# Why isn't the day backwards between leap years?

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So every four years, we add an extra day. A leap year. This is because a year is actually $365_{1/4}$ days long. But what happens between leap years? After two years, it would get dark at 8:00 AM instead of 8:00 PM. This is obviously not the case. What's going on here?

As a simplification, think of the length of the year as where the Earth is in its orbit. After 1 year of 365 days, the Earth has not returned to the same spot in its orbit. If we did not have leap years, then the date when seasons occur would change. Leap years keep the seasons in synch with the date. After 365+365+365+366 days (that is, 3 regular years and 1 leap year = 365.25*4), the Earth is at the same spot in its orbit. (This is approximately true because the year is not exactly 365.25 days long).

On the other hand, when it gets dark is related to the length of the day, and that is independent of the length of the year. In order for it to get dark at 8 am, you would need to reset your clocks to 0 after 1 exact orbit (365.25 days).

Now for a little more detail. There is a slight difference between a year measured "when the Earth returns to the same spot in its orbit" as I described above and a year measured "from one vernal equinox to the next". (The first definition is the sidereal year, and the second definition is the tropical year). The "Sidereal vs. Synodic Motions" webpage explains why the sidereal year is about 20 minutes longer than the tropical year. Our calendar is based on the tropical year. So after 1 tropical year (365.242 mean solar days), the Earth still has not returned to the same spot in its orbit! Details, details, details!

Leap seconds keep the clock in sync with solar time of day. Leap years keep the calendar in sync with the seasons. The two (leap seconds and leap years) have nothing to do with one another. We have leap seconds because a day is now a tiny bit longer than 86400 seconds. We have leap years because a year (tropical year) is about 365.24219 days long.

If we didn't have leap years but did have leap seconds, solar noon and noon by the clock will continue to occur at more or less the same time (ignoring cyclical changes such as the equation of time and daylight saving time). The calendar would become out of sync, becoming almost a month off from the seasons in just a century. Adding an extra day every four years doesn't quite do the trick; this is why 2100, for example, will not be a leap year.

## Why isn't the day backwards between leap years? - Astronomy

How would you define a year? To many people, it’s the time from birthday to birthday, or it might be the days from January 1 to December 31. This is known as a calendar year. A year might also be defined as the time it takes for the earth to orbit the sun. This is called a solar year. The problem is that the earth takes about 365.25 days to go around the sun in relationship to the stars. Over time, this means that every four years, the earth is out of sync with the calendar by one day. Pioneers in science realized that this would be a problem.

This may not seem like a big deal in one person’s lifetime, but after 100 years, the calendar and solar years would be out of sync by 25 days. The calendar might say March 20, the first day of spring, but the solar system would be well into the growing season. In a few more centuries, people might be celebrating Christmas during the summer. Because the world relies on the calendar year, instead of the solar year, it’s imperative that the two be in sync.

Astronomers Noticed Problems with the Calendar and the Seasons

Julius Caesar and a group of scientists and astronomers in the first century studied and researched this phenomena, but they didn’t really have a scientific plan to offset the problem. His calendar system, known as the Julian calendar, sometimes added an extra day to February. In the 1500s, the calendar and the seasons were still off by about 11 days. Pope Gregory XII and his astronomers continued to observe and study this problem with time. Eleven days were added. In 1582, everyone went to bed on March 11 and woke up on March 22.

Using mathematics, technology of the time, and science, the Pope’s astronomers came up with the current calendar system, the Gregorian calendar. This is where the science of leap year started. One additional day would be added to the calendar every four years. In the Gregorian calendar, century years would only be leap years if they were divisible by 400. It was a small change, but necessary to keep the seasons and calendar in sync. Because the solar calendar isn’t exactly an extra one-quarter day, in about 3,000 years, scientists will need to further adjust the calendar.

Legend has it that in the 5th century, St. Patrick of Ireland gave permission for women to propose to men on February 29. Another tradition states that if the man refused the proposal, he would have to pay a fine to the lady, like maybe buy her a skirt or new pair of gloves. In Greece, it’s considered bad luck to begin an engagement or get married during a leap year.

Each state has different laws about how birthdays on February 29 are handled when it comes to getting your driver’s license. In Michigan, leap year babies have to wait until March 1 to go to the DMV, but in some places the date is February 28. This law doesn’t affect too many people in the United States, only about 187,000. A baby only has about a 1 in 1,500 chance of being born on February 29.

