# Why do our clocks not go out of sync with the day over a year?

Ok, so our clocks time 24 hours, our planet takes 24 hours to rotate completely and our planet revolves around the sun in 365 days.

Imagine at the start of the year, the side of Earth facing Sol is 'Side A' and the dark side is 'Side B'. The side of the sun that Earth sees is 'Side A' and the opposite side is 'Side B'.

After half a year, wouldn't 'Side B' of Earth be facing 'Side B' of Sol, and thus the day/night cycle would be out of sync by 12 hours?

I've been trying to get my head around this problem for ages and I can't seem to figure it out. It seems like the angle that the sun hits the Earth must change by about a degree per day until it's gone around 360 degrees. Would that not mean the clocks offset by 1/365th of 24 hours every day over a year?

• An Earth day is not exactly 24 hours long. Rather it is 23 hours 56 minutes and 4 seconds long. For the sake of simplicity, rounds up to 24 hours. So, yes it does offset about 1/365th of 24 hours everyday, but not quite. – CipherBot Aug 26 '16 at 13:20

You are correct, and in fact the clocks are offset. But most people never notice this because of the way days are defined.

If you measure the "day" length by the stars (instead of the sun) you will see it's not 24 hours at all. It's around 23 hours 56 minutes. (Check this by going out at night, picking a bright star, and noting the exact time it passes due south. Then observe it the following night and note it passes 4 minutes earlier.) By the way this shortened "day" is the sidereal day.

Each day, the Earth shifts along in its orbit (by about a degree, as you correctly observed in the question). So if you go out and point at the Sun at Noon every day, you are pointing in a slightly different direction. (I'll also neglect the Solar Analemma at this point too as it's just too confusing.)

Really, the "day" of 24 hours is not related to the true rotation period of Earth at all; loosely speaking it's just the average time between sunrises, or sunsets, or noons.

• So if we time exactly 24 hours and the day is only 23 hours and 56 minutes, shouldn't it be that halfway through the year, the clocks are out by about 12 hours and we have night time at 12 noon? – JamEngulfer Aug 26 '16 at 14:04
• If we adjusted our clocks so they marked a full "24 hours" on the dial in 23 hrs 56 minutes of real time (i.e. we set them to run 4 minutes fast!), then yes - after six months they would read mid-day when it was actually midnight. (Astronomers can use such clocks in fact. Here is an old example) – Andy Aug 26 '16 at 14:18
• This answer has left me more confused than I was before I read it :( If the clocks are 24 hours but the days are 23:56 then how is it that my 24 hour clock on my nightstand lines up with my 23:56 days all year... ? – Jason C Aug 26 '16 at 14:41
• The (normal) clocks are 24 hours, and the days are 24 hours too - a day has always been defined by the apparent movement of he sun (even before people knew about astronomy). So the clocks stay in synch with the sun - because that is how long a day is defined. (We only need to worry about the 23:56 jazz if we wonder why the stars at night are getting out of synch as the year progresses.) – Andy Aug 26 '16 at 14:49
• Great explanation. You might add that the difference between siderial and solar day is also the reason why we see some constellations only in summer or only in winter. Another illustrative example is the moon - it rises about 1 hour later every day because one orbit is 28 days - after 360 degrees in 24 hours the earth has to catch up by a further 1/28th rotation (and 24/28 is just about 1). – Alex Aug 26 '16 at 18:38

I was looking at the answer provided by Andy and the comments attached to it, and together they add up to a reasonable answer.

There are several ways to measure a day, the two most common are sidereal and solar. A sidereal day is the time it take earth to rotate 360°; a solar day is the amount of time it takes the earth to rotate such that the sun appears at the same meridian as the day before. (Sunrise and sunset aren't really good references, as they are influenced by atmospheric conditions that affect refraction.) The solar day, or more accurately the mean solar day, is the day our calendars measure. The mean solar day is exactly what it says, the average amount of time during the course of a year that it takes for the sun to appear over the same meridian from day to day.

Unfortunately, the definition of a sidereal day is very often given as the definition of a day, which is totally inaccurate, and very confusing.

The length of the solar day varies during the year because the of Earth's distance from the sun; it is closer in January and farther in July. Because it is closer in January; it is also moving faster, which means that the planet has to rotate more for the sun to appear over the same meridian.

If you can get your head around this, the concept really isn't very complicated.

Wow, I am amazed that none of the answers mentioned leap seconds.

A day is defined by the average time it takes 'the sun to rotate around earth'. See the picture below, 24 hours passed between step 1 and 3. The time between step 1 and 2 is slightly shorter (~4 minutes shorter) and is called sidereal day. So the a day the reference point is the Sun, while for the sidereal day the reference are celestial objects.

Unfortunately, as a clever person may note, the period of Earth's rotation can vary in time, but the definition of 1 second is fixed (based on cesium radiation cycles). If we define a day as a 24*3600 seconds then it will also be fixed and hence unable to accommodate the variability of Earth's rotation period. We are lucky as the average solar period is currently very close to 24*3600 seconds.

However, in case the time of day goes out of sync we have a leap seconds such that we can make certain days slightly shorter or longer if desired - eg we can make 3rd of November 2020 last 24*3600 + 1 seconds instead of the usual, this way we ensure that the time is always in sync.

It will be interesting to see what happens in the future when the earths rotation slows down - will we have, say 3599 seconds per hour? :) Adjusting the definition of a second or an hour is definitely a bad idea, so are constant leap seconds. I guess we will have a leap minute ~4 times a year (on regular predefined times) to keep the solar time in sync.