Homework 9. Finding Distance With Parallax

Name: ________________________ DUE 10/30 ID number: ________________________

When your point of view changes, nearby objects appear to shift with respect to more distant ones. This is called parallax, and it's a basic tool for measuring astronomical distances. The same idea can be used to measure distances to objects on Earth.

The diagram above is an overhead view showing how parallax can be used to measure the distance D of the target object. Such a measurement requires observations from two different places separated by a known distance. This distance, the baseline, is represented by the symbol b. Besides the baseline, you also need to determine the sides of the small grey triangle.

The diagram to the left shows the small grey triangle in more detail. Here, L is just the distance you can hold a ruler at arm's length in front of you; s is the apparent separation between the landmark and the target you measure on the ruler.

Pick a fairly nearby target which you can view in front of a background much further away (for example, you might use the pole of a street light as your target, with the side of the valley as a background). For the first observation, line the target up with some definite landmark in the background (for example, a rock on the side of the valley). Now move to your second observation point, and hold the ruler at arm's length to measure the apparent separation s between your target and the background landmark. The distance D to your target is

The key to this assignment is not just to make a measurement -- you will also have to make some choices, and explain why you made those choices. At every step, your choices affect the accuracy of your result, so think carefully before choosing.

1. Describe the target you chose and the background landmark you will use for your measurement.

2. Pick a value for the baseline distance b, and explain your choice. Ease of measurement is a valid reason for picking a certain baseline, but accuracy is also a consideration. If your baseline is too small, it will be hard to measure the separation s accurately. (Note that it does not matter what units you use for b; you will automatically get D in the same units!)

3. Now record the length L and separation s you measured, using the same units for both. Then use the equation on the other side of the page to find D.

4. Finally, try to guess the size of any errors you might have made in measuring b, L, and s. Which part of the assignment was most difficult? How would you improve your measurements?

Joshua E. Barnes (barnes@ifa.hawaii.edu)

Last modified: October 23, 2001