb 22, 1732

http://archives.cnn.com/

When is Easter?

• Easter, the death and resurrection of Jesus in about 30 AD

• Easter is the first Sunday after the first full moon after the (vernal) spring equinox

• March 21 is considered the spring equinox

• Catholic Church’s Council of Nicea in 325 AD

http://www.adventurepostoffice.com/cards/easter/bunny99-05-l.gif

Lunar Calendars

• Ancient calendars, still used by Jews and Muslims

• New moon begins each month• Islamic calendar, crescent moon is sighted • Jewish calendar kept aligned with the

seasons• Islamic calendar dates drift through the

seasons• Used mainly for religious purposes

http://www.observetheheavens.homestead.com/files/crescent_moon_website.JPG

Jewish Lunar Calendar

• Ancient, used for religious observances

• Hebrew calendar aligned with the seasons by adding “leap months” when needed

• Year contains 12-13 months, 353-385 days

• Jewish year linked to equinoxes

Jewish CalendarMonth Name Length Gregorian Holidays (dates)

1 Nissan 30 days Mar-Apr* Passover (15 Nissan)

2 Iyar 29 days Apr-May

3 Sivan 30 days May-June

4 Tammuz 29 days June-July

5 Av 30 days July-Aug

6 Elul 29 days Aug-Sep

7 Tishri 30 days Sep-Oct** Rosh Hashanah (1-2)

8 Cheshvan 29 or 30 days Nov-Dec

9 Kislev 29 or 30 days Nov-Dec Chanukkah (25)

10 Tevet 29 days Dec-Jan

11 Shevat 30 days Jan-Feb

12 Adar I 30 days Feb-Mar

13 Adar II (leap) 29 days Feb-Mar

*Mar Equinox, **Sep Equinox

Islamic Lunar Calendar

• Ancient, used for religious observances

• Year contains 12 months, 354-5 days

• Islamic calendar is purely lunar and dates drift through the seasons

2008 Islamic CalendarMonth Name Gregorian Holidays (dates)

1 Muharram 1429 Jan 10 New Year

2 Safar Feb 8

3 Rabi-I Mar 9

4 Rabi-II Apr 7

5 Jumada-I May 6

6 Jumada-II June 5

7 Rajab July 4

8 Sha’ban Aug 2

9 Ramadan Sept 1 Ramadan

10 Shawwal Oct 1

11 Dhul-Qi’dah Oct 30

12 Dhul-Hiija Nov 29 Pilgrimage to Mecca

1 Muharram 1430 Dec 29 New Year

Lunar Calendar HolidaysGregorian Easter Jewish New Year Muslim New Year

2001 Apr 15 Sept 18 Mar 26

2002 Mar 31 Sept 7 Mar 15

2003 Apr 20 Sept 27 Mar 5

2004 Apr 11 Sept 16 Feb 22

2005 Mar 27 Oct 4 Feb 10

2006 Apr 16 Sept 23 Jan 31

2007 Apr 8 Sept 13 Jan 20

2008 Mar 23 Sept 30 Jan 10

2009 Apr 12 Sept 19 Dec 29

2010 Apr 4 Sept 9 Dec 18

March Equinox September Equinox

Competing Years (2009)

Western Calendar

2009 AD Birth of Jesus

Jewish Calendar

5760 Age of universe in Torah (Genesis)

Islamic Calendar

1430 Mohammed flees to Medina (Hegira)

Calendar Current Year Start

Counting the Years

• Dionysius Exiguus, a Scythian monk, created the BC, AD system of counting years

• Based on estimation of the birth of Jesus• 1 AD was the year of Jesus’s birth, 1 BC would

have been the year before• No year “0”, which has created some confusion• Modern scholarship reveals that Jesus was

actually born in 4 BC

http://www.mike.lawton.clara.net/Homersweb/doh.jpg

Counting the Years, Cont.

• Years before the birth of Jesus are labeled BC, (“Before Christ”)

• Years after the birth of Jesus are labeled AD (Anno Domini, “In the year of the Lord”)

1 BC Birth of Jesus 1 AD

BCE, CE

• BCE (Before the Common Era) = BC• CE (Common Era) = AD• Ex:

Battle of Thermopylae

480 BC

480 BCE

Fall of Constantinople

1453 AD

1453 CE

Millenia

• The first millenia, or thousand year period, began in 1 AD

• Millenia have special significance due to statements in the Bible (Revelations)

• The millenia are counted:– 1st millenium: 1-1000– 2nd millenium: 1001-2000– 3rd millenium: 2001-3000

