Solar cycle (calendar)
The solar cycle is a 28-year cycle of the Julian calendar, and 400-year cycle of the Gregorian calendar with respect to the week. It occurs because leap years occur every 4 years and there are 7 possible days to start a leap year, making a 28-year sequence.[1]
This cycle also occurs in the Gregorian calendar, but it is interrupted by years such as 1800, 1900, 2100, 2200, 2300 and 2500, which are divisible by four but which are common years. This interruption has the effect of skipping 16 years of the solar cycle between February 28 and March 1. Because the Gregorian cycle of 400 years has exactly 146,097 days, i.e. exactly 20,871 weeks, one can say that the Gregorian so-called solar cycle lasts 400 years.[2]
Calendar years are usually marked by Dominical letters indicating the first Sunday in a new year, thus the term solar cycle can also refer to a repeating sequence of Dominical letters. Unless a year is not a leap year due to Gregorian exceptions, a sequence of calendars is reused every 28 years.[3]
The name solar cycle comes from Sunday, the traditional first day of the week.
Examples
Julian calendar
Dominical letter
The dominical letter in the Julian calendar depends only on the remainder of the year mod 28.[4]
| Year mod 28 | Dominical letter |
|---|---|
| 0 | DC |
| 1 | B |
| 2 | A |
| 3 | G |
| 4 | FE |
| 5 | D |
| 6 | C |
| 7 | B |
| 8 | AG |
| 9 | F |
| 10 | E |
| 11 | D |
| 12 | CB |
| 13 | A |
| 14 | G |
| 15 | F |
| 16 | ED |
| 17 | C |
| 18 | B |
| 19 | A |
| 20 | GF |
| 21 | E |
| 22 | D |
| 23 | C |
| 24 | BA |
| 25 | G |
| 26 | F |
| 27 | E |
Doomsday
| Year mod 28 | Doomsday |
|---|---|
| 0 | Sunday |
| 1 | Monday |
| 2 | Tuesday |
| 3 | Wednesday |
| 4 | Friday |
| 5 | Saturday |
| 6 | Sunday |
| 7 | Monday |
| 8 | Wednesday |
| 9 | Thursday |
| 10 | Friday |
| 11 | Saturday |
| 12 | Monday |
| 13 | Tuesday |
| 14 | Wednesday |
| 15 | Thursday |
| 16 | Saturday |
| 17 | Sunday |
| 18 | Monday |
| 19 | Tuesday |
| 20 | Thursday |
| 21 | Friday |
| 22 | Saturday |
| 23 | Sunday |
| 24 | Tuesday |
| 25 | Wednesday |
| 26 | Thursday |
| 27 | Friday |
Friday the 13ths
| Year mod 28 | 1st | 2nd | 3rd |
|---|---|---|---|
| 0 | February 13 | August 13 | |
| 1 | May 13 | ||
| 2 | January 13 | October 13 | |
| 3 | April 13 | July 13 | |
| 4 | June 13 | ||
| 5 | February 13 | March 13 | November 13 |
| 6 | August 13 | ||
| 7 | May 13 | ||
| 8 | January 13 | April 13 | July 13 |
| 9 | September 13 | December 13 | |
| 10 | June 13 | ||
| 11 | February 13 | March 13 | November 13 |
| 12 | May 13 | ||
| 13 | January 13 | October 13 | |
| 14 | April 13 | July 13 | |
| 15 | September 13 | December 13 | |
| 16 | March 13 | November 13 | |
| 17 | August 13 | ||
| 18 | May 13 | ||
| 19 | January 13 | October 13 | |
| 20 | September 13 | December 13 | |
| 21 | June 13 | ||
| 22 | February 13 | March 13 | November 13 |
| 23 | August 13 | ||
| 24 | October 13 | ||
| 25 | April 13 | July 13 | |
| 26 | September 13 | December 13 | |
| 27 | June 13 |
Gregorian calendar
The years 1700, 1800, and 1900 were not leap years (unlike the Julian calendar) and do not fit in the tables of Dominical letters below.
Doomsday
| Century | Year | |||||||
|---|---|---|---|---|---|---|---|---|
| 00 | 01 | 02 | 03 | 04 | 05 | |||
| 06 | 07 | 08 | 09 | 10 | 11 | |||
| 12 | 13 | 14 | 15 | 16 | ||||
| 17 | 18 | 19 | 20 | 21 | 22 | |||
| 23 | 24 | 25 | 26 | 27 | ||||
| 28 | 29 | 30 | 31 | 32 | 33 | |||
| 34 | 35 | 36 | 37 | 38 | 39 | |||
| 40 | 41 | 42 | 43 | 44 | ||||
| 45 | 46 | 47 | 48 | 49 | 50 | |||
| 51 | 52 | 53 | 54 | 55 | ||||
| 56 | 57 | 58 | 59 | 60 | 61 | |||
| 62 | 63 | 64 | 65 | 66 | 67 | |||
| 68 | 69 | 70 | 71 | 72 | ||||
| 73 | 74 | 75 | 76 | 77 | 78 | |||
| 79 | 80 | 81 | 82 | 83 | ||||
| 84 | 85 | 86 | 87 | 88 | 89 | |||
| 90 | 91 | 92 | 93 | 94 | 95 | |||
| 96 | 97 | 98 | 99 | |||||
| 1600 | 2000 | Tue | Wed | Thu | Fri | Sat | Sun | Mon |
| 1700 | 2100 | Sun | Mon | Tue | Wed | Thu | Fri | Sat |
| 1800 | 2200 | Fri | Sat | Sun | Mon | Tue | Wed | Thu |
| 1900 | 2300 | Wed | Thu | Fri | Sat | Sun | Mon | Tue |
See also
References
- ↑ Alexander Philip (2012). The Calendar: Its History, Structure and Improvement. Cambridge University Press. p. 45. ISBN 9781107640214. Search this book on
- ↑ Stephen G. Christianson (2000). The American Book of Days. H.W. Wilson. p. 875. ISBN 9780824209544. Search this book on
- ↑ Jacques Ozanam (1840). Recreations in mathematics and natural philosophy, recomposed by m. Montucla and tr. by C. Hutton. p. 486. Search this book on
- ↑ George Crabb (1823). Universal Technological Dictionary: Or, Familiar Explanations of the Terms Used in All Arts and Sciences. Baldwin, Cradock, and Joy. p. 93. Search this book on
Further reading
- C. R. Cheney (rev. Michael Jones), 2012: Handbook of dates (2nd edition), CUP
External links
- The ISO 8601 calendar using week numbers, explained using Dominical letters.
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