Take time this year to make February 29 a day of science and knowledge. Study astronomy to understand the early scientists who gave us leap year. Much of today’s GPS technology and advancements in aerospace is thanks to the understanding and science of the stars. Scientists developed theories about the nature of the stars by studying their position. Look to the sky and see the beauty, but don’t forget to see the physics and science of the observation of the stars.

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Leap years in the western calendar were first introduced over 2000 years ago by Roman general Julius Caesar. The Julian calendar, which was named after him, had only one rule: any year evenly divisible by four would be a leap year.

This formula produced too many leap years, causing the Julian calendar to drift apart from the tropical year at a rate of 1 day per 128 years. This was not corrected until the introduction of the Gregorian calendar more than 1500 years later, when a number of days were skipped to realign our calendar with the seasons.

You're right that a "sidereal" day is about 23 hours, 56 minutes, 4 seconds. But this is not a day in the everyday sense.

A sidereal day is how long it takes the earth (on average) to make one rotation relative to the faraway stars and other galaxies in the sky.

If you find a star that is directly above you at midnight one night, the same star will be directly above you again at 11:56:04 p.m. the next evening.

Similarly, if you were sitting on the star Proxima Centauri looking through a powerful telescope at earth, you would see Toledo, Ohio, go by every 23 hours, 56 minutes, and 4 seconds.

However, we don't keep time by the faraway stars -- we measure time by a much closer star, the sun! And we are actually in orbit around the sun, orbiting in the same direction that the earth is spinning on its own axis. From our perspective, the sun goes a little slower in the sky because we are also orbiting around it.

How fast are we orbiting around the sun? We make one full orbit every year, or roughly 366.25 sidereal days.

So after a year, the faraway stars will have done 366.25 rotations around the earth, but the sun will only have done 365.25 rotations. We "lose" a sunset because of the complete orbit. (The extra quarter day is why we need a leap year every four years.)

So there are 365.25 "mean solar days" in 366.25 "sidereal" days. How long is a "mean solar day"? Let's do the math: One sidereal day is 23 hours, 56 minutes, 4 seconds, or 86164 seconds. Multiply this by 366.25 sidereal days in a year, and you get 31557565 seconds. Divide by 365.25 solar days, and we get that a solar day is. 86,400 seconds. That's 24 hours exactly!

It's this "mean solar day" (24 hours) that is the normal definition of day.

If you want to do the math more exactly, a sidereal day is 86164.09054 seconds, and a tropical year is 366.242198781 sidereal days. That works out very closely.

(P.S. Unfortunately, the earth's spin has been slowing down because the moon is sucking away the earth's energy. Every time the high tide of the Atlantic Ocean slams into the east coast of North America, the earth slows its spin a little bit. The definition of the second is based on the speed the earth was spinning back in 1820, and we have slowed down since then. As a result, we occasionally have to add in a "leap" second to the world's clocks. See http://online.wsj.com/article_email/SB112258962467199210-lMyQjAxMTEyMjIyNTUyODU5Wj.html?mod=wsj_valetleft_email )

So after a year, the faraway stars will have done 366.25 rotations around the earth, but the sun will only have done 365.25 rotations.

Isn't that a wrong statement.

Shouldn't that be: "So after a year, the earth will have done 366.25 rotations around the faraway stars, but will only have done 365.25 rotations around the sun."

No, because we can take the Earth as the centre of the universe (relatively speaking). Since historically (but also PRACTICALLY today!) we observe motion relative to our own frame of reference, the centre of which is the Earth, not the sun or a star. (Obviously we rotate around the sun and with the sun around a galactic centre, but from our perspective we are at the centre)

Hence the stars appear to rotate around the Earth, just like the sun apears to rotate around the Earth. Just like the rails and the trees appear to move when you are on the train and everything on the train with you appears to be still.

Hence the difference between a sideral and a solar day: one is based on the RELATIVE motion of the "fixed stars" around the Earth and the other the relative motion of the sun.

(btw the stars are caled "fixed", because they appear not to move at all. since they are so far away. Hence before modern technology it was very difficult to detect any motion of the stars, since a perceptible change in the position of the stars might be detected only between quite long time spans, centuries or millennia even.)

