Subscribe to WIRED Magazine

What Is Daylight-Saving Time?

Oh sure, you know what it is … but do you really know what is going on? There is some interesting physics here.

What is Daylight-Saving Time?

Let me start with the sun. Suppose you were to watch the sun (but not look directly at it; that is a bad thing) over the course of a day. Also suppose you were to observe the sun’s motion on different days of the year. Oh, I get it. You’re too busy and too impatient to do this. Well, there is a simple solution. Download and install some type of astronomy software. I recommend Stellarium. It’s free and it works on all the major operating systems. With Stellarium, you can enter a location and a time and it will show you the sky. This way you can play around with the views on different days without having to wait half a year. Instant sky gratification.

Let me show you the sun at different times of the day for my location on both Dec. 21 and June 21. This image might look crazy, but I tried to show all the locations at the same time.

Sky 2dayssun

What is different on these two days? Hopefully, you can notice that in June, the sun is much higher in the sky than in December. Oh, I have a wide-angle view of the sky so that you can see as much of the sun’s path as possible. But if you play with Stellarium, you might also notice that the sun is in the sky for a much longer period of time in June than in December. In fact, this shows that on June 21 the sun rises at around 6:30 a.m. and sets at around 7:30 p.m. (13 hours of daylight). In December the sun rises around 7:30 a.m. and sets at around 4:30 p.m. (9 hours of daylight).

So, there is less daylight time in the winter. Well, everyone can notice that. But go back to Stellarium. Find the exact time that the sun crosses the meridian (a line in the sky going from south to north – you can turn this on in Stellarium). For my location in December, this time is at 12:03 p.m. In June, this time is 1:07 p.m. This is also approximately the time that the sun is at the highest position in the sky. Although the length of the day light time is different, the sun should be at the highest point around 12 noon. It isn’t because of daylight saving.

The simple answer is that during the summer hours of daylight, the clock is shifted so that the sun rises at 6:30 a.m. instead of 5:30 a.m. This also makes the sun set at 7:30 p.m. instead of 6:30 p.m. Is daylight actually saved? I guess you could say that. If there is sunshine at 5:30 a.m. and no one is awake to use that sunlight, it would be wasted. Shifting the clock time by an hour saves this sunshine. I still don’t like the term “daylight saving”. I prefer daylight shifting.

Why Does the Length of Daylight Change?

This is a better physics question. The length of the day changes over the course of the year because the rotation axis of the Earth is not parallel to the orbit axis around the sun. Here is a diagram of the Earth showing its axis of rotation.


Look at the red dot on the Earth and the path it travels as the Earth rotates. Half the Earth is in the sunlight and half is in the dark. However, the path this red dot would take would be more in the light side than in the dark side since this circular path is not perpendicular to the day-night line. This shows a location in the northern hemisphere during the summer.

What about a location in the southern hemisphere during this same time? If you drew the same kind of circular path you would see that it spends more time in the dark than in the light. So for the same time in the southern hemisphere, the days are shorter than the night. If you drew a circular path very near either the north or south pole, you could be at a case where you are only in the light or only in the dark. Yes, that would be crazy.

Let me just show one more cool thing. The motion of the sun in the sky isn’t as simple as most people guess. Since the motion of the Earth around the sun isn’t a completely circular orbit, the Earth moves faster at sometimes than others. The effect is difficult to notice from day to day, but if you were very very very patient, you could make an analema. This is basically a map of the location of the sun at its highest point for every day during a year. Here is a diagram showing an analema.


Image: Wikipedia

I am pretty sure this isn’t a real analema, but just a graphic. Like I said, making these things is a tough task.

Why Does the Earth’s Axis Point the Same Way?

Well, technically, it doesn’t. The orientation of Earth’s rotation axis does change a bit – just not very fast. Let me pretend that it doesn’t change it all. (Like I said, this is wrong.)

If you take an object and push it, it will have momentum. (I guess you could call this linear momentum.) The momentum of an object will only change when there is an external force on the object. This is why the Earth moves around the sun. The sun exerts a gravitational force on the Earth, causing it to change its momentum and orbit the sun.

