Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

What is the cosmological distance ladder?

Douglas Adams was absolutely right when he wrote in The Hitchhiker's Guide to the Galaxy

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.

The question scientists ask is How big?

For the next two weeks, we will investigate the methods that astronomers have developed to measure distances to celestial objects. As we will discover, all methods are imperfect -- but some are much less certain than others. Moreover, we will see that, in general,

The farther away an object is ..... the greater the uncertainty in its distance

Most of the reasons for these growing uncertainties are due to the difficulty of measuring the properties of faint stars and galaxies properly. This course concentrates on observational astronomy, which is a good thing, because I am definitely an observational astronomer; my theoretical skills and knowledge are not very good. So, in this course, I'll explain things from the observational point of view. Perhaps you can find a good theorist who can provide a different point of view on some of the topics.

But, as we meet over the next few weeks, I'll be much happier if you do more than just sit quietly and take notes. I will try to give you plenty of exercises in class to illustrate the examples I provide. I'll try to bring recent papers published in the astronomical literature into class and refer to them.

    So, if you hear any interesting news about 
    methods for measuring distances to objects in
    space -- maybe the latest news from Gaia --

             PLEASE LET ME KNOW!   

    I hope that we can discuss the latest news
    about such topics in class.

Why is it called "the distance ladder?"

Imagine that you need to climb to the roof of your house. You don't have a ladder, but you do have a set of small pieces which could be used to make one.

So, you place the first piece on the ground.

This first piece is solid and sturdy. It won't fall over. You can stand on this tiny ladder and be confident that you are safe. However, it's not high enough for you to reach the roof.

So, you get a second piece and stack it on top of the first. If you could place it PERFECTLY on the first one, with no error, then your new, taller, ladder would still be firm and safe.

Unfortunately, when you place the second piece on top of the first, you can't avoid making a small error. It's not too bad, and the second piece is still quite strong.

But -- it is still not tall enough for you to reach the roof of your house. So, you get a third piece. When it stack it on the second piece, you make another small error in a somewhat different direction.

When you try to climb up onto the third step, you can feel the structure starting to shake a little.

But it's STILL not high enough!

So, you add a fourth section. There is no way to avoid it if you must reach the roof. But this step involves yet another error in the stacking.

Now, at least, the ladder is tall enough to reach the roof of your house. But -- is it safe? Probably not. As you add more and more sections to the ladder, each one

By the time you CAN reach the roof, it's probably NOT SAFE to try.

Astronomers face a similar set of problems when they try to measure the distance to objects in the sky.

                    the ladder                      real astronomy 

first step        close to ground                   close to Earth
                   very secure                    very well determined

second step       sits on top of first step      relies on smaller distances
                   has small uncertainty          has small uncertainty

third step        sits on top of steps 1, 2      relies on previous measurements
                   more unstable                  has more uncertainty

fourth step       sits on top of all steps       relies on all other measurements
                   very unstable                  very large uncertainty
                   unsafe to stand                unsafe to publish


An example of a "ladder" calculation

To give you an idea of the dangers involved in using any sort of "ladder," let's work our way through a simple example. It's difficult to perform astronomical observations during the day, and inside a classroom, so we'll make an analogy: instead of distances, we'll measure volumes of

Your goal is to figure out how many spoons it would take to fill the big storage container. In astronomy, we use a method involving nearby objects to calibrate a second method which applies to distant objects; in this example, we'll use a method involving small objects to calibrate the volume of bigger objects.

You can perform these steps inside the classroom:

  1. determine F1 = number of spoons required to fill a cup. Measure this 3 times, compute mean and uncertainty.
  2. determine F2 = number of cups required to fill a dish. Measure this 3 times, compute mean and uncertainty.
  3. determine F3 = number of dishes required to fill a bucket.

For the final step, please go outside, so that we can use a hose and spill water on the ground. Because the final step involves a difficult measurement with big instruments -- like using the Subaru or Keck telescopes -- you only get 1 attempt per team. You'll have to estimate the uncertainty as you go.

  1. determine F4 = number of buckets required to fill one storage container. Measure this 1 time only, estimate value and uncertainty.
  2. using all your values, compute S = number of spoons required to fill the storage container. Estimate the uncertainty in this value.

When every team has finished, we'll compare all the values. I wonder if the values will agree with each other ....

(You can see pictures of members of our class performing this experiment by looking in this directory. Thanks very much to Inoue-san for taking the photographs)

The history of the term "distance ladder" or "cosmological ladder"

When did astronomers start to use these terms? Searching through the literature for uses of these terms, I found the following candidates:

I can't find any instances earlier than 1972, which leads me to believe that Steven Weinberg may have coined the term. If you know of an earlier appearance, please let me know!

A list of the methods we will discuss

This course is too short to describe all the methods astronomers have adopted over the years to measure distances to celestial objects --- let alone to discuss each one in detail. I've chosen just a few of the methods which are perhaps most relevant to the current state of the field. We'll cover these topics in future lectures:

For more information

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.