Actually,the sun moves away from the center of the universe. As it moves,the planets "try to escape the gravitational pull from our star" . There is "drag and push " energies. Also the moon doesn't "spin"around the earth. As the earth "travels" around the sun,the moon "weaves" a path,around earth,around the sun and rotates so the same side faces earth. Quite a statement for there being a GOD! No man could do this.

well I think theis (*this) is obsruse becuswe (*because) whe are trying to lie to us the earth doeasn't spin because it is flat you sillies the sun and moon and stars orbit around us.

Yes, well of course if a man couldn't do it, it must be god. You've figured it out! No science here! Just god! (idiot.)

Please don't say 'God did it' when you clearly don't understand any of the smallest fundamentals. Just because you don't understand doesn't make it magic.

First of all every point in this universe is it's centre so there is no centre around which the sun is moving. The sun is actually revolving around a huge black hole which is situated at the centre of our galaxy ( not universe). Secondly, no planets are trying to escape the gravitational force, the gravitational force is what makes planets revolve around their stars. Finally, the moon also rotates around it's axis and I don't think that god intervenes in any of these physical laws anymore and he must have let the universe evolve according to these laws.

Before reading this article, I entered a question, "Why is the day not exactly 24 hours?" While I found the message here very well written and I learned a lot. My question is still not answered.

My problem and this question are quite similar. One day represents the amount of time it takes for the Sun to appear in the same point in the sky one day from now. Or in terms of a Sun dial, when the shadow on the Sun Dial appears at the same place twice, one day has elapsed. If the last statement is true, then why is our definition of a day so flawed?

I get that a day back in 1820 was slightly different than a day now. This fluctuation makes it hard (or at least harder) to come up with a day that is actually 24 hours. With modern day technology having a day that is exactly 24 hours is certainly possible. What is preventing us from adopting this type of hour?

Please forgive the tone of this message. I find it frustrating how hour falls short of its definition. Thoughts?

Kevin, it's because the time in a day actually fluctuates on a constant basis. A day today might be 24 hours and .72 milliseconds but tomorrow it may be 24 hours and .91 milliseconds and 5 months from now it may be actually ever so slightly under 24 hours. We have to add time every so often to account for the fact that our measuring for a day ends up being a fraction of a millisecond shorter than an average real day. If it was always the same amount shorter and never fluctuated, I think we would account for it with our abilities today, as you suggested.

@Michael Burton
Yes, just because you don't understand things doesn't make it magic. I wholly agree on that.
But if you did understand it, would you yourself believe that it was a result of a random accidental chance?

Who was it that said that magic would be indecipherable from incredibly advanced technology? Or something along those lines? Its not god and magic, its an alien who got bored and said "screw it, lets see how far i can take this." Or whatever that would translate into in his/her alien language.

NO! That isn't correct either. Relative to other stars the Sun is (sort of) fixed. Because of the Earth's rotation around the Sun, the other stars APPEAR to rotate around the Earth. In fact, they don't. And the Earth would have to travel an incredible distance to rotate around a faraway star.
The Sun's position to a faraway star is not really fixed - everything is in motion - but it does not play in this discussion.

There Are Actually 365.25 & There Are 24 & Almost 1 Extra Minute

ALL OF YOU ARE WRONG. WE ACTUALLY HAVE 26 HOURS A DAY, 13 HOUR CLOCK, BECAUSE THERE IS SMALL ISLANDS THAT NOT A LOT OF PEOPLE LIVE THERE, THERE IS UTC+13 AND 14, SO WE HAVE ADDITONAL 2 HOURS, BUT WE JUST NORMALLY DON'T COUNT THE ISLANDS, SO WE JUST SAY 24 HOURS IN A DAY. SCREW YOUR SELF NOW, I'M DONE FOR NOW, BUT WILL BE BACK, I HOPE, I GUESS, BYE NOW.

ALL OF YOU ARE WRONG. WE ACTUALLY HAVE 26 HOURS A DAY, 13 HOUR CLOCK, BECAUSE THERE IS SMALL ISLANDS THAT NOT A LOT OF PEOPLE LIVE THERE, THERE IS UTC+13 AND 14, SO WE HAVE ADDITONAL 2 HOURS, BUT WE JUST NORMALLY DON'T COUNT THE ISLANDS, SO WE JUST SAY 24 HOURS IN A DAY. SCREW YOUR SELF NOW, I'M DONE FOR NOW, BUT WILL BE BACK, I HOPE, I GUESS, BYE NOW.

this is the single greatest response on this topic.

