The Cosmological Distance Ladder

Parallax Intro

Parallax is nothing unusual or difficult to understand.  We use it in our everyday life to judge distances in the world around us.  Parallax is simply the apparent shift in a nearby object's position relative to the much more distant background when the nearby object is viewed from two different vantage points.  This is shown in the picture below.  When the nearby tree is observed from position 1, it appears to be in line with the rocky ridge on the right, but if we move to position 2, the nearby tree now appears to be in line with the twin peaks on the left.  Our brain interprets this to mean that the tree in the foreground is closer to us than the trees and mountains in the background.  By measuring the distance between the observing points 1 and 2, and the angle of the tree's apparent shift in position, we can determine how close the tree actually is to us.

There are two important things to note.  First, the further away the tree is, the less it's position will appear to shift relative to the background, (indeed, when it is as far away as the background, there will be no shift in position).  Second, the greater the distance between vantage points, (i.e. the greater the distance between points 1 and 2) the more the nearby tree will appear to shift it's position relative to the background.

 

The exact same principle applies with stellar parallax.  In this case we are measuring the apparent shift in position of a nearby star relative to more distant background stars.  The big problem though is that stars are so far away that the distance between the two vantage points must be very large before we can detect any change in a nearby star's position.  The distance has to be more than a few feet as in the example of the nearby tree relative to the mountains in the background.  In fact, it is not possible to detect any change in a star's position when observed from any two points on Earth.  The only way to get enough distance to observe any change in a star's position is to use the radius of the Earth's orbit around the sun as the baseline between the two observing points.  That is the star must be observed twice, six months apart as shown in the diagram below.

 

So that is where the difficulty is.  We need to know how big the Earth's orbit is before we can use stellar parallax to determine the distance to the stars.  The next several pages will focus on determining the distance between the Earth and the Sun.  These are the preliminary steps in the distance ladder, working up to the all important stellar parallax step, the most solid first step in the cosmological ladder.

It's important to keep in mind in the following pages that knowing the distance between the Earth and the Sun is key to being able to apply stellar parallax measurements.  The distance between the Earth and the Sun is called the astronomical unit.  As already mentioned, we can't measure the distance between the Earth and the Sun with radar, so we will have to build up to even that.

If Step 1 of the cosmological distance ladder is stellar parallax, then we will need to build a smaller ladder with steps A, B, C to get us there.  These steps are:

A.  Find the relative distances between the planets and the Sun,

B.  Use radar to measure the distance between the Earth and another planet,

C.  Use that information to determine the Astronomical Unit, the distance between the Earth and the Sun.