# Planetarium

## "Could you please explain 'parallax' again? How does it work when you're measuring the distances to the stars?"

- Richard H., Brunswick

Greetings!

We would be happy to explain parallax. Stellar parallax illustrates how a branch of mathematics as terrestrial as 'geometry,' can be used in the service of celestial science. We'll begin with a famous illustration. Find an object in your background, such as a tree, a stop sign, or a hand boiler that you might have purchased at the Southworth Planetarium for the criminally exorbitant price of five dollars, which does come with free bubble wrap and a prepossessingly beautiful box. Close one eye and extend an index finger out in front of your face. Align the finger with the chosen background object. While keeping the finger steady, close the open eye and open the closed eye. You might notice that the finger's position relative to the background object shifted. If you extend the finger out to its maximum extent and repeat the demonstration,* you'll observe the shift is small. If you hold the index finger just in front of your face and repeat the demonstration, the shift will be quite large.

The apparent shift of an observed object's position resulting from a change of perspective is called "parallax." With the previous demonstration, we've established an inverse relationship. The closer the object, the greater the parallax angle.

We can apply the same principle to the stars. Astronomers can measure the position of a star relative to the background stars at one moment and then, in six months - when Earth is as far from its original orbital position as possible - the astronomers measure the star's location again. Provided the star is sufficiently close,** its parallax angle will yield its distance.

Without delving into all the delicious details pertaining to right angle trigonometry, we can share a simple equation relating the parallax angle and the distance. If the distance is expressed in parsecs - one parsec equals 3.26 light years - and the parallax angle is expressed in arc-seconds,*** the star's distance is 1 divided by the parallax angle.

For instance, let's say a star's parallax angle is 0.5." Its distance would therefore be 1/0.5" = 2.0 parsecs, or about 6.52 light years.

In 1838, Friedrich Wilhelm Bessel estimated the distance to the star 61 Cygni based on the observed parallax angle. Though his calculation of 10.3 light years was about ten percent less than the currently accepted value of 11.4 light years, Bessel was the first to successfully employ stellar parallax to measure a star's distance.

The Hipparcos satellite, launched by the European Space Agency in 1997, catalogued about 118,000 stars and their distances. The GAIA probe, launched in 2013, might collect the distances and positions of more than 1 billion stars within our galaxy.

I hope this response was helpful.

*We could have referred to this exercise as a 'experiment,' except that it was nothing of the sort. Any exercise that will yield a known result is a demonstration. An exercise that will lead to a result that, though predicted, isn't certain, is an experiment.

**For ground based observations, the range has been about 500 parsecs. (A parsec equals about 3.26 light years.)

***One degree can be equally sub-divided into 60 arc-minutes. One arc-minute can be equally sub-divided into 60 arc-seconds. An arc-second is a particularly small angle.