I'm just going to say hi ( ͡o ͜ʖ ͡o)

I'm pretty sure there are 24.3 hours in a day,making 365.25 days in a year.The .25 adds up to one day known as the leap day every 4 years.However it doesn't add up to a full day,WHICH IS 24.3 HOURS.

Wow, your stupidity is truly impressive.

Leap year was created to help scientists fudge numbers to fit into theory of spinning round globe. If earth is a sphere it is 360 degrees dived by 24hrs= 15 degrees per hour. End of story only they have to change the story to fit their wrong model. They know if they keep 24 hr day noon will turn to midnight in 6 months.

The flat Earth model can't predict the length of days, the phases of the Moon, the need for leap years, the timing of eclipses or anything else. Come back when your model predicts something.

Just put the fucking number. You don't have to write an entire article about it fuckhead.

Wow! Your command of civilised speech is truly UNimpressive. Best that you keep the vulgar stuff for just you and your mates.

Andy: so right about vulgarity, I prefer civility, but please dont enter any spelling bees, you spell civilised. civilized.

Mate, just because a man puts an 's' in his words instead of a 'z' doesn't mean he cannot spell. Snelt isn't the only fuckhead in this thread.

People from other countries exist, and have different spellings than American English (simplified). Are you going to shit on my oxford comma as well? Read the Chicago style guide before you jump off a cliff.

no bad word i'm a kid not a ault

I thought the hours in a day were just however a person wants his or her clock calibrated ,time a night on a power pole from sunrise to sunrise and have a clock computer programmer divide that into how many hours minutes and seconds you want , a digital watch is just a computer program basically. anything a person wants ,

Hah, very nice post, respect.

This comment has been removed by the author.

This entire model is wrong and very easy to prove so. If it is noon on Jan 1 and the sun is directly overhead, i.e. you are facing the sun, and as we have concluded, except for brainiac above who thinks there are 26 hours in a day, the rest of us know there are basically 24hrs in a day. We can also say this model of the sun and the earth makes 1 full complete 360 degree rotation in that 24 hours. Now fast forward 180 days to about July. It is now noon again, and you have made exactly 180, full 360 degree turns. You are also exactly 180 degrees from where you started on January 1. Problem is you are facing 180 degrees opposited the sun in complete darkness with the sun on the opposite side of the earth, yet it is still noon. It doesn't work no matter what you do to try and make it so. It's a little fact they have always hidden in plain sight. Now, ask your self why your education programs, your teachers, and your governments have lied to you and told you the the earth is a round ball that circles around a sun your entire life. Simply it can not be.

I just randomly had this thought earlier in the evening and my friends couldn't grasp what I was tryig to explain to them. It seems like such a stupid thing to try to cover up, but at the same time seems impossible for me to try to prove false. Can't find anything on the subject!

A full orbit around the sun (a year) is not 360 days. A non-leap year has 365 days. The earth rotates another two and a half times on its axis by the time it completes a full 180° around the sun.

Shaun, I have been pondering this same thing. And wondering Why if the true day is 23hr 56 minutes but we have a 24 hour clock, then in one year of 365 days we will have 1,460 minutes or 24.3 hours of time Ahead of where 365 rotations Should be. So that is one thing.

The other is, with that in mind from a ball earth POV. I thought, if we keep the same facing point/direction for our full rotation. I know the thing about compasses but just work with me on this for a moment, ok. in 23hr 56 minutes the ball Earth will have made one rotation from N facing to N facing. We agree on this (I am using N only as a directional marker and not an actual direction, it could just as easily be 12 oclock on a clock face for this purpose). BUT, from Ball Earth POV, it will also now be slightly to the Side of the Sun, which was also originally N of our starting point but is now ever so slightly NW now compared to the start point. With the 24 hour clock we don't consider the rotation to be complete for another 4 minutes. In that time BE will have Spun just a small amount more and so while the True full rotation was 360 deg in 23 hrs 56 min, our 24 rotation is 360 + a bit. And with that extra Bit we now still face the Sun.

