Parallax

Posted by on May 13, 2011

Fictitious scenario: My science project is due tomorrow! I’m supposed to talk about stars, and planets, and such! Better run to Wikipedia and grab some quick facts. (Note: I do not advocate the use of Wikipedia for academic research, but it’s sometimes a good place to start to familiarize yourself with a topic)

According to this crowd-sourced website, Proxima Centauri is the nearest star to us. It’s about 4.2 light years away. But how do they know how far away it is?

Turns out, it’s not that hard. If you have the right kind of eyes, of course.

A Quick Experiment

Hold your finger, pointing up, in front of your eye, and keep it there. Now focus on something that’s on the other side of your finger, the farther away the better. Now move your head from left to right (kinda like Michael Jackson while pretending to be an Egyptian). Notice how your finger seems to be moving relative to the distant object, while the distant object is moving very little or not at all. This is called parallax. The less something moves as we move our heads, the farther away it is. Our finger moves a lot because it’s right there. If it were an inch from your nose it would seem to move about as much as your head has.

If you want, do the same experiment with two distant objects in-line with you, notice how the one in the middle moves so much less in relationship with the far one.

Moving Our Heads Isn’t Good Enough

It’s a bit hard to measure a star’s distance from us by simply moving our heads, so our clever little brains figured out that the solar system kind of takes care of this for us. We take two measurements 6 months apart. In January, we’re on one side of the sun, and in July we’re on the other one. That’s as good as we can get.

Simple Enough, How’s It Done?

Notice how for a nearby far-away star (on the left), the parallax angle (the circle on top) is way smaller than that on the right.

The equation is so ridiculously simple my child could do it! Granted, my child started reading at age 3, but hey, I’m a proud parent.

Where d = the distance to the star measured in pc (parsecs), and p = the parallax angle measured in arcseconds.

A parsec is 3.26 light years, and a light year is the distance light travels in a year. Note: light goes really freaking fast. 300 million meters per second fast. That’s 671 million miles per hour. An arcsecond is 1/3600th of a degree (a degree has 60 arcminutes, and an arcminute has 60 arcseconds)

In Practical Terms

So if we looked at the sky and saw a star next to another, much distant star, then we looked again six months later and it had just moved 0.1 arcseconds away, the parallax angle is 0.1. Since d = 1/p, therefore d = 1/0.1, and the star is 1 parsec away, or 3.26 light years away.

Here’s the tricky part: it’s hard to measure deflections that are smaller than 0.001 arcseconds, even using powerful instruments, so we can only use this for nearby stuff. We can probably reliably determine distances of about 1000 parsecs (or 3260 light years). After that, we have to use some really creative methods which are beyond the scope of this post. How wide is an arcsecond? Hold a human hair at arm’s length. This is, of course, a lot easier when looking through a telescope. When looking under an eyepiece at regular magnifications, the entire field of view is usually just one degree, and it’s much easier to separate it into sixtyeths.

There’s actually a really neat trick for figuring out angular distances in the sky: your hand!

The sun and the moon are about half a degree wide.

It’s hard to overestimate our insignificance. It’s also hard to underestimate how much we’ve figured out from out little corner in the middle of nowhere. We will continue to discover things and feel great, then brought down a notch when we realize we haven’t put a dent into the amount of things that remain to be discovered.