But what about spinning? If you spin an object, it will have angular momentum. (Now you see why I added the “linear” to the above case.) And just how do you change the angular momentum of an object? Not with a force, but with a “rotational force” – also known as a torque. In the most basic explanation, torque is the product of the force and the distance this force is applied from the rotation point. That definition sucks, but the real definition isn’t so pretty. Just think of pushing a door to open it. If you push on the side with the handle, it is fairly easy to rotate around the axis (where the hinges are). If you push with the same force but on the side with the hinges, you are not going to open the door. You will look like an idiot instead. Oh, if you try to push a door that needs to be pulled to open, you will have a bad time. But with the doors, the larger the distance from the point of rotation, the greater the torque.

What about the Earth? Is there a torque on the Earth? Well, if we just consider the gravitational force from the sun then no. The sun doesn’t really exert a torque on the Earth. Why? Because the Earth’s mass is pretty evenly distributed spherically. This means that the gravitational force on one part of the Earth is about the same as any other part. It is like trying to rotate a pencil on a desk by pushing the tip and the eraser in the same direction. This just causes the pencil to slide – but not turn.

Since there isn’t any torque on the Earth, its angular momentum doesn’t change. Here is the key point: Angular momentum is a vector. It doesn’t just depend on how fast the Earth is spinning but also the axis of the rotation. So, as the Earth orbits, its axis of rotation stays constant. Like this.

Sunorbit 1

Warning: The above image is not drawn to scale. In this case, the Earth acts just like a gyroscope. A gyroscope is just a spinning wheel that is free to rotate. You can put one (or two or three) of these in an aircraft. When the aircraft turns, the gyroscope stays in the same orientation since it is in an enclosure with zero torque. Then by measuring the relative orientation between the aircraft and the gyroscope you can get the orientation of the aircraft. This is very useful in low visibility weather. In a sense, the Earth is a gyroscope for the solar system.

But Why is the Earth’s Axis Tilted?

If it takes a torque to change the angular momentum, then why is the Earth’s axis tilted in the first place? Well, I guess you should first ask why did it start in its current orientation? Why would you expect anything else? Most of the planets in the solar system have an axis of rotation that is perpendicular to their orbital axis. Some notable exceptions are Venus (it is perpendicular but rotating in the opposite direction) and Uranus. Why are all the others mostly the same? They have the same orientation because of the formation of the solar system. If the initial matter that formed the solar system had some initial angular momentum, the angular momentum of all the stuff after it condensed should be the same value without an external torque. So, as the dust stuff that formed the planets and sun collapsed, stuff started spinning the same way.

Then why is the Earth’s axis off? It is probably due to some interaction with some other object during the formation. If a large mass collided with the Earth, this could exert a torque and change its angular momentum.

Sometimes the Sun Does Exert a Torque


Image: NASA

Take a look at Mercury. Actually, Mercury is sometimes difficult to see if you don’t have a clear view of the horizon. Where I live, there are so many pine trees that you never get a good view. But Mercury is one of the planets visible to the naked eye – so you should see it sometime just to check it off your list.

The cool thing about Mercury is that it is close enough to the sun that the gravitational force on different parts of the planet can be significantly different. This is especially true if the mass of the planet is not spherically uniform. The result is a 3-2 spin orbit resonance. This means that for every 2 orbits around the sun, Mercury rotates three times around its own axis. So, in this case the spinning and orbital motion are connected and not independent like the Earth’s motion. Oh, the moon does this too with its orbit around the Earth – except that it is in a 1-1 spin orbit resonance.

Bonus Haiku:

Sun is not yet up.

I want to ride my bike now.

Dumb daylight savings.

Maybe DLS isn’t dumb. Maybe I am just angry at the darkness.

How Much Money Does DLS Save?

Time for another crazy estimation.  Let’s start with a U.S. population of 300 million.  But it isn’t the population that matters; it is the number of light bulbs that would be turned off because of DLS (Daylight Saving). Let me just guess that there are 100 million households and on average, each household turns off two lights because they are sleeping with a power consumption of 100 watts. This is tough since some people still have the lights on even if it isn’t dark outside – later in the afternoon it is still dark enough that lights might be needed.

So, in one day during DLS, I have 100 million households using 100 watts less than they normally do for one hour.  Since power is the change in energy over time, this means that the energy saved would be:

Now let me assume an average price for energy at $0.1 per kilowatt*hour.  Of course, this price varies with location.  This would put the cost savings per day at $10 million dollars. If DLS is 200 days (I think it is actually 238), this would put a total yearly savings of $2 billion. That is compared to a gross domestic product of 14 trillion dollars for the USA.

Then does it matter?  I guess it could.  But there are many other factors that I did not include – this was just a basic estimation and not intended for government policy decisions.