Parallax

Introduction

In this lab you will be introduced to the concept of Stellar Parallax.  This is the only way Astronomers have to directly measure the distances to stars.  

By the end of this lab, you'll understand why there's a certain distance where the stellar parallax method breaks down, and we have to use other means to determine cosmic distances.

 


Part 1: Parallax

 

1 - Hold your thumb at arm's length.

2 - Point your thumb at something on the other side of the room.

3 - Look at your thumb.

4 - Close one eye.

5 - Now, without moving anything, alternate which eye is closed.

6 - What happens?

You should see that your thumb appears to move back and forth, across the room.  But nothing actually moved!  So what's going on here?

This effect is called Parallax, and it's responsible for giving us depth perception.  It allows us to estimate how far away things are.

It requires two detectors equally spaced apart - like the eyes on your head!  By overlapping the two images and moving our head around, we can tell that objects that are closer appear to move around faster, and objects that are further away don't appear to move at all!

Take for example driving down the highway in Colorado - trees near the highway are a blur, but the mountains in the distance barely appear to move, and everything in between moves according to its distance.

 

Now, if you take those two images of the thumb and overlay them, you can actually estimate how far away your thumb is from your face!  Behold:

The separation between the two thumbs, labeled by the red line, is actually the angular size of the apparent separation between the thumbs - this is an angle!

As we did in the previous lab, we can use this with the small angle formula to determine how far away your thumb is.  To wit:

Ok, but instead of looking at thumbs, how does this relate to astronomy?

It's very similar, but instead of taking pictures of thumbs, we take pictures of stars.

The difference is that rather than taking a picture of the sky with two eyes simultaneously, astronomers take two pictures of the sky 6 months apart, and then overlay them.  By doing this, we get a depth perception of the sky, and we use the separation between the earth and the sun the same way we use the distance between our eyes to use parallax to navigate around town.

For example:

As you can see the small angle formula can be used to solve for the distance to a star, since we know 2 parts of the equation:  the angle and the 'opposite' side of the triangle.

Solving for the distance, we get the following simple equation:

Distance = 1 AU / ø

Now there is another thing we have to introduce here, and that is the unit of Arc Second.

206,265 arc seconds = 1 radian

Take a look at that again - there are 206,265 arc seconds in 1 radian!  Do you remember how much 1 radian is?  About 57 degrees.  So in 57 degrees, there are 206,265 arc seconds, which means 1 arc second is 1 radian/206,265.

Why do I bring up arc seconds?  Well because astronomers invented a new unit using arc seconds, called the Parsec.

1 parsec = 3.26 light years = 30,856,770,000,000 kilometers

And 1 parsec is defined as the distance to a star that has a parallax angle of 1 arc second:

Distance = 1 AU / ø

1 Parsec = 1 AU / 1 Arc Second

1 Parsec = 1 AU / 1''

The Hipparcos Satellite launched in 1989 could measure as small as 0.002' (0.002 arc seconds).

The Gaia spacecraft, launched in 2013, is the follow up mission to Hipparcos and can measure angular sizes as small as 24 microarcseconds, or 0.000024 arc seconds.

When you put it all together, this animation below is the result!  As you can see, the closer stars appear to move more, and the stars further away move less.  (Notice the Orion constellation in there?)

How far must an object be before we can't measure the parallax angle anymore?