How many minutes are there in a day of 24 hours?

Our system of telling time is based on the premise that every day is exactly 24 hours long — quite precisely, with no exceptions. This concept is fully ingrained into our culture, a core principle of our modern technological society. At the same time, we are taught in school that a day corresponds to one complete rotation of the Earth on its axis. Unfortunately, these two concepts don’t quite match up — and the mismatch is more than just a few milliseconds. In fact, the mismatch amounts to several minutes every day. Furthermore, because our traditional concept of a “day” is actually defined by the cycle of sunlight and darkness — and not by one rotation of the Earth — the length of a real day is not consistent, but varies somewhat during the year. We only pretend that all days are the same length — by averaging the length of all the days in the year, and then defining this average as a “standard day” of exactly 24 hours.

This is not a bad thing. In fact, it has been quite helpful to define our system of time in this manner. But once you understand why this system does not quite match up with the real world, then you can begin to make sense of several interesting phenomena. For example, you would think that the earliest sunset and the latest sunrise would both occur on the shortest day of the year, which is the first day of winter. But this is not the case at all.

If our definition of a day was truly based on one complete rotation of the Earth on its axis — a 360 degree spin — then a day would be 23 hours, 56 minutes, and 4 seconds. This is nearly 4 minutes shorter than our 24-hour standard day. However, our concept of a “day” has long been based on the natural cycle of sunlight — a period of daylight followed by a period without daylight. The mismatch of nearly 4 minutes is because the Earth must rotate more than 360 degrees between one dawn and the next. As you know, the Earth experiences two simultaneous motions — it not only spins on its axis, but it also travels in orbit around the sun. In a period of one day, the Earth travels about 1/365 of the way around the sun (because it takes about 365 days to go all the way around, which is how we define a year). This daily progress in the Earth’s orbit is almost exactly a degree (defined as 1/360 of a circle). Therefore the Earth has to spin an extra degree in order to line up with the sun again each day. The result is that one complete cycle of sunlight and darkness — one day — represents a rotation of about 361 degrees, not 360 degrees. Although a year consists of 365 and a quarter days, the Earth actually spins 366 and a quarter times during a year. From the standpoint of sunrises and sunsets, one complete spin is negated each year by the journey around the sun.

A Stellar Day

Another way of expressing this idea is that the length of a day depends upon our frame of reference. For reasons that are both traditional and logical, we normally use the sun as our reference when defining a day. But if we should want to define a day as one complete spin of the Earth on its axis, then we can use the stars as our reference. By observing the locations of the stars in the sky, we can determine when the Earth has completed exactly one rotation. We call a day defined in this manner a stellar day or a sidereal day. (The two terms have slightly different definitions, but nearly identical results.)

In a stellar day, any given star rises at approximately the same time every day. More precisely, any given star reaches its highest point in the sky at the same time each stellar day. This is because, at the beginning and end of one complete rotation of the Earth, any given point on Earth now faces the same direction in space. (In other words, any point on Earth now faces the same direction with reference to the other stars in our galaxy.) But because a stellar day is about 4 minutes shorter than a traditional solar day, this means that any given star rises about 4 minutes earlier each day. For example, if you enjoy spotting the constellation Orion in the autumn and winter, then you’ll notice that it rises slightly earlier each night. If you go out at precisely 11:00 PM each night to note the position of Orion, you’ll see that every night the constellation is a little bit higher in the eastern sky than it was the night before.

Unlike a solar day, whose true length varies throughout the year, the length of a stellar day is quite constant — always 23 hours, 56 minutes, and 4 seconds. However, if you want to be precise to the millisecond (1/1000 of a second), then you have to consider several kinds of “wobbles” that affect the direction of the Earth’s axis. (The largest of these wobbles is a 26,000-year cycle called an axial precession.) You also have to consider the very gradual slowing of the Earth’s spin. (One complete rotation takes about 1.7 milliseconds longer than it did a century ago.)

A Solar Day

In contrast to a stellar day, a solar day — one complete cycle of sunlight and darkness — is much more variable in length. However, the amount of variability depends in part upon when you consider the day to begin. For example, you can consider “a new day” as beginning at dawn, when the sun rises, or you can consider the day as ending when the sun sets — in which case the next day begins at sunset. (Several prominent religions still use the latter system.) A third choice is to say that the new day begins at the exact middle of the night — halfway between sunset and sunrise. (This moment can be called “true midnight”.) In any of these systems, the length of a day varies throughout the year, but the average length is 24 hours. However, the midnight system exhibits considerably less variability in day length than either the dawn or the dusk systems.