I already showed that with the extra 4 minutes there is an entire day ahead of ourselves. But over 6 months that is 12 hours ahead of actual. That places us on the opposite side of the Sun to which we started in BE model, the True rotation starting face is facing Away from the Sun as you know and said, but we, with our 4 extra minutes are a full 12 hours out of sync with that and are facing in the opp direction, or To the Sun.

In other words, after 6 months of BE rotations, the point which did face the Sun is now on the opp side of the Sun and facing away from the Sun. YOu are correct. BUT, because we added 4 minutes every day, and we go by that man made clock time, in 6 months time our man made clock has us a full 12 hours out of sync and thus we are in daylight instead of darkness, as it would be if we had used a 23.56 clock time.

IN terms of clock minutes. actual 23.56 rotation is 1436 minutes in a day while we work on 1,440. After 182 days (or 182.5 for a 365 day year) the Earth 23.56 clock has done 182 spins for 261,352 minutes or 4,356 hours. The 24 hour clock will be 262,080 minutes or 4368 hours. The difference between the two is 12 hours. So we are 12 hours out of sync and facing 180 deg in the opp direction, and thus To the Sun.

This still doesn't prove BE, but explains why we aren't facing away from the Sun after 6 months.

## Conclusion

When do leaplings, people who were born on February 29, celebrate their birthdays during common years? Most leapers, as leaplings are sometimes known, celebrate either on February 28 or March 1 in common years. If I were a leapling, I’d probably celebrate both days.

So, enjoy your Leap Day 2020 (it is a Saturday). What is one thing people can do differently today? According to ancient tradition, it’s OK for a woman to propose to a man on Leap Day. I certainly am not one to object to tradition.

## Why do we have leap years? Illuminating video exposes truth about Earth's wonky orbit

In 2020, we are blessed with an extra day, February 29. Every four years, we experience a leap year — a 366-day-long year that exposes a discrepancy between our calendar year and how long it actually takes for the Earth to orbit the Sun.

But a new visualization reveals that far from being just a conveniency of the calendar, leap years are actually critical if we want everyday life on Earth to run the way we need it to.

The visualization, created by James O’Donoghue, planetary scientist at Japan Aerospace Exploration Agency, explains the astronomical reasoning behind leap years

Earth takes a little more than 365 days to orbit around the Sun. In fact, the Earth takes exactly 365.2422 days, which is about six hours longer than what we account for in a calendar year.

As a result, each year the Earth falls a little short of being in the exact same spot as last year in its season.

“It’s funny because we measure our year in the number of rotations of Earth, that is already the problem right there,” O’Donoghue tells Inverse.

“We don't have a set number of rotations per orbit so there’s always going to be a little bit of a change in the end, and in this case it’s .24 days.”

Leap years account for that extra time. Over four years, the six hours add up to 24 hours — penciled in to the calendar as February 29.

### Why we need leap years

An alternative solution would be to add an additional six hours at the end of every year, O’Donoghue says.

“This is all fine, if you don’t mind the Sun rising six hours earlier on January 1,” he says.

“We do it every four years so we can pretty much make one day as a shift, otherwise we would ruin our lives.”

So what if we didn't have leap days at all, and instead just pretended the extra few hours did not matter?

Without the extra days, celestial events like equinoxes and solstices would shift a little bit each year, and in turn shift the seasons' dates around.

In fact, if we stopped accounting for those extra six hours for just one century, "summer" would shift to mid-July, according to NASA.

Leap years only take place in years that are divisible by 400. But even this is not a perfect accounting for the extra time it takes for Earth to make its way round the Sun. In reality, 0.24 days does not equate to six hours, but five hours, 48 minutes and 45 seconds.

To make up for our rounding up, we have to do a little extra accounting work every century. Each 100 years, we skip a leap year to make up for the accumulated 0.03 days. As a result, the year 2400, which is supposed to be a leap year, will be treated as if it was nothing of the sort, with just 365 days counted.

### Celebrating science explained

O’Donoghue started creating his astronomical visualizations in late 2018, when he was working at NASA’s Goddard Space Flight Center and a government shutdown kept him out of the office for 35 days.

During his time off, he dabbled with Adobe After Effects, which he had used before to illustrate a video for a paper he co-authored on Saturn’s rings in December, 2018.

“I substituted my hobby for playing video games and made about 40 animations during the year 2019,” he says.

