Hubble Diagram - Teacher's Guide
Sloan Digital Sky Survey III
SkyServer DR9
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Hubble Diagram
 Teacher's Guide
     - Goals
     - Background
     - Structure
     - Questions
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The Hubble Diagram Project

This project takes students through the evidence that the universe is expanding. The discovery of the expanding universe was one of the greatest revelations of 20th Century astronomy. They will make a "Hubble diagram," named for the astronomer who first made one, for galaxies from the SkyServer database.

If you are short on time, you can do a shorter version of the project consisting of the Introduction and Simple Diagram sections, up to and including Exercise 4.

The student project's Introduction and Conclusion give some information on how the expanding universe was discovered, and what logical steps lead from the Hubble diagram's straight line to the expanding universe concept. For more information on the expanding universe, its discovery, and the big bang theory, read the About Astronomy: Expanding Universe section of SkyServer, or look up one of the following references:

Hartmann, William K., Astronomy: the Cosmic Journey, Wadsworth, 1989

Sagan, Carl, Cosmos, Random House, 1983

Project Goals

By the end of the project, students should be able to:

  • Describe what scientists mean by an "expanding universe" in their own words

  • Explain how the Hubble diagram supports the idea of an expanding universe

  • Understand how theory and experiment come together to create scientific evidence

  • Explain what the big bang is, and how it relates to the expanding universe

  • Look up data using several interfaces

  • Understand the relationship between magnitude, brightness, and distance in astronomy

  • Explain the concept of redshift, and give examples

  • Make a simple x-y graph

  • Understand the concept of statistical fit

  • Find relative distances to galaxies using algebra

  • Understand the advantages and disadvantages of various methods for finding relative distances in astronomy

  • Identify galaxies and galaxy clusters in images, and determine which galaxies are members of which clusters

  • Judge the precision and accuracy of scientific data

  • Identify emission and absorption lines in spectra

  • Understand the two interpretations of redshift, and when it is appropriate to use either

  • Use spectral templates to find the redshifts of unknown spectra

  • Understand Hubble's Law, c z = H0 d

  • Calculate the age of the universe

  • Use deductive logic to analyze arguments

Background Knowledge

To begin this project, students should have a basic familiarity with astronomical ideas. They should know what galaxies and galaxy clusters are. They should know that light is composed of waves with definite wavelengths and frequencies. They should have some experience with scientific reasoning. They should have completed Algebra I. Exercises 8 and 9 require trigonometric functions and the small angle approximation (when x << 1, tan x = x). If your students have not had trigonometry, you may skip these Exercises and complete the rest of the project.

They should also have basic computer skills. They should know how to look up information using a Web-based interface. It is helpful to know how to use Microsoft Excel or some other graphing program, but not necessary.

Project Structure

The first page is an Introduction. It tells students the history of how astronomers in the early 1900s discovered that the universe was expanding.

After the Introduction, the project is divided into four parts. In the first part, students make a simple Hubble diagram from pre-selected data. They read through background material that explains how astronomers use magnitude and redshift. Then, they look up six galaxies in the SDSS data, finding their magnitudes and redshifts.

Part I should take about 2 hours to finish. For a short version of the project that introduces students to the idea that the universe is expanding, and to the evidence astronomers use to prove the expansion, use only the Introduction and Exercises 1-4. The second half of Part I, Exercises 5-6, is intended as a "teaser" - students discover that proving the universe is expanding is not as easy as Exercises 1-4 made it seem. The galaxies in Exercises 5-6 were chosen to give Hubble diagrams with widely scattered data.

In the second part, students learn how to turn their direct measurements of galaxy properties into actual measurements of relative distances. Then, they learn how astronomers deal with a fundamental confusion: if a galaxy looks large and bright, does that really mean it is close to us? Or, could it actually be large and bright, but farther away? Students study clusters of galaxies to determine which galaxies are members of the same cluster. Lastly, they examine three clusters in the same area of space, and find the relative distances to galaxies in each cluster.

Part II should take about 8 hours to finish.

Part III tells students how astronomers calculate redshift. In Part I, students simply looked up redshifts from the Skyserver data; in Part III, they will calculate redshifts themselves, the same way astronomers do.

Part III should take about 6 hours to complete.  Skip part III if you would rather have students look up the redshifts on the spectra to save time.

Part IV brings together the conclusions from Parts II and III to make a new, better Hubble diagram. Students learn how the Hubble diagram implies that the universe began with the big bang, then make their own Hubble diagrams. Be sure to emphasize what an important result this is. The students repeated almost exactly the process that made Hubble famous - he nearly won the Nobel Prize for doing what they did.

Part IV should take about 3 hours to complete. The last exercise, Exercise 21, is the final challenge for this project. Exercise 21 should not be done in the classroom for credit. It is designed to be completely open-ended, and to take many hours to complete. You may wish to give extra credit for completing it. When students finish Exercise 21 on their own, encourage them to E-mail their diagrams to us so we can put them up on the project web site.

Questions and Exercises

Questions are designed to get students thinking about the way scientists work. Exercises are designed to get students to explore how the SkyServer data suggests that the universe is expanding. For answers to all questions, click here. To see the answers, you must have the Adobe Acrobat PDF viewer installed on your computer. Acrobat is available for free download at Adobe's web site.

Students should be evaluated based on their written answers to the questions and exercises. You may use our sample scoring rubric or develop your own. If you use our scoring rubric, print out a copy for each student and attach it when you return his or her work.

For specific information on any part of the project, click Next.