5 t ime
5.6 A short history of calendars
Calendars are part of a complete timekeeping system: the date and time of day together specify an exact moment in time. This then makes it possible to calculate past or future time, for example to calculate how many days until a certain event takes place.
The calendar year (the number of days in the year) must be synchronised to the cycle of the seasons, so that the seasons start on the same dates every year. This means that the calendar year must be synchronised to the solar year (the exact time that it takes the Earth to move around the Sun once).
The problem with designing a calendar is that a calendar year must have a whole number of days (why?), but the solar year is not a whole number of days (it is about 365 days 5 hours 48 minutes 46 seconds).
To solve the problem, we must approximate the solar year with a whole number of days, over a period of time. Throughout history, people tried to make better calendars by making better and useful approximations of the solar year. This is done by adding extra whole days in some years.
Roman Calendar
The Roman Calendar was invented by King Romulus at around
753 BCE. It was a lunar calendar, based on the phases of the moon. The year started in March and had 10 months with a total of 304 days, with 61 days in the winter not included.
Around 700 BCE King Pompilius added the months of January and February to the calendar, increasing the calendar year to 355 days. The addition of two extra months meant that some of the months’ names no longer agreed with their position in the calendar. For example, December was originally the 10th month (deci = tenth).
1. Do some research about the origins of the names of the months, and the names of the days of the week. Why July? Why Monday?
Julian Calendar
To create a more standardised calendar, the Roman Emperor Julius Caesar followed the advice of Sosigenes, an astronomer and mathematician from Alexandria in Egypt. He made some sweeping changes to the calendar. This calendar was named the Julian Calendar.
• To bring the calendar back in step with the seasons, the year 46 BCE was made 445 days long.
• The year 45 BCE began on 1 January, not in March as before.
• The solar year was approximated as 365 days 6 hours or 36514 days.
This meant that the calendar year was a whole number of days over a period of 4 years. Not all years had the same number of days: three normal years had 365 days, and every fourth year had 366 days (called a leap year). The extra day was 29 February.
2. What is the error (the time difference) between the Julian calendar year of 365 d 6 h and the real solar year of 365 d 5 h 48 min 46 sec (a) in one year (b) in 1 000 years?
Gregorian Calendar
The Julian Calendar was effective for many centuries. However, it was 11 min 14 sec too long. By the 16th century it was about10 days
ahead of the seasons. Pope Gregory XIII implemented the advice of astronomers:
• To bring the calendar in step with the seasons, the day after
5 October 1582 was designated as 15 October, removing 10 days from the calendar.
• The solar year was approximated as 365 d 5 h 49 min 12 sec or 36540097 days. Over a period of 400 years, this is 3 days less than the Julian Calendar. To make this change, it was suggested that 3 out of every 4 century years should not be leap years (as they would have been in the Julian Calendar). The new rule for leap years in the Gregorian Calendar was:
A year is a leap year if it is divisible by 4, but century years are not leap years unless they are divisible by 400.
The Gregorian Calendar is now the internationally accepted calendar.
3. What correction did the Gregorian Calendar bring to the Julian Calendar? That is, what is the time difference between the Julian calendar year of 365 d 6 h (36514 days) and the Gregorian calendar year of 365 d 5 h 49 min 12 sec (36540097 days)
(a) in one year (b) in 400 years?
4. The flow diagram below is a recipe to find out if a year is a leap year or not in the Gregorian Calendar.
Which of the following years are leap years?
(a) 1600 1700 1800 1900 2000 2100 2200 2300 2400 Is it true that 3 out of every 4 century years are not leap years?
(b) 2010 2016 2017 2018 2019 2020 2024 2040 2044 5. Can a leap year be an odd number? Explain.
6. How many leap years can occur in a decade?
Are there decades with fewer than two leap years? Explain.
7. Give all the leap years in the 21st century, that is, from 1 January 2001 to 31 December 2100.
8. 1 January 2016 was on a Friday. What day of the week is 1 January 2017? What day of the week will 1 January 2030 be?
9. Look at a calendar of the current year. On what day of the week is 1 July? On what day of the week will 1 July be 20 years from now?
is the year number divisible by 4?
Does the year number end on 00?
The year is not a leap year.
is the year number divisible by 400?
The year is a leap year.
The year is a leap year.
The year is not a leap year.
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