In our current system of standard time, a new day does indeed begin at midnight — except that it is not true midnight. At any given location, on any given day, there can be a significant difference between true midnight and midnight according to standard time. In the U.S., the difference can be as great as an hour — and during the months of Daylight Savings Time, the difference can even reach two hours. In far western China, the difference between standard time and true time is three hours, a result of stuffing the entire country into a single time zone.

Although you can consider the length of a true solar day to be the amount of time from one true midnight until the next true midnight, a reasonable alternative is to consider it as the amount of time from one true noon until the next true noon. At any given location, true noon occurs exactly halfway between sunrise and sunset (assuming a relatively flat horizon, without mountains). It is also the moment when the sun reaches its highest point in the sky for that day. In the northern temperate regions of the world, the sun is due south at true noon. In the southern temperate regions of the world, the sun is due north at true noon. In the tropics — that is, any place in the world that is south of the Tropic of Cancer and north of the Tropic of Capricorn — the sun will be either due north or due south at true noon, depending upon which day of the year it is. Furthermore, twice a year in the tropics the sun is directly overhead at true noon. The exact dates of this phenomenon vary according to the latitude of the location.

Variations in a Solar Day

If the Earth’s orbit around the sun was perfectly circular, then the length of a true solar day — the time from one true noon until the next — would be quite consistent throughout the year. However, the Earth’s orbit is actually an ellipse, although fairly close to circular. Consequently, the distance between Earth and the sun varies during the year by about 3% (roughly 3 million miles). The speed at which the Earth travels around the sun also varies by about 3% during the year, and is fastest when the Earth is closest to the sun. The changing distance and the changing speed both affect the length of a true solar day — because they both affect how many degrees the Earth must spin between two consecutive instances of true noon at any given location. The length of a true solar day in late December is about 24 hours plus 30 seconds. The length of a true solar day in mid-September is about 24 hours minus 21 seconds. Thus the length of a solar day varies by nearly a minute during the year.

Although this effect is relatively small when you consider only a single day, it is quite noticeable when accumulated over several months. Imagine that you have two clocks. The first clock, which is simply a very accurate sundial, shows true local time, including true noon. The second clock is electric, but instead of being set to standard time according to the local time zone, it is set to local mean time. In other words, the electric clock assumes that all days are exactly 24 hours (the word “mean” means average), but that the average time of noon should match up with the local true noon, as indicated by the sundial. Four times a year, the two clocks will agree as to when it is noon. But in early February, the electric clock indicates noon a full 14 minutes before the sundial does. In early November, the electric clock indicates noon 16 minutes later than the sundial does. This is a rather stark difference!

This mismatch is why the earliest sunset and the latest sunrise of the year do not occur on the shortest day of the year — the winter solstice — which occurs on or near December 21 in the northern hemisphere. (In the southern hemisphere, December 21 is the longest day of the year, and therefore the first day of summer.) If we actually used true sun time (in contrast to either local mean time or standard time), then the latest sunrise and earliest sunset of the year would indeed occur at the winter solstice, on the first day of winter.

Time Zones

The use of true sun time was abandoned when mechanical clocks allowed us — or perhaps forced us — to adopt a standard length of 24 hours per day, regardless of the actual position of the sun. Thus sun time was replaced by local mean time — several centuries ago. But of course, we don’t use local mean time anymore either. If we did, then whenever you traveled a few miles east or west, you would have to adjust your watch. Ever since the 1880s, we have relied instead on standard time, based on time zones. The idea is to divide the world into 24 north-south stripes or zones. Within each zone, everyone uses the same time. As you go from one zone to another, you usually adjust your clocks by exactly one hour. Each time zone has an average width of 15 degrees of longitude (by dividing 360 degrees into 24 equal pieces). This translates to a width of about 1000 miles at the equator, but the time zones get progressively narrower as you approach the Earth’s poles.

Within each time zone, standard time is based on the local mean time at a specific longitude within the zone. For example, in the Eastern Time Zone in North America, standard time is based on 75 degrees west longitude — the theoretical center line for this time zone. For any city or town with this same approximate longitude, such as Philadelphia, there is a near perfect match between local mean time and standard time. But for a city or town with a longitude of around 80 degrees west, such as Charleston (South Carolina), standard time and local mean time differ by around 20 minutes. In Indianapolis, located around 86 degrees west longitude, the difference between standard time and local mean time is about 45 minutes. During the summer, when Daylight Savings Time is in effect, another hour of difference is added to any location that is west of the center line — although an hour is subtracted for locations east of the center line (such as Boston). The result is that in the summer, standard time and local mean time differ by nearly two hours in Indianapolis.

