# Where do those extra four minutes go every day?

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The Earth fully rotates in 23 hours and 56 minutes. Where do those extra four minutes go??

I know the answer is supposedly leap day, but I still don’t understand it from a daily time perspective.

I have to be up early for my job, which right now sucks because it’s dark out that early. So every day I’ve been checking my weather app to see when the sun is going to rise, and every day its a minute or two earlier because we’re coming out of winter. But how the heck does that work if there’s a missing four minutes every night?? Shouldn’t the sun be rising even earlier, or later? And how does it not add up to the point where noon is nighttime??

In: Earth Science

Damn. I thought I knew the answer until I re-read your question. The leap year keeps the seasons from progressing but you raise a good point. After a month noon should be 2 hours earlier. I’m gonna sit down and wait for an answer with you.

23 hours and 56 minutes is how long it takes the Earth to make one rotation relative to the rest of the universe. However, while it is doing that, it also makes 1/365 of a revolution around the Sun. In order to face the Sun in the same direction as it did the previous day, it has to rotate for 1/365 of a rotation, which takes 4 minutes.

By the time the Earth has completed one rotation it has moved a little bit on its orbit around the Sun (about 1/365th of the full circle). So the Sun is now at a slightly different angle and the Earth needs to turn a bit more to face it exactly the same way as one rotation ago. It takes about four extra minutes.

The 4 minutes is because of the earth’s orbit around the sun. A day is an average time between two solar noon. Solar noon it the point in time when the sun is highest in the sku

If Earth was not rotating the sun would move around it once per orbit. so the orbit creates a day that is a year long. That means the sun will be in the same place in the sky 24*60/365=3.9 minutes later.

So earth rotation + earth orbital moment around the sun result that the average time between two solar noons is 24 hours.
This is the average length because earth orbit is elliptical. The shortest say is 21 seconds less than 24 hours and the longer 30s longer. This will change the time of solar noon by +-17 minutes during a year.

So if we based the clock on earth rotation noon would move around and it could be at any time during a year. But because we base our day on the solar noon is around the same time every day. The position of stars in the sky move around during the year because of this.

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This is not why days in the winter is short and long in the summer. It could not be because the southern hemisphere has summer when the northern have winter.

The length of days and the season is because the earth’s axis is tilted relative to our orbit around the sun. During the summer the hemisphere you are on point towards the sun and the days are longer and in the winter it points away from the sun.

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Leap days exist because a tropical year is 365.24219 days. To have a calendar that follows the season you need to have years with different lengths. 1 extra day every 4 years is a close match 365.24219*4-365*4-1=0.031 days. So we need special rules for years divisible with 100 and 400.

A topical year according to Wikipedia is

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>A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. This differs from the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars (the sidereal year) by about 20 minutes because of the precession of the equinoxes.

The 20 minuted difference from the obit around the sun is because the earth axis slowly changes direction. The difference is why the day of the zodiac do not match today and when the common variant was made around 2000 years ago.
20 minutes per year after 2000 years is 20*2000/60/24=27.7 days. So small difference per year adds up.

It has nothing to do with a leap day.

The earth takes about 23 hours and 56 minutes to turn around once on its axis in respect to the stars around us, but in that time the earth also moves forward in its orbit around the sun by about one degree.

Basically after the Earth turns once around its axis, the sun is no longer where it was before and the Earth has to turn a tiny bit (about 4 minutes) more to be in the same position it was in respect to the Sun.

Over the course of a year those 4 minutes add up to about one day.

Basically the earth turns around its axis 366 times a year but thanks to the fact that we also obit around the sun once we only get 365 days per year.

If you count days by the rising and setting of a star you will get one more day than if you counted days by the rising and setting of the sun.

The whole leap year thing is a completely different thing.

It comes from the fact that an orbit around the sun does not take exactly 365 days (as i pretended above) but more like 365 and a quarter days.

The length of the year is not a whole number of days. We take the quarter days that are left over each year and then when we have enough for a whole day we add a February 29th. This is sort of every 4th year.

