For this experiment you’ll need to take two measurements at least 250 km (a little more than 150 miles) due north or south of each other.

You will make a couple of observations, take some measurements, use some math, and discover if the surface of the Earth is curved, and, if so, by how much. Then we’ll do a thought experiment based on your observations to determine if the Earth is flat. The nest step is important: you will develop a description of Earth that is in agreement with your observations and find a way to test that description.

There are two ways to do this lab, one using shadows like Eratosthenes did, and another by measuring the position of Polaris in your sky.

## Using shadows:

To do this observation with shadows, you will need to make your observations the same time of day on two different days within about a week or two of each other. Attach a straight pole to a flat surface so the pole stands up exactly perpendicular to the flat surface. Measure the height of the pole exactly. From each location on Earth, measure the length of the shadow. Then use trigonometry to determine the angle of the shadow. Compare the angle at the two locations. Calculate size of Earth.

## Using Polaris:

You may want to try this method using Polaris. Your two observations should be done at

about the same time of night within about a week or two of each other. The measurements of this project can give good results for the size of Earth, but you must be very careful in measuring and marking the angles (see below). Depending on how far north/south you travel, the difference in angles will only be a few degrees for which a mistake of even one degree will add a significant error to your result.

- Tape a soda straw firmly to a piece of cardboard that’s at least 8.5″ X 11″. Hang a small weight such as a washer, from a string attached to the middle of the straw. (See illustration)
- On a clear night at the first location, hold the straw horizontally, then tilt it and sight Polaris (the North Star) through the straw. Now, without moving the cardboard, draw a vertical line on the cardboard. This may be most easily done by hanging a small weight (such as a stone) from a string. Hold the string up along the cardboard, and then draw a line with a ruler lined up along the string.
- Write next to the line the date, time and location of the observation.
- Do the same thing at the second location using the same piece of cardboard. You should draw a second line on the cardboard representing the hanging string at the
second location.

- Record the north-south distance between your two observing locations. The north-south distance should be measured using a map. This will be less than your actual travel distance, unless you traveled exactly straight north or south which is highly unlikely since roads weave about.
- Using a protractor, measure the angle between the two vertical lines. (The lines cross because the direction of vertical measured relative to the stars has changed as you moved around Earths surface. The angle between the lines is the number of degrees of latitude that you have moved.)
- Divide 360 degrees by the number of degrees between the two vertical lines and multiply the result by the north-south distance between the two locations where you made your observations. Your answer should be close to the circumference (of the Earth.

### Making a Model

Whichever way you collected your data, you now have measurements of the Earth. There are at least two possible models for the earth: either its flat, or its spherical. I bet you can think of at least one more model.

Think about the measurements you took and use them to describe a model of the Earth. Your model must be consistent with your measurements and be supported by a logical use of your observations .

**For example,** If your data indicates that the altitude of Polaris increases as the observer moves north, you might logically hypothesize that the Earth is spherical,

### Testing Your Model

Now that you have a model, propose other observations that might show the model to be incorrect. Yes, you want to try to prove that your own model is inaccurate. Scientists can produce all the data they want to support a model, but it’s consistently failing to prove your model wrong that begins to convince others.

If your second observation supports the model, then you may have an interesting theory on your hands, especially if n one has proposed it before. Share your experiment and observations with others so they might reproduce your results. If they can’t successfully reproduce your results supporting your model, something is wrong with your model. Adjust and try again.