Here’s Why There Is A Leap Day

There is a leap day because the Earth’s orbit and the 365-day calendar don’t precisely line up since the Earth orbits the sun in 365 days and 6 hours. Hence, every 4 years a leap day, February 29th, has to be added to correct for the difference.

Every four years, February gains an extra day. February 29th is known as a Leap Day, and it is in a Leap Year. Why is there a Leap Year and a corresponding Leap Day every four years? It has to do with how the Earth revolves around the sun. The Earth follows an elliptical orbit around the sun, and one year is counted by how long the Earth takes to complete one revolution around the sun. It is said that it takes the Earth 365 days to complete one revolution around the sun, but that’s not quite right. It actually takes slightly longer than that, about 365 days and 6 hours, or 365 and a quarter days.

Why does it take 365 and a quarter days to move around the sun? It is due to the sun’s gravitational pull.

How The Earth Rotates Around The Sun

Photo: RioMike via Pixabay, CC0

The amount of mass an object has is directly related to its gravitational pull. Greater gravitational pull comes from more mass. The sun has a mass of 1.98892 x 10 to 30th power kilograms. This mass is approximately 330,000 times greater than the mass of the Earth, meaning that the sun has a massive gravitational pull on the planets in the solar system. Due to the powerful gravitational pull of the Earth, it is forced to follow an orbit around the sun, much like the solar system’s other planets. This is similar to how the moon revolves around the Earth. The Earth’s gravitational pull is much more powerful than that of the moon, because the moon has less mass than the Earth, meaning the moon must follow an orbit around the Earth.

Gravity isn’t the only thing impacting the Earth though. The Earth also has velocity. This velocity is moving the Earth perpendicular to the pull of the sun. This velocity came from the formation of the solar system, from the spin the Earth first had during that time. Since space is a vacuum, there is no friction in space that can slow down the Earth’s velocity. The gravitational pull of the sun is just powerful enough that it pulls on the Earth but doesn’t change the planet’s own velocity. This means that the Earth is in a constant state of angular momentum, spinning around the sun. If the Earth didn’t have its own velocity, the sun’s gravity would simply pull the Earth into the sun.

Photo: Tauʻolunga via Wikimedia Commons, CC 1.0

It is possible for you to illustrate angular momentum by using a ball with a string tied to it. Tying the ball to one end of the string and swinging the string in a circular fashion will cause the ball to rotate, or orbit, around the center point of your hand. Though you are constantly pulling on the string, the ball’s own velocity prevents it from falling. If you were to suddenly let go of the string, the ball would go flying off straight away from you, and so would the Earth if the sun were not exerting influence on it with its gravitational pull.

This complex interaction of gravitational pull and velocity is what makes the Earth orbit the sun, and the Earth’s distance from the sun combined with its velocity influences how long it takes the Earth to complete one revolution around the sun, which is 365 and ¼ days.

Why Have A Leap Day?

Photo: Gothika via Wikimedia Commons, CC 3.0

The fact that the Earth takes 365 and a quarter days to revolve around the sun can cause problems when it comes to creating calendars to organize our schedules. The Gregorian calendar we follow today includes a leap year every four years, which adds in February 29th, an extra day. Because this is done it allows us to keep a consistent calendar based on a year and the seasons. If Leap Days were not employed we would be off by nearly a month at the end of every century.

The History of Leap Years and Leap Days

The first civilization to recognize the need for a leap year was Egypt, though the practice was not really used until the time of Roman emperor Julius Caesar. Prior to Caesar’s reign, the Roman calendar utilized a model that was based on the moon and needed an extra month added to maintain consistency. During Caesar’s reign, around 46 BCE, the astronomer Sosigenes made changes to the Roman calendar. The now familiar 12-month system with 365 days was created then, referred to as the “Julian Calendar”. The Julian calendar tried to account for the longer solar year by throwing in a leap day every four years.

This new system worked better than the old calendar system, but it still wasn’t perfect. The solar year is actually about 0.242 days longer than the calendar year, instead of an even 0.25, which meant that under the Julian Calendar system there was still 11 surplus minutes every year. This discrepancy leads to an accumulated 10 days off the solar year by the 14th century, or a drift of approximately one day ever 128 years. Pope Gregory XIII oversaw the creation of another calendar revision, the new calendar was dubbed the “Gregorian Calendar”. Under this new, and our current, calendar system leap years happen every four years. Almost. Technically, leap years occur only in years not evenly divisible by 100 (but not by 400), and as an example, the year 1900 was not a leap year.

Calendar experts have noted that there are still discrepancies with this system that will have to be handled in approximately 10,000 years.

Changes To The Earth’s Speed

While normally under the current calendar system it would take around 3,200 years for our calendar to be off for a single day, realistically it could be a shorter amount of time. The Earth’s rotation is actually changing subtly over time, thanks to two different phenomena.

Earthquakes actually change the mass of the Earth itself a little bit, and thanks to the conservation of angular momentum, the rotation of the Earth actually increases in speed. A large Earthquake in Japan during 2015 speed up the Earth’s rotation and made the day about 1.8 microseconds shorter, and the 2004 Sumatra earthquake made the day 2.8 microseconds shorter.

While Earthquakes speed up the Earth’s rotation a little, the moon also pulls on the Earth, in addition to the sun. Both the Sun and Moon actually exert greater gravitational influence on the sides of the Earth that are facing them. This effect, combined with the Earth’s natural rotation, causes “tidal braking” which slows the Earth down. The slowdown means that there’s a difference between the length of an actual day and our 86,400 seconds in a measured day. How do we compensate for this difference? We add in an extra “leap second” every 18 months.

Leap days and leap seconds point to how complicated creating a system of measurement for time can actually be. We take the calendar systems we live with for granted, but they are an impressive achievement of science.