Astronomy 10: Parallax

Measuring Distance using Parallax

Worth 20 points -- due Monday July 1st, 2002

This lab is best done after June 18th, when we will discuss the parallax of stars. However, it can be done before that as we will discuss the concept of angular size and distance earlier in the course.

This is a fun and easy lab designed by Prof. Gibor Basri of the UCB Astronomy Department. We will measure the angular size of the Moon, which will allow us to estimate the distance to the Moon. We will also measure the parallax of a pen held at arms length, which will allow us to estimate the length of your arm. The techniques in this lab are frequently used by professional astronomers.

Throughout this lab we will use the "small angle" formula. This is a formula that describes the relationship between size, angular size, and distance. Here we will use a variant of the formula which specifically uses degrees:

angular size (in degrees) = size/distance x 57.3°

The exact formula involves trigonometry, but because we will be measuring small angles, we will manage just fine with this approximate formula. Each time we use this formula the meanings of size, angular size, and distance will change, but the underlying principle will be the same.

I. Building an Angletron

Before we can measure the angular size of the Moon, we need to build a tool to help us measure small angles. Protractors are fine for measuring large angles, but we need something better for measuring small angles. Let's call our tool for measuring small angles an "Angletron." Here's how to build one:

II. Measuring the Moon

Now that we have constructed an Angletron, we can use it to measure the diameter of the Moon. For best results, the Moon's phase should not be a thin crescent since it's more difficult to discern the full diameter. This will not be a problem if you do this lab between June 12th and June 16th.

III. Measuring with Parallax

In this final section we will use the small angle formula in a slightly different way. The "size" will be the distance between your eyes, and the "angular size" will be the angle between two distant landmarks. We will use the small-angle formula to calculate the length of your arm, which corresponds to "distance" in the formula. This is how we measure parallax! NOTE: this is whole point of having binocular vision. Your brain receives two 2-dimensional images (one from each eye) separated by some distance and it turns them into a single 3-dimensional image using the parallax information contained within.

This procedure is very similar to the way astronomers measure the distance of nearby stars (but astronomers' Angletrons are much more accurate!) The differences are:
- The distance to the pen becomes the distance to the nearby star.
- The angle between the background features becomes the angle between very distant stars or galaxies.
- The spacing between your eyes becomes the distance between Earth's position on opposite sides of its orbit around the Sun.

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