O’Donoghue shares his visualizations through his YouTube channel and on Twitter, where they receive millions of views.

“That’s not bad for a hobby,” he says.

O'Donoghue's videos explain simple concepts related to astronomy, like the seasons, and the scale of the Solar System — things we take for granted, but, without an astronomer's training, aren't actually well understood.

“Given that there’s only about 10,000 astronomers on the planet, there is a very narrow overlap between us astronomers and people that would make an animation,” O’Donoghue says.

All of O’Donoghue’s videos are available to watch for free online. The planetary scientist would like to see more people have access to this kind of science, regardless of their level of education or background.

“I feel like there’s definitely not enough science out there, I don’t think it’s celebrated enough,” he says.

“I think it needs to have a larger role in society like sports, music and entertainment," he says. "It would be nice to see the public more scientifically literate.”

## Why isn't the day backwards between leap years? - Astronomy

Leap days are the extra days (February 29) that are added to the Gregorian calendar in leap years.

Since each 400 years of the Gregorian calendar has

days, of which 97 are leap days, the probability P of being a leap day baby is

The following table summarizes the years in which the leap day falls on given weekdays for the years 1900-2100.

 weekday leap years having that weekday at the leap day Sunday 1920, 1948, 1976, 2004, 2032, 2060, 2088 Monday 1904, 1932, 1960, 1988, 2016, 2044, 2072 Tuesday 1916, 1944, 1972, 2000, 2028, 2056, 2084 Wednesday 1928, 1956, 1984, 2012, 2040, 2068, 2096 Thursday 1912, 1940, 1968, 1996, 2024, 2052, 2080 Friday 1924, 1952, 1980, 2008, 2036, 2064, 2092 Saturday 1908, 1936, 1964, 1992, 2020, 2048, 2076

If birthdays are distributed randomly throughout the calendar, then there would be approximately four million leap day babies in the world (assuming a world population of six billion). However, as the figure above and chart below show, some refinement of this estimate is needed since there is a decided peak in September for births in the United States between 1978-1987 (Peterson 1998).

 month average daily birth frequency January 0.0026123 February 0.0026785 March 0.0026838 April 0.0026426 May 0.0026702 June 0.0027424 July 0.0028655 August 0.0028954 September 0.0029407 October 0.0027705 November 0.0026842 December 0.0026864

The premise of Gilbert and Sullivan's musical The Pirates of Penzance is based on the birth of the main character on a leap day. In more modern times, there is website devoted to leap day babies.

## The Physics of Leap Day

"When in doubt, make a fool of yourself. There is a microscopically thin line between being brilliantly creative and acting like the most gigantic idiot on earth. So what the hell, leap." -Cynthia Heimel

Once every four years, the elusive entity that is today -- February 29 th -- 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.

Image credit: Mrs. Snyder at the Seven Hills School.

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!

Image credit: Larry McNish at RASC Calgary Centre.

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.

Image credit: Greg Benson at Wikimedia Commons.

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 4 th 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 5 th through October 14 th 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. When did your country make the switch?

The adoption of the Gregorian calendar gives us a calendar of with -- over time -- 365.2425 days in the year. In comparison with the present, actual figure of 365.242188931 days, it will take over 3,200 years for us to be off by a single day, which is certainly good enough for a little while.

But if we want to be planning for the long term, we shouldn't simply be thinking about this difference. We should be thinking about the fact that the Earth's rotation rate is changing, and over long enough amounts of time, so should our definition of what a "day" is!

What am I talking about? Two things happen that change the Earth's rotation rate, and they push the day in opposite directions.

Every time we have an earthquake, that's mass inside the Earth rearranging itself so that -- by the conservation of angular momentum -- its rotation speeds up a little bit. For instance, last year's Japanese earthquake shortened the day by 1.8 microseconds, and the 9.1 Sumatra earthquake in 2004 shortened the day by 6.8 microseconds. On the other hand, there are two bodies out there with large gravitational effects on the Earth!

The Sun and the Moon both exert gravitational pulls on the Earth, all while the Earth itself rotates. If the Earth were just a point in space, this wouldn't matter the Earth would make its elliptical orbit around the Sun, the Earth-Moon system would orbit their center of mass, and nothing would change. But because the Earth is a sphere, both the Sun and the Moon exert greater gravitational pulls on the side of Earth that's closer to them than on the side that's farther away.

