Why Do We Have Leap Year ?

Date: 02/25/98 at 05:20:26
From: Pat
Subject: Why do we have Leap Year ?

Dear Dr. Math,

Why do we need to have one extra day each 4 years?  

Thanks,
Pat

Date: 02/25/98 at 13:45:33
From: Doctor Rob
Subject: Re: Why do we have Leap Year ?

This is an astronomical question, but I think I know the answer.

In short, the reason is to preserve the alignment of dates on the 
calendar with the seasons of the year.

As the Earth revolves around the Sun, it rotates on its axis.  
When it has made exactly one orbit around the Sun, it has made 
366.2422 rotations on its axis. One of those rotations is accounted 
for by its revolving about the Sun. (Think of a planet like Mercury 
for which one side always faces the Sun. After one revolution, it has 
made one rotation, but the Sun has never set on one side of Mercury, 
and never risen on the other.)  That means that 365.2422 days have 
elapsed. An ordinary year contains 365 days, not 365.2422 days.  
Since .2422 is about 1/4, every four years we have fallen behind by 
almost a full day. If we didn't do anything about this, after 700 
years we would have Summer in January and Winter in July! As a result, 
we insert an extra day, 29 February, to make a Leap Year.  

This arrangement results in what is called the Julian Calendar, 
supposedly invented by Julius Caesar (more likely just decreed by 
him). The average year is 365.25 days under this calendar.

Of course .2422 is not exactly 1/4, so we will be drifting a little, 
even with Leap Years. As a result, every year divisible by 100 is 
declared *not* to be a leap year. 1900 was not a leap year under this 
calendar. That means that the average year is 365.24 days, still a 
little off. To be even more accurate, every year divisible by 400 is 
declared to be a leap year, after all! Thus 2000 will be a leap year.  
This system is called the Gregorian calendar, since it was established 
by order of Pope Gregory in 1582. This was only adopted in English-
speaking countries in 1752, however, to be made retroactive. In the 
Gregorian calendar, the average year is 365.2425, which is off only 3 
days every 10000 years. No doubt someone will make more rules to fix 
even that slight deviation sometime in the future.

If you think this is complicated, you should see how the date of 
Easter is calculated!

-Doctor Rob,  The Math Forum
Check out our web site http://mathforum.org/dr.math/