What is a Leap
Year?
A
year whose numerical value is exactly divisible by 4 is called a leap year. But
if the last two digits of the year is zero, then it must be divisible by 400.
For
example, 2004, 2012, 2016, etc. are leap year because these are divisible by 4,
but 2100, 2200, 2300 are not leap years even they are divisible by 4 because
they are not divisible by 400.
Why
do we have a leap year?
Leap
days align our modern-day Gregorian calendar with the Earth's orbit around the
Sun. It takes the Earth about 365.242189 days, or 365 days, 5 hours, 48
minutes and 45 seconds to revolve around the Sun. It is called the Tropical
Year, and it begins on the March equinox.
However,
the Gregorian calendar has only 365 days in a year. If we do not add a leap day
on February approximately every four years, then each calendar year will begin
6 hours before the completion of its revolution around the Sun.
As
a result, our time calculations will gradually diverge from the tropical year
and rapidly fall out of sync with the seasons. With a deviation of about 6
hours per year, the weather will change to about 24 calendar days within 100
years. Let it be for some time, and residents of the Northern Hemisphere will
be seen celebrating Christmas in the middle of summer in just a few centuries.
Leap
days fix that error by giving the Earth extra time to complete a full cycle
around the Sun.
Why don't we
add a leap day every 4 years?
If
the tropical year was 6 hours longer than a calendar year with 365 days, we can
use the Julian calendar, which without exception adds one leap day every 4
years. The deviation will increase for exactly 24 hours in 4 years, and will
require exactly one day to hold the Earth in its orbit to the position where it
was 4 years ago.
However,
the deviation between the normal year and the tropical year is slightly less
than 6 hours. The Gregorian calendar employs a slightly more complex set of
rules to determine which years are leap years. This is still not true, but the
resulting deviation is very small.
Why we miss a leap year after
every 100 years?
Why we add a leap year after
every 4 years and 400 years?
For the Gregorian calendar, the average length
of the calendar year (the mean year) across the complete leap cycle of 400
years is 365.2425 days.
365.2425 days = 365 days + 0.24 day + 0.0025
day
Or 365.2425 days = 365 days + 0.25 day – 0.01
day + 0.0025 day ……………. (i)
We take 365 days in a year.
0.25 day makes 1 day in 4 years, because 0.25 × 4 = 1 day.
So,
we add this 1 day in the leap year after every 4 years.
Again,
0.01 day × 100 = 1 day
In equation (i), we can see that 0.01 is with
minus sign and it makes 1 day after 100 years.
So, we subtract 1 day after 100 years. And miss
a leap year after every 100 years.
For example, 2088, 2092, 2096 will be a leap
year but 2100 will not be a leap year. 2104, 2108, etc. will again be a leap
year.
Now, we see in equation (i), 0.0025 is with
plus sign.
0.0025 day × 400 = 1 day
So,
we add this 1 day after 400 years.
Thus,
the year 2400 will be a leap year.
Conclusion
If a year number is a multiple of 4, it is a
leap year. But if the year number is a multiple of 4 and contains 2 zeroes at
the end like 2100, 2200, 2300, etc., then it should be a multiple of 400 to be
a leap year.
