Learning Library

# Apparent Movement of the Sun

Our clocks don’t follow the Sun—they only do so approximately. The time on your watch is based off something called mean solar time, which is basically what time it would be if the Sun and Earth were a little more reliable. In this project, you’ll get to see just how far off our clocks are from the Sun.

### Problem

Design a simple sundial.

You’ll use this to keep track of how “solar time” (based on the apparent movement of the sun) changes with respect to “clock time” over the course of a year.

### Materials

• Wide board (20” x 4” x 8” or larger)
• Hammer and nail
• Watch
• Marker/pen
• Compass

### Procedure

1. Draw a line down the center of the board. Label one end “North”, the other “South”.
2. About 2” from the south end, hammer a nail partway into the line. Make sure the nail is perpendicular to the board.
3. About an hour before noon, set the board down outside on a flat surface (don’t worry about getting north and south lined up right just yet). Over the next couple of hours, keep track of the length of the nail’s shadow and record the time when it is shortest. (You may need to adjust for daylight savings time—all times should be in “standard” time, so don’t forget to subtract an hour if you observe daylight savings!) The time you identify is “solar noon.”
4. The next day, at solar noon, position the board so that the nail’s shadow lies along the line between “North” and “South”. The north end will be pointing towards “true north”—the direction towards the North Pole. This is slightly different from “magnetic north”—the direction a compass needle will point. We’ll use this difference to get the board lined up correctly from now on. Use a magnetic compass to record how much the needle deviates from true north (you can just make another mark on the board).
5. Once a week, place the board down in the same place roughly an hour before noon. Use the compass and the marks you made to align the board with true north.
6. Record the date and (standard) time that the nail’s shadow lines up with the line on the board (use a table like the one below). This will tell you the local time for solar noon.
7. Repeat steps 5 and 6 for as many weeks as you like. Ideally, you need a few months worth of data to track how solar noon changes over the year. If you’re feeling ambitious, make a plot tracking the difference between solar and standard noon as a function of date.
 Solar time vs. standard time data Date Clock time at solar noon Difference between solar noon and standard noon; ahead (+), behind (-) Jan 1 12:03 P.M. -3 May 11 11:56 A.M. +4

### Results

The exact results will depend on how far east or west you are within your time zone, but you’ll notice that the difference between solar noon and standard noon (clock time) slowly changes over the course of the year. In some months it will be ahead; in others, it will lag behind. If you plot the difference over an entire year, it will look something like this:

### Why?

Before clocks became popular, people kept track of time using the sun. Noon was the time when the sun passed over an imaginary line in the sky connecting north and south, known as the meridian. This also happens to be the time at which shadows are shortest—this is because the sun is at its highest point on that day’s trek across the sky. The time between one noon and the next is called a day.

The trouble is, when you define a day this way, its length changes over the course of the year. In fact, there can be as much as a half hour difference between noons recorded at different times of the year! Why? Because the Earth speeds up and slows down as it orbits the Sun.

Most of the Sun’s apparent motion comes from the Earth’s rotation. As our planet spins, the Sun, the Moon, and all the stars appear to move from east to west, just like if you spin around in an office chair and the walls all appear to move the other way.

Every time the Earth completes a spin, it also moves a little way along its orbit. Imagine you’re facing the sun now. After one full Earth rotation, you wouldn’t quite be facing the sun—it will have shifted a little bit in the sky. The Earth would have to rotate just a little bit more to account for the fact that it’s moved along its orbit. How much more depends on how far it has traveled, which in turn depends on how fast the Earth is traveling. The trouble is, the Earth’s orbital speed is not constant!

Here’s why: the Earth’s orbit isn’t a perfect circle. It’s actually an ellipse (which is basically a stretched out circle). The Sun doesn’t sit in the center of the ellipse, but at a point off to one side (called the focus of the ellipse). Over the course of one orbit, the distance between the Earth and Sun changes by a few percent. At its closest point—a spot called the perihelion—the gravitational force between the Earth and Sun is strongest, and the Earth is traveling at its maximum speed. As it moves away from the Sun, the planet slows down. At aphelion—the point along our orbit where we are farthest from the Sun—the Earth moves as slow it can. After that, it starts picking up speed again. Perihelion occurs sometime in early January, aphelion in early July.

Having noon bounce around during the year is pretty inconvenient, so astronomers came up with the idea of a “mean solar time”. Rather than use the exact location of the Sun to measure time, we imagine where the Sun would be if the Earth’s orbit were a perfect circle with a radius equal to the average distance between us and the Sun. This is the time that clocks use.

Time zones add an extra twist. In a time zone, everyone within a certain chunk of longitudes (roughly) sets their clocks to the same time. Typically, the time zone is based off the mean solar time somewhere in the middle of the zone. This means that people living on the eastern side of the time zone will see solar noon approximately an hour before people on the western end. So, depending on where you live, you might notice your mean solar noon occurring, on average, 30 minutes before or after noon on your clock.

Who knew time could be so confusing?

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