the history of the gregorian calendar

46
The History of the Gregorian Calendar ED STAPLES

Upload: santos

Post on 23-Feb-2016

131 views

Category:

Documents


1 download

DESCRIPTION

The History of the Gregorian Calendar. Ed Staples. Close up of My Watch. Lunar or Solar?. The story of the calendar is essentially centred around the three natural cycles of the daily sun rise, the lunar cycle, and the tropical year. . The 7 day week. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: The History of the Gregorian Calendar

The History of the Gregorian CalendarED STAPLES

Page 2: The History of the Gregorian Calendar

Close up of My Watch

Page 3: The History of the Gregorian Calendar

Lunar or Solar?

The story of the calendar is essentially centred around the three natural cycles of the daily sun rise, the lunar cycle, and the tropical year.

Page 4: The History of the Gregorian Calendar

The 7 day week

The seven day week has no natural markers. It is an intellectual creation and does not fit well with the lunar or solar calendar.

Page 5: The History of the Gregorian Calendar

Check your salary!

31312

GrossAnnualGrossFortnight

Page 6: The History of the Gregorian Calendar

Check your salary!

31312

GrossAnnualGrossFortnight

Because there are 313 fortnights in 12 years

Page 7: The History of the Gregorian Calendar

1st Roman Calendar: Romulus 753 BCMonth Days

1 Martius 312 Aprilis 303 Maius 314 Junius 305 Quintilis 316 Sextilis 307 September 308 October 319 November 3010 December 30

TOTAL 304

Page 8: The History of the Gregorian Calendar

Changes by King Numa: 7th Century BC

Month Days1 Februarius 282 Ianuarius 283 Martius 314 Aprilis 295 Maius 316 Junius 297 Quintilis 318 Sextilis 299 September 2910 October 3111 November 2912 December 29

TOTAL 354

29.5 X 12 = 354

Lunar Calendar

Page 9: The History of the Gregorian Calendar

Beware the ides of March!

Day Name Phase1 Kalends New Moon

13,15 Ides Full Moon

Page 10: The History of the Gregorian Calendar

1st Attempt to align with seasons: Numa 2

Month Days1 Ianuarius 292 Februarius 28

Mercendonius Intercalated3 Martius 314 Aprilis 295 Maius 316 Junius 297 Quintilis 318 Sextilis 299 September 2910 October 311 November 2912 December 29

TOTAL 355

29.5 X 12 = 355Lunar Year

Page 11: The History of the Gregorian Calendar

Julius Caesar 46BC (Sosigenes)

Month Days1 Ianuarius 312 Februarius 28,293 Martius 314 Aprilis 305 Maius 316 Junius 307 July 318 August 319 September 3010 October 311 November 3012 December 31

TOTAL 365,366

Tropical Year

The Julian Calendar

Page 12: The History of the Gregorian Calendar

Caesar’s adjustment to the vernal equinox

Year Days46 BC 445

Last Year of Confusion

Page 13: The History of the Gregorian Calendar

432BC : The Metonic Cycle (Greece)

235 Lunations is virtually identical to 19 Tropical Years

Page 14: The History of the Gregorian Calendar

Golden numbers still used to determine date of Easter Sunday

2014 2015 2016 2017 201820 20 20 20 2015 15 15 15 150 1 2 3 424 13 2 21 1024 13 2 21 1051 36 27 47 3220 5 27 16 1

April April March April April

Golden numbers

Page 15: The History of the Gregorian Calendar

Solar year re-calculated as 365.2219 years

The time between two successive vernal equinoxes can be estimated accurately by using a device first used by

Ptolemy of Alexandria (2nd Century AD) called an equatorial ring.