Image credit: the COMET program.

Throw in the Earth's rotation, and you not only get tides, you also get tidal braking, which causes the Earth's rotation to slow down!

Image credit: Purdue University.

The slow-down is small but pretty consistent, at an average of 14 microseconds per year, a much larger effect than the speedup due to earthquakes. And over geological times, this really adds up! If we go back to the daily patterns left in the soil from the tides -- known as tidal rhythmites -- we can calculate what the period of Earth's rotation was from it.

Image credit: Touchet formation by Williamborg.

If we look at the most ancient one we know of on Earth, from 620 million years ago, we find that a day back then was a little under 22 hours long!

If you extrapolate this tidal braking back to when the Earth was first formed, 4.5 billion years ago, you'll find that a day was originally only around 23,000 seconds, or six-and-a-half hours!

Image credit: Primeval Earth by Don Dixon.

And the best part about this is that the Earth continues to slow down! Every 18 months or so, because of the difference between 86,400 seconds and an actual day, we add an extra leap second to our clocks (for now). Wait around for around four million years or so, and the day will lengthen by about 56 seconds, enough that we won't even want leap year anymore a year will have exactly 365 Earth days!

So appreciate this leap day and our attention to detail to getting the Earth's seasons to remain constant from year-to-year, but also be aware that our Earth, however imperceptibly, means that these leap days, too, shall pass.

### More like this

Has the slowdown been consistent over Earth's history?

In geological history there have been times when the land-bearing tectonic plates all bunched together, forming a super-continent surrounded by a super-ocean.

This super-ocean allowed much more freedom for tidal effects on the Earth's ocean. By contrast, when the continents are scattered over the Earth, as they are now, there is only one region where a tidal wave can travel all the way round: the Antarctic Sea.

It is my understanding that it has been theorized that during ages of super-continents tidal effects were stronger hence friction from tidal effects was stronger, and a comparatively large proportion of the slowdown took place during these ages.

other countries skipping 10 days at a later date

Or more, as the Wikipedia page explains. For instance, Great Britain and possessions (including what later became the United States) adopted the Gregorian calendar in September 1752, which was only 19 days long. I have heard (not sure if it's true, as birth certificates weren't issued in those days) that George Washington was actually born on 11 February, but adjusted it to 22 February when Great Britain switched to the Gregorian calendar. Isaac Asimov noted in an essay on this topic that when his family emigrated from the USSR to the US, he lost 13 days as a result of switching from the Julian calendar (still in use in the USSR at the time the "October Revolution" actually occurred during Gregorian November) to the Gregorian calendar.

"And as it happens, it takes about 12 hours for a big wave to slosh across the Pacific Ocean and back--just in time for its height to be reinforced by the next high tide. So because of the size of the Pacific Basin, the Moon is very effective at slowing the Earth's rotation right now."

It's plausible that the rate of slowdown has varied over geological time, but it's not know by how much.

For what it's worth, I have heard others argue that, back at the Solar System's inception, Earth's rotational period may have been as long as eight hours, due to variations in the frictional torque that our planet has been susceptible to over our history.

I think the 6.5 hour estimate is close enough to even those very conservative estimates that I'd consider an argument to be splitting hairs at this point. But it is fun to think about!

Some places (like Ethiopia) still use the Julian calendar. It's currently 2003. Come step back into time (in more way than one)!

Now try the physics of the leap second.

Mind you, if anyone can tell me why the business world hate the leap day and explain THAT, that would be of far greater interest.

How come the angular forces of earthquakes only occur in the direction of Earth's rotation? I would have expected the direction to be random and for earthquakes to cancel each other out.

@6 Philipp:
Let me guess, because earthquakes represent a conversion of gravitational potential energy into heat energy driven ultimately by the earth cooling and shrinking. I suppose mountain-building must be driven by subsidence somewhere, how else? So the speedup doesn't come from a "push" by the earthquake, which has nothing to push against, but by conservation of angular momentum as the effective radius of the earth shrinks.

May also be for the same reason why low pressure weather systems all rotate the same way round: the Coriolis force. Therefore there isn't a random act, it's a driven one, and driven in only one direction.

From Pico to macro earth time change has been the order of the day, is now, and will be. What has been ignored in this discussion is back in time new arrivals adding to the mass of the earth and altering the earth's revolution and rotation cycle as the earth continues its spinning through space and time.