• The 3rd millenium, and the 21st century, started on January 1, 2001

• People tend to go crazy every 1000 years

http://www.american-buddha.com/2001SPACEODYSSEYABOL2.jpg

Julian Days (not years)

• Julian days (JDN) are a method of numbering days regardless of year, they provide a unique numerical value for any calendar date

• For example, on Friday, March 2, 2007, the JDN was 2,454,162

• Decimals provide fractions of one day. Ex: 0.1 = 2.4 hours

• Day 0 of this cycle occurred on Monday, January 1, 4713 BC in the Gregorian calendar. Because of this, multiples of 7 are Mondays

• Julian days are set to begin at noon, not midnight• Julian days are used in astronomy to minimize the

confusion of using calendars

Scaliger Days

• The Julian day number was proposed by Joseph Scaliger in 1583, at the time of the Gregorian calendar reform

• The Julian day is a multiple of three separate cycles:– 15 (Indiction cycle) × 19 (Metonic cycle) × 28 (Solar cycle) =

7980 years

• Its beginning point falls at the last time when all three cycles were in their first year together, 4713 BC—Scaliger chose this because it predated all historical dates

• According to legend, Scaliger named his cycle after his father, who was named Julius (confusing, yes)

Julian Day Cycles

• Indiction, 15 year tax collection cycle of the Roman Empire

• Metonic cycle, 19 years, represents an equal number of years and lunar phase cycles

• Solar cycle = 28 years, represents the time for a leap day to cycle through every combination of days (Mon-Sun)

15 × 19 × 28 = 7980 years

French Revolutionary Calendar

• New calendar created during the French Revolution in 1789• The year consisted of 365-366 days divided into 12 months of 30

days each, followed by 5-6 additional days• The months were named after seasons and weather (Ex:

Thermidor, Fructidor)• Each month was divided into three “decades” of 10 days, of which

the final day was a day of rest.• The 10 days of each decade were numbered (Primidi, Duodi, etc.).

The 5-6 additional days were unnumbered festivals• Each year was to start on the Autumnal Equinox (around Sept 22)• The Revolutionary calendar was used between Nov 24, 1793 and

Jan 1, 1806 (Gregorian). It’s “0” year was the French Revolution itself, in 1789.

• The French wanted to “de-Christianize” the calendar, but workers didn’t enjoy 9 days of work per “week”

Maya Calendar

• The Maya of Central America used systems of interlocking calendars, and they were adept at calculating dates in each calendar or converting one calendar to another

• The earliest Maya calendric system dates back to 500 BC and originated with the Maya ancestors the Olmecs

• Mayan Calendars:– Tzolkin-260 day “Divine calendar”– Haab-365 day Civil calendar– Long Count– Venus Cycle

Tzolkin & Haab• The Tzolkin was a 260 day calendar used to date religious

functions• The Tzolkin combines 20 day names with 13 days to produce

260 unique combinations• The origin of the 260 cycle is unknown• It might reflect the human gestation period of 9 months, or the

number of days that Venus is visible in the evening or morning sky

• The Haab represented a 365 day solar calendar• The Haab did not account for the extra ¼ day in the solar year,

so the Haab tended to drift through the seasons. It appears that the Maya, like the Egyptians, were aware of this discrepancy

• When combined, the Tzolkin and Haab created a 52 year Calendar Round

• Each Calendar Round date had a unique value

Long Count• Used for dates beyond the Calendar Round of 52 years• The Long Count used a 20 day number base

– The day was K’in– 20 Kins is one winal (20 days)– 18 winals make one tun (360 days~1 solar year)– 20 tuns make one katun (20 solar years)– 20 katuns make one baktun (400 solar years)

• The Long Count also had higher terms measuring up to 63 million years (1 alautun)

• Interestingly, the Maya placed special significance upon the end of 13 baktuns, and in the Gregorian calendar this occurs on the winter solstice in 2012

• The starting date of the first baktun in this cycle was August 11th, 3114 BC

Venus Cycle

• The Maya also kept track of the visibility of Venus

• The Dresden Codex, one of only two surving Maya books, describes the Maya calculation of the Venus cycle

• The Maya were able to calculate the visibility of Venus for thousands of years into the past or future

• It is conjectured that the Caracol, a round building at Chichen Itza, served as a Venus observatory

Maya Venus “Observatory” at Chichen Itza

http://centros.edu.aytolacoruna.es/sfxabier/world_links/mexico_observatory.jpg

World Calendar

• A new calendar proposed to replace the Gregorian

• Every year is the same• For example, your birthday would fall on the

same weekday every year• Includes a leap day and other corrections• Proposed in the 1920s, but never caught on• http://www.theworldcalendar.org/

TWCandDescription.pdf