DISTANCES TO NEARBY STARS
AND THEIR MOTIONS:
An Introductory Astronomy Lab

Introduction

This lab takes you to the next step in the cosmic distance ladder: figuring out the distances to stars other than the Sun. Astronomers derive distances to the nearest stars by a form of triangulation called stellar parallax, a most simple and direct method that relies on no assumptions other than the geometry of the Earth's orbit around the sun. Before we embark on our stellar journey, however, let us first understand the concept of parallax, and how it can be used in distance determination.

The parallax effect

Hold out your thumb at arm's length, close one of your eyes, and examine the relative position of your thumb against other distant (background) objects, such as a window, wall, a tree, etc. Do it! Now look at your thumb with your other eye. What do you notice? Move your thumb closer to your face and repeat the experiment. What was different this time?

This is a demonstration of the parallax effect: the apparent shift in position of a relatively nearby object against more distant ones when viewed from different vantage points. Parallaxes are usually measured as angles; your thumb should appear to move by about 3 degrees when your arm is fully extended.

[ Comet Hyakutake as seen by two observers ] Look at the following mosaic of photographs from the 1995 passage of comet Hyakutake. The pictures were taken at the same time by two amateur astronomers at different places: one in Portugal and the other in Denmark.

It is clear that the comet's position appears shifted with respect to the reference star (SAO 101241). This is yet another example of a parallactic shift; the comet is much closer to the Earth than the star, so that its position in the sky depends on the observer's location.

Images: Astronomy On-Line

Measuring distances

In the preceding demonstration you noticed that your thumb exhibits larger parallactic shifts as it gets closer to your face (this should make sense). It is easy to see, then, that the amount of shift is proportional to the ratio between the separation of the observation stations (the "baseline") and the distance to the object. Or, in other words, if we know our baseline (say, the separation between our eyes), then we can determine the distance to any object by simply measuring its parallax.

The formula of a trigonometric parallax distance is given below:

[Distance to a parallaxed source]