Indianapolis used to be in the Central Time zone, along with the entire state of Indiana. But now most of the state is in the Eastern Time zone. If Indianapolis still used Central Time, then standard time and local mean time would differ by only 15 minutes, instead of 45 minutes. The problem is that, on average, the sun would already be halfway across the sky by 11:45 AM. In early November, because of the difference between mean time and actual sun time, the sun would be halfway across the sky at 11:30 AM. Therefore dawn and sunset would both occur a half hour earlier than expected. Most people would prefer to have the sun halfway across the sky at 12:30 PM, rather than 11:30 AM, so that sunrise and sunset are a little bit later than expected. A similar issue affects any other place that is located to the east of the center line of the corresponding time zone. The upshot is that politicians are constantly tempted to shift the time zone boundaries westward. A majority of places in the U.S. (but certainly not all) are now located to the west of the center line for the corresponding time zone.

The Analemma

As nearly everyone knows, the sun rises higher in the sky in the summer than it does in the winter. Assuming that you live in the Northern Hemisphere, the high point each day occurs at true noon, and the highest point for the year occurs on the summer solstice (the first day of summer), around June 21. If you mounted a camera on a platform pointing due south, and you took a picture of the sky and horizon every day at true noon, then the sun would climb higher in each photo until June 21, then sink lower each day until December 21. But what if, instead of taking the photo at true noon, you took the photo at noon according to the clock (ignoring Daylight Savings Time)? As you flipped through the photos, the sun would continue to go up and down, but it would also weave slightly to the left and right, because of the mismatch of up to 16 minutes between true sun time and mean time. If you combine all of the images into a single photo, then you would see a figure-8 in the sky. If you shoot the photos at a consistent clock time other than noon, then the figure-8 will lean to the side:

You may have seen a diagram with this same shape — called an analemma — printed on a globe. The meaning is essentially the same. If you were to draw a dot on the globe at exact 24-hour intervals for a full year, indicating the point on the earth where the sun is directly overhead, then you would produce this same figure-8 on the globe:

Seasons of the Year

Contrary to what people in the Northern Hemisphere might expect, the Earth’s closest approach to the sun (called the perihelion) is in early January. The intensity of sunlight falling on Earth is 7% greater in early January than it is in early July, when the Earth is farthest from the sun. This causes a slight moderation in the differences between summer and winter temperatures in the Northern Hemisphere, and it causes a slight increase in the differences between summer and winter temperatures in the Southern Hemisphere.

Of course, our cycle of seasons is due to the tilt of the Earth’s axis, not the distance from the sun. The main factor affecting the intensity of sunlight is simply how high the sun is above the horizon. When the sun is low in the sky, the rays strike the Earth at an oblique angle, spreading the energy over a large area, thereby decreasing the intensity. Therefore sunlight is much more intense at noon than it is in the early morning or late afternoon. Likewise, sunlight is more intense in the summer, when the sun rises higher in the sky, than it is in winter. There are also more hours of daylight in the summer, which results in a longer daily period of heating and a shorter nightly period of cooling. In the tropics, the height of the sun at noon does not change much during the year, nor does the length of the daylight period. Therefore the tropics don’t experience much variation in average temperatures during the year.

In locations that are far from the equator, and therefore experience a sharp distinction between summer and winter, the effect is greatly magnified in locations that have a continental climate, as opposed to a marine climate. In other words, locations that are not only far from the equator, but also far from any ocean will experience the greatest difference between summer and winter temperatures. Siberia, located in the giant continent of Asia, is the prime example of such extremes — but the northern plains of North America (such as North Dakota and southern Saskatchewan) also provide a good example.

Summary

To conclude, let’s return to our original question: How long is a day? If we define a day based on an actual, daily, observable physical phenomenon, then we have two possible answers. If we define a day as one complete spin of the Earth on its axis — a stellar day — then a day is about 4 minutes less than 24 hours. If we define a day as the time between true noon one day and true noon the next day — a solar day — then the length of a day varies throughout the year, ranging from 21 seconds less than 24 hours to 30 seconds more than 24 hours. But if we take the average length of all the solar days in a year, then the result is exactly 24 hours, which is how we arrived at our standard day. However, there are only 4 times each year when the standard day and the true solar day have the same length. The upshot is that the standard 24-hour day is not something found in nature, but a human invention that only roughly corresponds to the real days — solar days or stellar days — that we actually experience on Earth.

For a more detailed discussion of this same topic, see the chapter “Twenty-Four Hours a Day” in my book The Stickler’s Guide to Science in the Age of Misinformation.

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