Why Do We Have Leap Years? July 12 2008

Learn why we have leap years and how the leap year system works.February 29th occurs only once every four years - “leap” years - but how and why did this practice develop?

Throughout history, cultures around the world have observed a relationship between celestial events and the cycle of life.

This relationship is most notable in terms of seasons.

Each spring, for example, the sun passes over the equator and climbs into the northern hemisphere, and around this same time:

  • Plants begin to grow and pollinate
  • Migrating animals return to their summer homes
  • The mating season of many animals begins

After observing this relationship, ancient cultures learned to use the sun’s position along with cycles of the moon for agriculture (i.e. when to plant, when to harvest, etc.). Over time, calendars were developed to allow for the prediction of seasons, and celestial events were used for alignment.

Traditionally, time has been measured in relation to two major events: the rotation of the earth on its axis, and the orbit of the earth around the sun:

  • 1 rotation of the earth on its axis is called a “day”
  • 1 orbit around the sun is called a “year”

In technical writing and conversation, however, these measurements are commonly referred to as “solar days” and “solar years,” because the length of time it takes the earth to spin on its axis is actually slowing over time and the length of time it takes the earth to orbit the sun is not an exact number of days (it cannot be evenly divided into 24-hour blocks).

Historically, cultures have accounted for this discrepancy in varying ways. One of the most complicated methods is used in the Chinese calendar, which follows an intricate set of rules that add in leap months to maintain the position of the Chinese New Year and the winter solstice.

The “Gregorian” calendar, today’s most widely used calendar, measures a common year (or non-leap year) as exactly 365 days. However, the earth actually takes 365 days, 5 hours, 48 minutes, and 45.36 seconds  to complete one orbit around the sun, or roughly 365¼ days. By adding an extra day every 4 years this calendar is able to more accurately maintain alignment with the earth’s orbit (For a complete description of the leap-year rules see below).

Interestingly, because the celestial events on which all known calendars depend are not constant and cannot be reliably predicted in the long term , in order to remain accurate over vast amounts of time, any calendar will have to be regularly adjusted to account for celestial changes.

Gregorian Leap Years

The complete rule for leap years in the Gregorian calendar states that a year will contain 366 days if:

  • it is divisible by 4
  • and it is not divisible by 100
  • or is also divisible by 400

Examples

  • Both 1896 and 1904 are leap years because they are divisible by 4
  • Because 1900 is divisible by 4 and 100 but not by 400, it is not a leap year
  • Because 2000 is divisible by 4, 100, and 400, it is a leap year

Explanation

The rule of adding an extra day every 4th year would by itself be accurate if the solar year was exactly 365.25 days long, but because it is closer to 365.24 days the more complex rule is used to increase accuracy over time.

Seasons

Today, there are two major methodologies used to determine the start and end of the seasons: Astronomical and Meteorological.

Astronomical

In this methodology, the start and end dates of the 4 seasons are marked by the equinoxes (the days during which the center of the sun is directly above the earth’s equator) and solstices (the days during which the sun has reached either is most northern or most southern point).

In the northern hemisphere,

    * Spring begins with the March equinox (20 March)
    * Summer begins with the June solstice (20 June)
    * Fall begins with the September equinox (22 September)
    * and Winter begins with the December solstice (21 December)

In the southern hemisphere,

  • Fall begins with the March equinox (20 March)
  • Winter begins with the June solstice (20 June)
  • Spring begins with the September equinox (22 September)
  • and Summer begins with the December solstice (21 December)

Meteorological

Using this methodology, the seasons divide the calendar year into four quarters of varying average temperatures with summer being the hottest and winter the coldest.

In the northern hemisphere,

  • Spring begins 1 March
  • Summer begins 1 June
  • Fall begins 1 September
  • and Winter begins 1 December

In the southern hemisphere,

  • Fall begins 1 March
  • Winter begins 1 June
  • Spring begins 1 September
  • and Summer begins 1 December

Birthdays

The legally recognized common-year birthday of an individual born on February 29th varies from country to country. In the U.S., “leaplings” are considered to have reached a “legal age” on 1 March in common years, while the day that is socially celebrated depends on the choice of the individual.

References

  • (Aslasken 2007)
  • (Wikipedia: Tropical Year 2008)
  • (Locke 1999) & (Leap Seconds 2006)
  • (Wikipedia: Season 2008)

Sources

  • Aslasken, Helmer. "The Mathematics of the Chinese Calendar." Department of Mathematics, National University of Singapore. February 15, 2007. http://www.math.nus.edu.sg/aslaksen/calendar/chinese.html (accessed February 11, 2008).
  • "Leap Seconds." US Naval Observatory, Time Service Department. Febraury 10, 2006. http://tycho.usno.navy.mil/leapsec.html (accessed February 11, 2008).
  •  Locke, William Ph.D. "Milankovitch Cycles." Montana State University. May 18, 1999. http://www.homepage.montana.edu/~geol445/hyperglac/time1/milankov.htm (accessed February 11, 2008).
  •  "Wikipedia: Season." Wikipedia, the free encyclopedia. February 9, 2008. http://en.wikipedia.org/wiki/Seasons (accessed February 11, 2008).
  •  "Wikipedia: Tropical Year." Wikipedia. February 5, 2008. http://en.wikipedia.org/wiki/Solar_year (accessed Febraury 11, 2008).

-by Dagan Henderson