Why do we have leap year in 2012, but not in 2011 or 2013? The issue is the length of time it takes the Earth to circle the sun. There is no reason in nature to expect the length of the year for a planet to be divisible evenly by its length of the day, but this failure has created a challenge for calendars throughout history. To account for the fact that it takes Earth 365.242196 days to orbit the sun, the ancient Roman implemented a system by which every fourth year would have an extra day (366 instead of 365). This “leap day” falls on the last day of February in 2012, as it did in 2008 and will in 2016, but not in-between. Later, during the Renaissance, this system was made more precise by omitting one leap day every four centuries; we leap a leap year if it is evenly divisible by 100 but not 400 (like 2100), giving us the "Gregorian" calendar that is now used throughout the world.
Figure this! On average, how many seconds does the month of February have? Assume a day is 24 hours (it isn’t but that’s for another column). Since 3,600 seconds are in an hour, 3600 × 24, or 86,400 seconds are in a day. But the answer isn’t an average of 2,419,200 seconds!
Hint: February usually has 28 days, except during leap years, when it has 29 days.
Get Started: In a 400-year span, how many leap versus non-leap Februarys occur?
Solution: 2,440,152 seconds. In 400 years, ninety-seven leap years occur. February has an average of 28.2425 days, since 303 × 28 = 8484, and 97 × 29 = 2813, so 8848 + 2813 = 11297 days. Dividing 11,297 by 400 equals 28.2425 days. Multiplying 28.2425 days by 86,400 seconds means February averages 2,440,152 seconds.
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