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The Physics of Leap Day
Category: Astronomy • Physics
Posted on: February 29, 2012 12:30 PM, by Ethan Siegel
Once every four years, the elusive entity that is today -- February 29th -- comes along. The historical origins and urban legends associated with it are incredibly interesting, but the reason there's any such thing as Leap Day at all is because of the physics of planet Earth.
The Earth, of course, is rotating on its axis while simultaneously revolving around the Sun. Rotation, as we all learn, is responsible for sunrise, sunset, moonrise, moonset, the Coriolis effect, and the rotation of all the stars in the night sky about the poles. Revolution, on the other hand, is responsible for the seasons; when your hemisphere tilted away from the Sun, that's when you have your winter (and minimum daylight), and when your hemisphere is tilted towards the Sun, that's when you have your luminous summer.
And you probably learned that a day is 24 hours, due to the rotation, while a year is 365 days (with an occasional 366 for leap years), taking care of the revolution. It turns out it's a little more complicated than that, so let's dive in!
The Earth completes a full rotation in less than 24 hours: 23 hours, 56 minutes and 4.09 seconds, to be more precise. But even though we've spun around a full 360 degrees, we've progressed just a little bit in our orbit around the Sun. If we insisted on using the 23:56:04.09 figure as our day, the Sun would be out at midnight for half the year! To fix the motion of the Earth around the Sun, we need those extra 3 minutes and 56 seconds to orient ourselves correctly.
That takes care of what a day is, but what about a year? A revolution -- for the Earth to return to the same position with respect to the Sun -- might be an interesting astronomical thing to mark, it isn't a useful definition for a year on Earth.
In order for the Earth to achieve the same seasonal position in its orbit around the Sun -- and trust me, if you live on Earth, you'll want to mark your calendars by the seasons -- you'll need for the Earth to be oriented the exact same way with respect to the Sun as it was exactly one revolution ago. We could do this from winter solstice to winter solstice, when the Earth's north pole (for me) points maximally away from the Sun, or any other arbitrary point in its orbit. This way of measuring the year, known as the tropical year, is actually a little shorter than the astronomical measurement of a year we might be tempted to make.
Because the Earth only needs to revolve slightly less than 360 degrees around the Sun to make one tropical year. The difference is tiny -- 359.986 degrees instead of 360 -- but enough to make the tropical year about 20 minutes shorter than the sidereal (or astronomical) year. This difference is known as precession, and it explains why the pole star in the night sky appears to change very slowly over a period of about 26,000 years. (25,771 years, for the sticklers.)
Combine all three of those effects together -- rotation, revolution, and precession -- and you can answer the question of how many days will it take the Earth to make a tropical year?
The answer, as precisely as we can figure for 2012, is 365.242188931 days. If we just had 365 days in the year every year, we'd be off by nearly a month every century, which is pretty lousy. Putting in a leap year (with an extra day) every 4th year gets us closer, giving us 365.25 days in a year. (This was how we kept time with the Julian Calendar, which we followed for 1,600 years!)
Still, this difference was significant enough that, by 1582, we had put in 10 too many days. For this reason, October 5th through October 14th of 1582 never existed in Italy, Poland, Spain and Portugal, with other countries skipping 10 days at a later date.
The Gregorian calendar, which we now follow, is exactly the same as the Julian calendar, except instead of having a leap year if your year is divisible by 4 (as 2012 is), you don't get a leap year on the turn-of-the-century unless your year is also divisible by 400! So even though 2,000 was a leap year, 1,900 wasn't and 2,100 won't be, but 2,400 will be again.
Category: Astronomy • Physics
Posted on: February 29, 2012 12:30 PM, by Ethan Siegel
Once every four years, the elusive entity that is today -- February 29th -- comes along. The historical origins and urban legends associated with it are incredibly interesting, but the reason there's any such thing as Leap Day at all is because of the physics of planet Earth.
The Earth, of course, is rotating on its axis while simultaneously revolving around the Sun. Rotation, as we all learn, is responsible for sunrise, sunset, moonrise, moonset, the Coriolis effect, and the rotation of all the stars in the night sky about the poles. Revolution, on the other hand, is responsible for the seasons; when your hemisphere tilted away from the Sun, that's when you have your winter (and minimum daylight), and when your hemisphere is tilted towards the Sun, that's when you have your luminous summer.
And you probably learned that a day is 24 hours, due to the rotation, while a year is 365 days (with an occasional 366 for leap years), taking care of the revolution. It turns out it's a little more complicated than that, so let's dive in!
The Earth completes a full rotation in less than 24 hours: 23 hours, 56 minutes and 4.09 seconds, to be more precise. But even though we've spun around a full 360 degrees, we've progressed just a little bit in our orbit around the Sun. If we insisted on using the 23:56:04.09 figure as our day, the Sun would be out at midnight for half the year! To fix the motion of the Earth around the Sun, we need those extra 3 minutes and 56 seconds to orient ourselves correctly.
That takes care of what a day is, but what about a year? A revolution -- for the Earth to return to the same position with respect to the Sun -- might be an interesting astronomical thing to mark, it isn't a useful definition for a year on Earth.
In order for the Earth to achieve the same seasonal position in its orbit around the Sun -- and trust me, if you live on Earth, you'll want to mark your calendars by the seasons -- you'll need for the Earth to be oriented the exact same way with respect to the Sun as it was exactly one revolution ago. We could do this from winter solstice to winter solstice, when the Earth's north pole (for me) points maximally away from the Sun, or any other arbitrary point in its orbit. This way of measuring the year, known as the tropical year, is actually a little shorter than the astronomical measurement of a year we might be tempted to make.
Because the Earth only needs to revolve slightly less than 360 degrees around the Sun to make one tropical year. The difference is tiny -- 359.986 degrees instead of 360 -- but enough to make the tropical year about 20 minutes shorter than the sidereal (or astronomical) year. This difference is known as precession, and it explains why the pole star in the night sky appears to change very slowly over a period of about 26,000 years. (25,771 years, for the sticklers.)
Combine all three of those effects together -- rotation, revolution, and precession -- and you can answer the question of how many days will it take the Earth to make a tropical year?
The answer, as precisely as we can figure for 2012, is 365.242188931 days. If we just had 365 days in the year every year, we'd be off by nearly a month every century, which is pretty lousy. Putting in a leap year (with an extra day) every 4th year gets us closer, giving us 365.25 days in a year. (This was how we kept time with the Julian Calendar, which we followed for 1,600 years!)
Still, this difference was significant enough that, by 1582, we had put in 10 too many days. For this reason, October 5th through October 14th of 1582 never existed in Italy, Poland, Spain and Portugal, with other countries skipping 10 days at a later date.
The Gregorian calendar, which we now follow, is exactly the same as the Julian calendar, except instead of having a leap year if your year is divisible by 4 (as 2012 is), you don't get a leap year on the turn-of-the-century unless your year is also divisible by 400! So even though 2,000 was a leap year, 1,900 wasn't and 2,100 won't be, but 2,400 will be again.
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