Once there was a 30th February.

It has only happened once in one country

Funny fantasy, since the planets don't orbit the sun. The planets follow the sun in a vortex as the sun moves through the galaxy. Even Stellarium gets it right and shows the planets visible to each other nearly all year long.

Would like to know to details all information

It's a leap day, so add one.

"The planets follow the sun in a vortex as the sun moves through the galaxy"

1) That's not a vortex
2) That still means they orbit the sun.

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## The Year 2016 Will Be One Second Longer

By: Tony Flanders December 29, 2016 5

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Do you think 2016 has seemed unusually long? An international agency has decided to make it even longer. A leap second will be added to December 31st.

On July 6, 2016, the International Earth Rotation and Reference Systems Service (IERS) issued an inobtrusive bulletin addressed to the “authorities responsible for the measurement and distribution of time.” It states that “a positive leap second will be introduced at the end of December 2016.” In other words, the last minute of the last day of 2016 will have 61 seconds rather than the usual 60 seconds.

This is what the NIST website looked like when the last leap second was added.
NIST / USNO / Wikimedia Commons

This happens just before midnight on December 31st Universal Time, which is 7 p.m. Eastern Standard Time, 6 p.m. Central Standard Time, 5 p.m. Mountain Standard Time, and 4 p.m. Pacific Standard Time. Assuming that the Official U.S. Time website doesn't crash due to overuse, you can actually watch the time progress from 6:59:59 to 6:59:60 and then to 7:00:00 EST (or the equivalent for your time zone).

### What Is a Leap Second?

Let's take a deeper look at what's going on. The first thing to realize is that the real intent is to alter the length of the day changing the length of the year is an unintended side-effect. Leap seconds are needed because the average length of a day is a little longer than 24 hours. To put that another way, Earth rotates a little more slowly than it would need to for days to average out to 24 hours apiece. If there were no leap seconds, the times of sunrise, noon, and sunset would gradually drift later and later due to the fact that clocks run faster than Earth does.

When the IERS was established, its name was simply the International Earth Rotation Service, which sounds as though they're the people who actually make the world go around. If that were true, the IERS could eliminate the mismatch between Earth's rotation and clock time just by pushing a little harder! Presumably, they added that bit about “Reference Systems” to their name to make it crystal clear that their job is actually to measure Earth's rotation, not to make it happen.

Among its other duties, the IERS is charged with keeping clock time in sync with Earth's rotation. Since they can't speed Earth up, their only other option is to slow clocks down, which they do by adding leap seconds.

The actual length of the day, as determined by Earth's rotation, has fluctuated from about four milliseconds more than 24 hours to one millisecond less than 24 hours in the past few decades.
USNO / IERS

Unfortunately, Earth's rotation isn't predictable, which is why leap seconds have to be added based on actual observations rather than using a formula similar to the one used for leap years. Over the very long run, the average length of the day is increasing one or two milliseconds per century due to tidal interactions between Earth and the Moon. For historical reasons, the Standard International second was defined as 1/86400th of the presumed average day length in 1900, and it's unlikely that the average day length will ever again be that short for any length of time. That's why leap seconds are always added, never subtracted.

But as the graph above shows, the actual day length fluctuates quite a lot on shorter time scales. Contrary to the long-term trend, it has actually decreased since the leap-second system was instituted in 1972, from about 24 hours plus 3 milliseconds in the 1970s to 24 hours plus 1 millisecond right now. That's why the IERS added one leap second every year during the 1970s, but has added only four during the last decade. That means that the average clock day during the 3,652-day period between January 1, 2006 and January 1, 2016 will be 4/3652

= 0.0011 seconds longer than 24 hours, matching the actual day length shown in the graph.

The short-term fluctuations come about because Earth isn't actually solid the relatively rigid crust that we live on is the exception rather than the rule. The quickest fluctuations are probably due to changing wind patterns transferring angular momentum between the crust and the atmosphere. Others may be due to ocean currents. The longer-period oscillations are presumably due to currents deep inside our planet — either the convection currents in the 1800-mile-thick mantle that drive continental drift, the currents in the iron-nickel core that generate Earth's magnetic field, or some interaction between then.

For more information about how time is defined and measured, see our article Time in the Sky and the Amateur Astronomer.