Saturday, January 28, 2017
February the 29th
February the 29th
February is usually the cold-dark-and-sneeze month that we all wish will end soon, but this year it got extended by one extra day. Leap year. 2012 is divisible by 4 (I checked: 2012 / 2 = 1006, 1006/2 = 503), so here we have February the 29th. I vaguely remembered that this extra day comes because earth rotation around the sun is not exactly a 365 day cycle, but rather a bit more - something like 365 and 1/4. Therefore, we need to add an extra day every 4 years to catch up with the nature. This story was good enough for me but wont be for my kids. These curious monkeys will interrupt with some unexpected questions. It will be too late at night to Google it, and next day we will all forget. So, lets prepare the bases and research this a bit more.
How do we know the precise time it takes for the Earth to rotate around the Sun? Each year we have two special days: one around March 20-21st and another around September 22-23rd. We mark these days as the beginning of Spring and the beginning of Autumn in the Northern Hemisphere and on opposite in the Southern Hemisphere. At some point during these days the Sun is positioned right above the Earths equator making day and night approximately equal in length all over the world. Remember that nights are shorter than days during winter and longer in summer. Astronomical year defines a full cycle of the Earth around the Sun and is measured in-between these "equal" Spring moments (that are called "equinox"). Right now this period is 365.242374 days and it is slowly increasing! Increasing??? Why? Does the Earth gets older and moves slower or the Earths orbit around the Sun expands? Aha! Now you remember hearing that the Earth is slowly moving away from the Sun. So, thats true..
Back to the 365.242374 number. How to count the tiny remainder in our calendars? Lets try avoiding it altogether and always count 365 days in a calendar year: in about 4 years Spring (and all the rest of the seasons will shift by 1 day), in 120 years by 1 month, in 720 years by 6 months and the seasons will completely swap. Imagine a heat wave on Christmas and freezing cold during a summer vacation!
So, we have to account for the 0.242374 to prevent such weather scrabble. Every four years: 4 x 0.25 = 1 extra day. Here it is - February 29th. But wait, there is more! The remainder is not exactly a quarter, rather a bit less: 0.25-0.242374=0.007626 Small number that gains weight only when multiplied by a 100 or so. We need to weed out some leap years about every 100 years. It was agreed that years that are divisible by a 100 and not divisible by 400 will not be considered leap years (even though they are divisible y 4). For example, years 1600, 200, 2400, 2800 are leap years while 1700, 1800, 1900, 2100, 2200 are not.
Now it makes sense why it is called a "leap" year - calendar year is catching up with the actual astronomical year to avoid snow on summer vacation. And different calendars (Julian, Gregorian, Chinese, Hebrew, Islamic etc. ) do it differently. But this is another much more complicated story.
P.S. Satisfied with the information I learned I told it to my kids at bedtime on February the 29th and my son did startle me with an unexpected question: when was the first leap year? Was it year 4?
I still couldnt find the exact answer to his question but I read that Egyptians were the first to come up with the idea of using leap day to keep the calendar in sync with the earth rotation. Julius Caesar adopted the idea in the Roman empire. However, the Julian calendar had only a simplified leap rule - leap year every four years that over the years resulted in accumulation of too many extra days. This got corrected only when Gregorian calendar was introduced in 1752 and a leap of 11 days was necessary to catch up with the Earth and Sun.
Image by jronaldlee, distributed under CCL.
How do we know the precise time it takes for the Earth to rotate around the Sun? Each year we have two special days: one around March 20-21st and another around September 22-23rd. We mark these days as the beginning of Spring and the beginning of Autumn in the Northern Hemisphere and on opposite in the Southern Hemisphere. At some point during these days the Sun is positioned right above the Earths equator making day and night approximately equal in length all over the world. Remember that nights are shorter than days during winter and longer in summer. Astronomical year defines a full cycle of the Earth around the Sun and is measured in-between these "equal" Spring moments (that are called "equinox"). Right now this period is 365.242374 days and it is slowly increasing! Increasing??? Why? Does the Earth gets older and moves slower or the Earths orbit around the Sun expands? Aha! Now you remember hearing that the Earth is slowly moving away from the Sun. So, thats true..
Back to the 365.242374 number. How to count the tiny remainder in our calendars? Lets try avoiding it altogether and always count 365 days in a calendar year: in about 4 years Spring (and all the rest of the seasons will shift by 1 day), in 120 years by 1 month, in 720 years by 6 months and the seasons will completely swap. Imagine a heat wave on Christmas and freezing cold during a summer vacation!
So, we have to account for the 0.242374 to prevent such weather scrabble. Every four years: 4 x 0.25 = 1 extra day. Here it is - February 29th. But wait, there is more! The remainder is not exactly a quarter, rather a bit less: 0.25-0.242374=0.007626 Small number that gains weight only when multiplied by a 100 or so. We need to weed out some leap years about every 100 years. It was agreed that years that are divisible by a 100 and not divisible by 400 will not be considered leap years (even though they are divisible y 4). For example, years 1600, 200, 2400, 2800 are leap years while 1700, 1800, 1900, 2100, 2200 are not.
Now it makes sense why it is called a "leap" year - calendar year is catching up with the actual astronomical year to avoid snow on summer vacation. And different calendars (Julian, Gregorian, Chinese, Hebrew, Islamic etc. ) do it differently. But this is another much more complicated story.
P.S. Satisfied with the information I learned I told it to my kids at bedtime on February the 29th and my son did startle me with an unexpected question: when was the first leap year? Was it year 4?
I still couldnt find the exact answer to his question but I read that Egyptians were the first to come up with the idea of using leap day to keep the calendar in sync with the earth rotation. Julius Caesar adopted the idea in the Roman empire. However, the Julian calendar had only a simplified leap rule - leap year every four years that over the years resulted in accumulation of too many extra days. This got corrected only when Gregorian calendar was introduced in 1752 and a leap of 11 days was necessary to catch up with the Earth and Sun.
Image by jronaldlee, distributed under CCL.
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