A Little Atmosphere

Science Snack
A Little Atmosphere
Use a little bit of math to make a bonus accessory for your globe of the earth—an atmosphere, to scale.
A Little Atmosphere
Use a little bit of math to make a bonus accessory for your globe of the earth—an atmosphere, to scale.

The earth’s atmosphere may seem thick when compared to something like your height—but it’s surprisingly thin when compared to the earth’s radius. Here, you can find out exactly how thin, using strips of plastic to model the correctly scaled thickness of the atmosphere on a globe.

Tools and Materials
• Earth globe
• Measuring tape (or a meter stick and string)
• Ruler
• Two sheets of overhead transparency material
• Scissors
• Small binder clip
• Transparent tape
Assembly

None needed.

To Do and Notice

Looking at your globe, how thick would you guess its atmosphere would be, if it were shown to scale? Let’s find out.

Start by measuring the diameter of the your Earth globe. Divide this diameter in half to get the globe’s radius. If you divide this radius by the radius of the actual earth (6371 km, or 3959 miles), you’ll have a scaling factor that you can use to calculate the thickness of your globe’s atmosphere. Here’s an example (click to enlarge the equation below):

The average depth of the troposphere (the layer of the atmosphere that’s closest to the earth’s surface and that contains 75% of the atmosphere's mass), is 12 km (7.5 miles). Multiply that by your scaling factor to calculate the scaled troposphere thickness for your globe (see an example below).

Once you have the correctly scaled thickness of the troposphere, you’ll need to figure out how to use transparency material to represent it on your globe.

Transparency material is much too thin to measure with a ruler. However, one technique for measuring very small things is to measure many of them. To do this here, cut one overhead transparency sheet into 50 small rectangles (they don’t need to be exactly the same size). Stack the rectangles and clip them together with the small binder clip (see photo below). Measure the height of the stack and divide by 50 to determine the thickness of a single sheet.

In our example, the thickness of the single sheet of overhead transparency was 0.1 millimeter (0.004 inches), so we needed three strips of transparency, stacked one on top of the other, to model the 12-kilometer-thick troposphere.

Use the technique described above to find out how many strips of your type of transparency will make the correct thickness to model the atmosphere at this scale. Once you know how many strips you need, you can cut the second transparency sheet into strips. It’s hard to cover the whole globe, so simply cut strips that are about about 3 centimeters wide, tape the correct number of strips together, and then tape the strips to the earth globe’s equator. Congratulations: Your globe now has an atmosphere—to scale, no less.

What's Going On?

Earth’s atmosphere has no definite boundary, but most of its mass (about 75 to 80 percent) is in the lowest layer, the troposphere. The name of this layer comes from the Greek word tropos, which means “to turn or change.” Most types of clouds are found in the troposphere, and almost all weather occurs within this layer.

Here we used an average value for the thickness of the troposphere; the actual thickness varies with latitude and with the seasons. It’s thickest at the equator (up to 20 km, or 12.4 miles), and thinnest at the poles (7 km, or 4.3 miles) in winter.

In the troposphere, temperature decreases with increasing height. You may have experienced this if you’ve ever traveled to the mountains and noticed that it’s cooler up there. Cooler temperatures at higher elevations in the troposphere cause convection, the instability that drives much of our weather.

In the atmosphere, pressure also decreases with increasing height—and the decrease is exponential. Every time you add 5 km (3.1 miles) to your elevation above sea level, the atmospheric pressure is cut in half.

This is necessarily an approximation, since the exact change in pressure also depends on the temperature, but gives the basic idea. In equation form:

pressure = Po 2h/5km

where Po is the atmospheric pressure at the surface, and h is the height in km.

Notice that, according to this equation, the pressure never goes to zero, but just gets smaller and smaller. Similarly, our own atmosphere grows thinner and thinner with height, but has no definite “top.”