Page 22: The History of the Gregorian Calendar

Like a coil of rope

SolsticeSolstice

EAST

Page 23: The History of the Gregorian Calendar

The precise moment of the equinox

East

Page 24: The History of the Gregorian Calendar

Walking south to Canberra Lat:35S

If we walk south back to Canberra from the equator, the rising vertical star lines will appear to lean away from us (lean toward the north)

This is because we are on a spherical earth

Page 25: The History of the Gregorian Calendar

Canberra Sun rising

SouthEast

North

Lat

90 - Lat

Page 26: The History of the Gregorian Calendar

Motion of the Sun over the year

North South

Lat

Page 27: The History of the Gregorian Calendar

Looking East in Canberra

Page 28: The History of the Gregorian Calendar

Looking South in Canberra

South

Canberra Latitude 35 degrees

Page 29: The History of the Gregorian Calendar

The equatorial ring

90 - Lat

Page 30: The History of the Gregorian Calendar

The equatorial ring

90 - Lat

Page 31: The History of the Gregorian Calendar

The equatorial ring

90 - Lat

Page 32: The History of the Gregorian Calendar

The equatorial ring

90 - Lat

Page 33: The History of the Gregorian Calendar

The equatorial ring

Equinox point

Shadow falls

90 - Lat

Page 34: The History of the Gregorian Calendar

The equatorial ring

Post Equinox point

Shadow falls

90 - Lat

Page 35: The History of the Gregorian Calendar

Equinox by Sundial?

The, shadow is shortest in Summer and longest in winter, so at some stage in its “vertical” journey, the shadow tip will touch the equinox line. (twice a year )

Page 36: The History of the Gregorian Calendar

A Canberra Sundial (35 deg gnomon)

Equinox line

Summer Solstice

Winter Solstice

Page 37: The History of the Gregorian Calendar

Hence….

Actual Tropical Year 365.24219 days

Julian assumption 365.25 days

Difference 0.00781 days

(Spotted by the Venerable Bede in AD 725

Page 38: The History of the Gregorian Calendar

Do the Maths!

0.00781 X 24 X 60 = 11 minutes and 15 seconds

Page 39: The History of the Gregorian Calendar

How the small difference accrues

11 minutes 15 seconds each year

45 minutes over 4 years

1 day over 128 years

4,500 minutes or 75 hours or

3 days 3 hours over 400 years

Page 40: The History of the Gregorian Calendar

Luigi Lilio’s solution

Drop 3 leap years every 400 years

If a centurial year is not divisible by 400, drop the leap year!

So 1800,1900,2100,2200,2300,2500,… NOT leap years even though they are divisible by 4.

Page 41: The History of the Gregorian Calendar

Pope Gregory: 1582 (Lilio)Month Days

1 January 312 February 28,293 March 314 April 305 May 316 June 307 July 318 August 319 September 3010 October 311 November 3012 December 31

TOTAL 365,366

Tropical 365,366Year

Pope Gregory AD 1582

The Gregorian calendar

Page 42: The History of the Gregorian Calendar

The UK experience 1751

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar DAYSOLD 1 2 3 4 5 6 7 8 9 10 11 12 11750 25 M A M J J A S O N D J F M 24 365

1751 25 M A M22 J J A S O N D 31 282

NEW 1 2 3 4 5 6 7 8 9 10 11 121752 1 J F M A M J J A 2 14 O N D 31 11 days deleted 355

1753 1 J F M A M J J A S O N D 31 365

Page 43: The History of the Gregorian Calendar

10 minute break

Page 44: The History of the Gregorian Calendar

Zeller 1883Month Number Cumulative Excess ZellerMarch 3 0 0.4April 4 3 3May 5 5 5.6June 6 8 8.2July 7 10 10.8

August 8 13 13.4September 9 16 16

October 10 18 18.6November 11 21 21.2December 12 23 23.8

January 1 26 26.4February 2 29 29

Page 45: The History of the Gregorian Calendar

Conway’s DoomsdayDay Month Remember

4th 4th 4th April6th 6th 6th June8th 8th 8th August

10th 10th 10th October12th 12th 12th December

5th 9th 5th September9th 5th 9th May

7th 11th 7th November11th 7th 11th July

Last Day February 28th, 29th February

Page 46: The History of the Gregorian Calendar

Corrections

Calendar A B A/B True Value Difference M SJulian 100 400 0.25 0.242193 0.007807 11 15

Gregorian 97 400 0.2425 0.242193 0.000307 0 27CF 225 929 0.242196 0.242193 0.000003 0 0.6

SPOT 31 128 0.242188 0.242193 -0.000005 0 -1