How to Measure Stellar Distances

Note the position of a nearby star in the sky, say Proxima Centauri, using a telescope. Using trigonometric parallaxes usually involves simultaneous measurements from two different vantage points, but since the distances to the stars are so great, you'll need to wait six months, until the earth is on the extreme other side of its orbit, in order to view the star from a significantly different position.

View the star from the second vantage point six months later. This reveals the apparent motion, that is, the motion of the star relative to the background. This is where variables pollute the measurement. First, our atmosphere distorts light, so measuring this tiny movement is difficult even with the best instruments. Second, the background stars are in motion as well. However, because they are of a much lower magnitude relative to your target star, the apparent motion of this background is undetectable.

Draw your baseline on a piece of paper to help you visualize the calculation. The baseline extends from the Earth at the first position, through the sun to the Earth at its second position. Complete the triangle by drawing lines from the two vantage points to a target star. This is just to help you understand what is being measured. You need not draw to any kind of scale.

Find the parallax angle to your target star. Unless you have instruments sensitive enough to measure it yourself, consult the Hipparcos catalog (available online), which contains a list of 100,000 nearby stars and their parallax angles. The parallax angle is the angle created by the two lines extending from the star to the two Earth positions. Because the distance to the stars is so great and our baseline is so comparatively short, the parallax angle is almost non-existent, less than one arc second. To visualize this measurement, think of a circle with 360 degrees. Each degree (which is already pretty small) is divided into sixty minutes. Each minute is divided into 60 seconds. The parallax angle to our nearest star, Proxima Centauri, is 0.772 arc seconds.

Compute the distance to the star using the formula d = 1/p, where "d" is the distance and "p" is the parallax. The distance is measured in parsecs, a unit of measurement created for such large distances; you may have heard of it from science fiction novels or movies. In our example, we can calculate that Proxima Centauri is 1.3 parsecs away from Earth.