Lab Exercise

In this section, you will be applying the method of topocentric parallax on a smaller scale to determine the distance to the Old Capitol Building from Van Allen. Instead of having observations across the earth, we will be using the width of the roof as our baseline and a compass.

To measure the parallax of the building, one group member will stand at one end of the roof and face it. Note the angle on the compass that the building makes with respect to North. Have a second group member stand at the other corner of the roof, and read the angle the same building makes with respect to North. You should use these two measurements to determine the parallax, or the apparent change in position, of the building.

Now you will calculate the distance to the building using your parallax measurement and the small angle formula. Here are some hints to guide you.

small angle formula
  • The thick posts supporting the guardrail running around the edge of the roof are all 1.3 meters apart (save for a few obvious exceptions). How can you use this to determine your baseline, d?
     
  • Think about the geometry of your observation. How do we define the parallax angle with this geometry? If it helps, revisit the image on the Stellar Parallax (Part 2).
     
  • Use Google maps and a ruler to determine the distance to the building. How accurate were you?

Background

determining distance

Astronomers often use parallax to measure distances to objects within our solar system, such as comets and asteroids. To measure distances to these kinds of objects, astronomers use a different method to measure parallax than the one described in the previous section. The reasons for this are 1) you want to know the instantaneous distance to an object, and if you had to wait six months, it may be a completely different distance away from Earth, and 2) many comets and asteroids are moving quickly through our solar system, so they may not be in it after six months.

So, to measure parallax to objects within our solar system, astronomers use topocentric parallax, which is when you view the same object from different places on the Earth simultaneously.

Topocentric parallax was used to determine the distance to the Sun from Earth using the transit of the asteroid Eros in 1931. At the time, Eros was within Mars’ orbit and in opposition with the Sun, meaning it was behind the Sun from Earth’s point of view. When it was viewed simultaneously from two points on the Earth, the apparent position of Eros compared to the background stars was different. By observing Eros as it orbited around the Sun, astronomers could calculate the distance to Eros using parallax. Once the distance between Eros and Earth was established, the distance to the Sun was calculated from Kepler’s Third Law.