So why do star charts have a full 24 hours of right ascension on them? Is a sidereal second slightly less than a SI second?

EDIT: I looked it up. Yes, a sidereal second is shorter by the amount one would expect.

they dont go in a leap day theyre made up by the earths movement around the sun.

take an example:
you have a bare light bulb in the middle of the floor. you move a tennis ball around the lamp the light on it will rotate around it so that once you complete one full rotation the entire ball has seen light. now if the ball starts spinning if it stayed still itd get a light/dark cycle the same as the speed f rotation but as it starts moving around the light source it adds a little bit of the rotation around the light to the same number. the reason the number is so odd (23 hrs and 54 mins) is because we set the length of a day fro which the other units are derrived based off a solar day, not off the rotation of the earth. you could redefine the time span based off the movement of the stars instead of the sun and it would be accurate to the earths rotation then

Why doesn’t the sun move 4 minutes per day? Because the stars do! The earth spins once every 23h 56m compared to distant stars. But the earth also orbits around the sun. So during that time it’s also moved along its orbit by one day. So it needs an extra 4 minutes of spin for you to see the sun in the same place in the sky. And this is why the stars move 4 minutes per day. And why the stars have seasons. Each part of the year the night side of the earth is facing outward from the solar system in a new direction.

It’s not leap day.

If the earth weren’t spinning at all, the sun would still move across the sky because the earth is going around the sun — a day would be the same length as a year. The sun would move about 1 degree East per day, so it’d be going backwards.

We spin the same direction we orbit the sun (counter clockwise if you’re looking down from the north pole), so in the time we’ve made a full rotation, we’ve also moved about 1/365^th of our orbit around the sun. That means the sun is about a degree “back” from where we’d expect it to be. So we need to rotate an extra degree, which takes about 4 minutes.

Or another way to look at it… In a year, we spin ~366.25 times, not 365.25. But moving around the sun “unwinds” one of those spins. That unwound day is spread across the days of the year. 1440 minutes in a day, split among 365 days, is about 4 minutes.

Look up 1752, I think the year was? There’s a September where 11 whole days just *poof* vanished. VSauce did a video on this very subject.

A nominal solar day (say sunrise to sunrise) is 24 hours. If you time when a star rises each day it’s 23 hours, 56 minutes. That’s called a sidereal or star day. A given star will rise 4 minutes earlier every day, or about 1/2 hour a week, or 2 hours a month. This is why the sky shifts and changes over the course of the year–if you look at the sky before sunrise in winter, it’s the same stars you’ll see 6 months later in the evening sky (12 hours timewise), because we’ll have gone halfway around the sun.

Conversely the bright stars of winter you see now in the evening sky will be in the morning sky come summer. And as mentioned, it’s all because of Earth’s orbit around the sun, and our point of view shifting that tiny bit day by day over the course of the year.

There are plenty of other great replies in here, but I thought I’d add a gif that shows what others have already described really well:
https://imgflip.com/gif/3o07r3

A sidereal year is 365.256363004 days. A tropical year is 365.256363004 days. A sidereal year is the time it takes for the Earth to return to the same position in relation to a certain star (the Point of Aries). A tropical year is 365.24219 days. A tropical year is the time it takes the mean position of sun to advance 360 degrees. This is what the calendar is based on.

Leap years are added to correct for the difference of the odd length of the year compared to an integer number of days. We add an extra day to the year every 4 years, unless the year number is evenly divisible by 100, then an extra day is not added, unless the year number is evenly divisible by 400, then an extra day is added after all.

Thus:

1996 was a leap year, it follows rule 1

1900 was not a leap year, it follows rule 2

2000 was a leap year, it follows rule 3

This system has been working for the last about 500 years. There is a small error but it will not amount to a full day until about 3800 AD.

Ok putting together some of these responses, I think the main idea is that we don’t define 24 hours as the time it takes for the earth to spin exactly 360 degrees, but instead as the time it takes for the sun to re-appear in the closest position in the sky from one day to the next. Therefore the 4 minute time difference is irrelevant to daily timekeeping with respect to the sun. (?)